Entropy
http://www.mdpi.com/journal/entropy
Latest open access articles published in Entropy at http://www.mdpi.com/journal/entropy<![CDATA[Entropy, Vol. 16, Pages 6263-6285: A Thermodynamical Selection-Based Discrete Differential Evolution for the 0-1 Knapsack Problem]]>
http://www.mdpi.com/1099-4300/16/12/6263
Many problems in business and engineering can be modeled as 0-1 knapsack problems. However, the 0-1 knapsack problem is one of the classical NP-hard problems. Therefore, it is valuable to develop effective and efficient algorithms for solving 0-1 knapsack problems. Aiming at the drawbacks of the selection operator in the traditional differential evolution (DE), we present a novel discrete differential evolution (TDDE) for solving 0-1 knapsack problem. In TDDE, an enhanced selection operator inspired by the principle of the minimal free energy in thermodynamics is employed, trying to balance the conflict between the selective pressure and the diversity of population to some degree. An experimental study is conducted on twenty 0-1 knapsack test instances. The comparison results show that TDDE can gain competitive performance on the majority of the test instances.Entropy2014-11-281612Article10.3390/e16126263626362851099-43002014-11-28doi: 10.3390/e16126263Zhaolu GuoXuezhi YueKejun ZhangShenwen WangZhijian Wu<![CDATA[Entropy, Vol. 16, Pages 6254-6262: On a Local FractionalWave Equation under Fixed EntropyArising in Fractal Hydrodynamics]]>
http://www.mdpi.com/1099-4300/16/12/6254
In this paper, based on fixed entropy, the adiabatic equation of state in fractal flow is discussed. The local fractional wave equation for the velocity potential is also obtained by using the non-differential perturbations for the pressure and density of fractal hydrodynamics.Entropy2014-11-281612Article10.3390/e16126254625462621099-43002014-11-28doi: 10.3390/e16126254Yu ZhangDumitru BaleanuXiaojun Yang<![CDATA[Entropy, Vol. 16, Pages 6240-6253: Generation and Nonlinear Dynamical Analyses of Fractional-Order Memristor-Based Lorenz Systems]]>
http://www.mdpi.com/1099-4300/16/12/6240
In this paper, four fractional-order memristor-based Lorenz systems with the flux-controlled memristor characterized by a monotone-increasing piecewise linear function, a quadratic nonlinearity, a smooth continuous cubic nonlinearity and a quartic nonlinearity are presented, respectively. The nonlinear dynamics are analyzed by using numerical simulation methods, including phase portraits, bifurcation diagrams, the largest Lyapunov exponent and power spectrum diagrams. Some interesting phenomena, such as inverse period-doubling bifurcation and intermittent chaos, are found to exist in the proposed systems.Entropy2014-11-281612Article10.3390/e16126240624062531099-43002014-11-28doi: 10.3390/e16126240Huiling XiYuxia LiXia Huang<![CDATA[Entropy, Vol. 16, Pages 6212-6239: Ordinal Patterns, Entropy, and EEG]]>
http://www.mdpi.com/1099-4300/16/12/6212
In this paper we illustrate the potential of ordinal-patterns-based methods for analysis of real-world data and, especially, of electroencephalogram (EEG) data. We apply already known (empirical permutation entropy, ordinal pattern distributions) and new (empirical conditional entropy of ordinal patterns, robust to noise empirical permutation entropy) methods for measuring complexity, segmentation and classification of time series.Entropy2014-11-271612Article10.3390/e16126212621262391099-43002014-11-27doi: 10.3390/e16126212Karsten KellerAnton UnakafovValentina Unakafova<![CDATA[Entropy, Vol. 16, Pages 6195-6211: Complex Modified Hybrid Projective Synchronization of Different Dimensional Fractional-Order Complex Chaos and Real Hyper-Chaos]]>
http://www.mdpi.com/1099-4300/16/12/6195
This paper introduces a type of modified hybrid projective synchronization with complex transformationmatrix (CMHPS) for different dimensional fractional-order complex chaos and fractional-order real hyper-chaos. The transformationmatrix in this type of chaotic synchronization is a non-square matrix, and its elements are complex numbers. Based on the stability theory of fractional-order systems, by employing the feedback control technique, necessary and sufficient criteria on CMHPS are derived. Furthermore, CMHPS between fractional-order real hyper-chaotic Rössler system and other two different dimensional fractional-order complex Lorenz-like chaotic systems is provided as two examples to discuss reduced order and increased order synchronization, respectively.Entropy2014-11-271612Article10.3390/e16126195619562111099-43002014-11-27doi: 10.3390/e16126195Jian Liu<![CDATA[Entropy, Vol. 16, Pages 6186-6194: What You See Is What You Get]]>
http://www.mdpi.com/1099-4300/16/11/6186
This paper corrects three widely held misunderstandings about Maxent when used in common sense reasoning: That it is language dependent; That it produces objective facts; That it subsumes, and so is at least as untenable as, the paradox-ridden Principle of Insufficient Reason.Entropy2014-11-211611Article10.3390/e16116186618661941099-43002014-11-21doi: 10.3390/e16116186Jeff Paris<![CDATA[Entropy, Vol. 16, Pages 6166-6185: Self-oscillating Water Chemiluminescence Modes and Reactive Oxygen Species Generation Induced by Laser Irradiation; Effect of the Exclusion Zone Created by Nafion]]>
http://www.mdpi.com/1099-4300/16/11/6166
Samples of water inside and outside an exclusion zone (EZ), created by Nafion swollen in water, were irradiated at the wavelength l = 1264 nm, which stimulates the electronic transition of dissolved oxygen from the triplet state to the excited singlet state. This irradiation induces, after a long latent period, chemiluminescence self-oscillations in the visible and near UV spectral range, which last many hours. It occurs that this effect is EZ-specific: the chemiluminescence intensity is twice lower than that from the bulk water, while the latent period is longer for the EZ. Laser irradiation causes accumulation of H2O2, which is also EZ-specific: its concentration inside the EZ is less than that in the bulk water. These phenomena can be interpreted in terms of a model of decreasing O2 content in the EZ due to increased chemical activity of bisulfite anions (HSO3−), arisen as the result of dissociation of terminal sulfonate groups of the Nafion. The wavelet transform analysis of the chemiluminescence intensity from the EZ and the bulk water gives, that self-oscillations regimes occurring in the liquid after the latent period are the determinate processes. It occurred that the chemiluminescence dynamics in case of EZ is characterized by a single-frequency self-oscillating regime, whereas in case of the bulk water, the self-oscillation spectrum consists of three spectral bands.Entropy2014-11-211611Article10.3390/e16116166616661851099-43002014-11-21doi: 10.3390/e16116166Sergey GudkovMaxim AstashevVadim BruskovValeriy KozlovStanislav ZakharovNikolai Bunkin<![CDATA[Entropy, Vol. 16, Pages 6152-6165: Improving the Authentication Scheme and Access Control Protocol for VANETs]]>
http://www.mdpi.com/1099-4300/16/11/6152
Privacy and security are very important in vehicular ad hoc networks (VANETs). VANETs are negatively affected by any malicious user’s behaviors, such as bogus information and replay attacks on the disseminated messages. Among various security threats, privacy preservation is one of the new challenges of protecting users’ private information. Existing authentication protocols to secure VANETs raise challenges, such as certificate distribution and reduction of the strong reliance on tamper-proof devices. In 2011, Yeh et al. proposed a PAACP: a portable privacy-preserving authentication and access control protocol in vehicular ad hoc networks. However, PAACP in the authorization phase is breakable and cannot maintain privacy in VANETs. In this paper, we present a cryptanalysis of an attachable blind signature and demonstrate that the PAACP’s authorized credential (AC) is not secure and private, even if the AC is secretly stored in a tamper-proof device. An eavesdropper can construct an AC from an intercepted blind document. Any eavesdropper can determine who has which access privileges to access which service. For this reason, this paper copes with these challenges and proposes an efficient scheme. We conclude that an improving authentication scheme and access control protocol for VANETs not only resolves the problems that have appeared, but also is more secure and efficient.Entropy2014-11-191611Article10.3390/e16116152615261651099-43002014-11-19doi: 10.3390/e16116152Wei-Chen WuYi-Ming Chen<![CDATA[Entropy, Vol. 16, Pages 6133-6151: Application of Entropy and Fractal Dimension Analyses to the Pattern Recognition of Contaminated Fish Responses in Aquaculture]]>
http://www.mdpi.com/1099-4300/16/11/6133
The objective of the work was to develop a non-invasive methodology for image acquisition, processing and nonlinear trajectory analysis of the collective fish response to a stochastic event. Object detection and motion estimation were performed by an optical flow algorithm in order to detect moving fish and simultaneously eliminate background, noise and artifacts. The Entropy and the Fractal Dimension (FD) of the trajectory followed by the centroids of the groups of fish were calculated using Shannon and permutation Entropy and the Katz, Higuchi and Katz-Castiglioni’s FD algorithms respectively. The methodology was tested on three case groups of European sea bass (Dicentrarchus labrax), two of which were similar (C1 control and C2 tagged fish) and very different from the third (C3, tagged fish submerged in methylmercury contaminated water). The results indicate that Shannon entropy and Katz-Castiglioni were the most sensitive algorithms and proved to be promising tools for the non-invasive identification and quantification of differences in fish responses. In conclusion, we believe that this methodology has the potential to be embedded in online/real time architecture for contaminant monitoring programs in the aquaculture industry.Entropy2014-11-191611Article10.3390/e16116133613361511099-43002014-11-19doi: 10.3390/e16116133Harkaitz EguiraunKarmele López-de-IpiñaIciar Martinez<![CDATA[Entropy, Vol. 16, Pages 6116-6132: Entropy Generation during Turbulent Flow of Zirconia-water and Other Nanofluids in a Square Cross Section Tube with a Constant Heat Flux]]>
http://www.mdpi.com/1099-4300/16/11/6116
The entropy generation based on the second law of thermodynamics is investigated for turbulent forced convection flow of ZrO2-water nanofluid through a square pipe with constant wall heat flux. Effects of different particle concentrations, inlet conditions and particle sizes on entropy generation of ZrO2-water nanofluid are studied. Contributions from frictional and thermal entropy generations are investigated, and the optimal working condition is analyzed. The results show that the optimal volume concentration of nanoparticles to minimize the entropy generation increases when the Reynolds number decreases. It was also found that the thermal entropy generation increases with the increase of nanoparticle size whereas the frictional entropy generation decreases. Finally, the entropy generation of ZrO2-water was compared with that from other nanofluids (including Al2O3, SiO2 and CuO nanoparticles in water). The results showed that the SiO2 provided the highest entropy generation.Entropy2014-11-191611Article10.3390/e16116116611661321099-43002014-11-19doi: 10.3390/e16116116Hooman YarmandGoodarz AhmadiSamira GharehkhaniSalim KaziMohammad SafaeiMaryam AlehashemAbu Mahat<![CDATA[Entropy, Vol. 16, Pages 6099-6115: Image Fusion Based on the \({\Delta ^{ - 1}} - T{V_0}\) Energy Function]]>
http://www.mdpi.com/1099-4300/16/11/6099
This article proposes a \({\Delta^{-1}}-T{V_0}\) energy function to fuse a multi-spectral image with a panchromatic image. The proposed energy function consists of two components, a \(TV_0\) component and a \(\Delta^{-1}\) component. The \(TV_0\) term uses the sparse priority to increase the detailed spatial information; while the \({\Delta ^{ - 1}}\) term removes the block effect of the multi-spectral image. Furthermore, as the proposed energy function is non-convex, we also adopt an alternative minimization algorithm and the \(L_0\) gradient minimization to solve it. Experimental results demonstrate the improved performance of the proposed method over existing methods.Entropy2014-11-181611Article10.3390/e16116099609961151099-43002014-11-18doi: 10.3390/e16116099Qiwei XieChao MaChunzhao GuoVijay JohnSeiichi MitaQian Long<![CDATA[Entropy, Vol. 16, Pages 6059-6098: How to Read Probability Distributions as Statements about Process]]>
http://www.mdpi.com/1099-4300/16/11/6059
Probability distributions can be read as simple expressions of information. Each continuous probability distribution describes how information changes with magnitude. Once one learns to read a probability distribution as a measurement scale of information, opportunities arise to understand the processes that generate the commonly observed patterns. Probability expressions may be parsed into four components: the dissipation of all information, except the preservation of average values, taken over the measurement scale that relates changes in observed values to changes in information, and the transformation from the underlying scale on which information dissipates to alternative scales on which probability pattern may be expressed. Information invariances set the commonly observed measurement scales and the relations between them. In particular, a measurement scale for information is defined by its invariance to specific transformations of underlying values into measurable outputs. Essentially all common distributions can be understood within this simple framework of information invariance and measurement scale.Entropy2014-11-181611Review10.3390/e16116059605960981099-43002014-11-18doi: 10.3390/e16116059Steven Frank<![CDATA[Entropy, Vol. 16, Pages 6042-6058: Informational Non-Differentiable Entropy and Uncertainty Relations in Complex Systems]]>
http://www.mdpi.com/1099-4300/16/11/6042
Considering that the movements of complex system entities take place on continuous, but non-differentiable, curves, concepts, like non-differentiable entropy, informational non-differentiable entropy and informational non-differentiable energy, are introduced. First of all, the dynamics equations of the complex system entities (Schrödinger-type or fractal hydrodynamic-type) are obtained. The last one gives a specific fractal potential, which generates uncertainty relations through non-differentiable entropy. Next, the correlation between informational non-differentiable entropy and informational non-differentiable energy implies specific uncertainty relations through a maximization principle of the informational non-differentiable entropy and for a constant value of the informational non-differentiable energy. Finally, for a harmonic oscillator, the constant value of the informational non-differentiable energy is equivalent to a quantification condition.Entropy2014-11-181611Article10.3390/e16116042604260581099-43002014-11-18doi: 10.3390/e16116042Maricel AgopAlina GavriluțGabriel CrumpeiBogdan Doroftei<![CDATA[Entropy, Vol. 16, Pages 6033-6041: Effect of Atmospheric Ions on Interfacial Water]]>
http://www.mdpi.com/1099-4300/16/11/6033
The effect of atmospheric positivity on the electrical properties of interfacial water was explored. Interfacial, or exclusion zone (EZ) water was created in the standard way, next to a sheet of Nafion placed horizontally at the bottom of a water-filled chamber. Positive atmospheric ions were created from a high voltage source placed above the chamber. Electrical potential distribution in the interfacial water was measured using microelectrodes. We found that beyond a threshold, the positive ions diminished the magnitude of the negative electrical potential in the interfacial water, sometimes even turning it to positive. Additionally, positive ions produced by an air conditioner were observed to generate similar effects; i.e., the electrical potential shifted in the positive direction but returned to negative when the air conditioner stopped blowing. Sometimes, the effect of the positive ions from the air conditioner was strong enough to destroy the structure of interfacial water by turning the potential decidedly positive. Thus, positive air ions can compromise interfacial water negativity and may explain the known negative impact of positive ions on health.Entropy2014-11-181611Communication10.3390/e16116033603360411099-43002014-11-18doi: 10.3390/e16116033Chien-Chang Kurt KungGerald H. Pollack<![CDATA[Entropy, Vol. 16, Pages 6006-6032: Entropy Generation through a Deterministic Boundary-Layer Structure in Warm Dense Plasma]]>
http://www.mdpi.com/1099-4300/16/11/6006
The computational prediction of nonlinear interactive instabilities in three-dimensional boundary layers is obtained for a warm dense plasma boundary layer environment. The method is applied to the Richtmyer–Meshkov flow over the rippled surface of a laser-driven warm dense plasma experiment. Coupled, nonlinear spectral velocity equations of Lorenz form are solved with the mean boundary-layer velocity gradients as input control parameters. The nonlinear time series solutions indicate that after an induction period, a sharp instability occurs in the solutions. The power spectral density yields the available kinetic energy dissipation rates within the instability. The application of the singular value decomposition technique to the nonlinear time series solution yields empirical entropies. Empirical entropic indices are then obtained from these entropies. The intermittency exponents obtained from the entropic indices thus allow the computation of the entropy generation through the deterministic structure to the final dissipation of the initial fluctuating kinetic energy into background thermal energy, representing the resulting entropy increase.Entropy2014-11-171611Article10.3390/e16116006600660321099-43002014-11-17doi: 10.3390/e16116006LaVar Isaacson<![CDATA[Entropy, Vol. 16, Pages 5976-6005: A Quantitative Analysis of an EEG Epileptic Record Based on MultiresolutionWavelet Coefficients]]>
http://www.mdpi.com/1099-4300/16/11/5976
The characterization of the dynamics associated with electroencephalogram (EEG) signal combining an orthogonal discrete wavelet transform analysis with quantifiers originated from information theory is reviewed. In addition, an extension of this methodology based on multiresolution quantities, called wavelet leaders, is presented. In particular, the temporal evolution of Shannon entropy and the statistical complexity evaluated with different sets of multiresolution wavelet coefficients are considered. Both methodologies are applied to the quantitative EEG time series analysis of a tonic-clonic epileptic seizure, and comparative results are presented. In particular, even when both methods describe the dynamical changes of the EEG time series, the one based on wavelet leaders presents a better time resolution.Entropy2014-11-171611Article10.3390/e16115976597660051099-43002014-11-17doi: 10.3390/e16115976Mariel RosenblattAlejandra FigliolaGustavo PaccosiEduardo SerranoOsvaldo Rosso<![CDATA[Entropy, Vol. 16, Pages 5954-5975: Self-Organization at Aqueous Colloid-Membrane Interfaces and an Optical Method to Measure the Kinetics of Exclusion Zone Formation]]>
http://www.mdpi.com/1099-4300/16/11/5954
Exclusion zone (EZ) formation at water-membrane interfaces was studied via bright- and dark-field microscopy. Various aqueous colloids including suspensions of charged microspheres, silicon dioxide particles, and raw whole milk were studied with Nafion® hydrophilic membranes. Interfacial formations observed included EZs and more complex patterns including striations, double layers, banding, dendritic aggregates of particles, and double-stranded structures resembling Birkeland current filaments in cold plasmas. A complex three-dimensional dynamic structure and continuous flow patterns persist in and around EZs, maintaining movement of the colloidal particles even after EZs are fully formed, for which a schematic is proposed. Since radiant energy is critical for EZ formation, we hypothesize that these interfacial phenomena are non-equilibrium dissipative structures that self-organize and self-maintain due to ongoing dynamic processes that may involve hydrodynamic interactions. Another experimental approach undertaken involved the construction of a microscope flow cell to measure the kinetics of EZ formation using sequential microphotography analyzed with macro-programmed ImageJ software to investigate effects of different types of conditioned water. No significant difference was found between spring water and the same water treated by a magnetic vortexer. A significant difference was found for municipal tap water compared to electrolyzed alkaline tap water from the same source.Entropy2014-11-171611Article10.3390/e16115954595459751099-43002014-11-17doi: 10.3390/e16115954Harry JabsBeverly Rubik<![CDATA[Entropy, Vol. 16, Pages 5935-5953: Performance Analysis of a Coal-Fired External Combustion Compressed Air Energy Storage System]]>
http://www.mdpi.com/1099-4300/16/11/5935
Compressed air energy storage (CAES) is one of the large-scale energy storage technologies utilized to provide effective power peak load shaving. In this paper, a coal-fired external combustion CAES, which only uses coal as fuel, is proposed. Unlike the traditional CAES, the combustion chamber is substituted with an external combustion heater in which high-pressure air is heated before entering turbines to expand in the proposed system. A thermodynamic analysis of the proposed CAES is conducted on the basis of the process simulation. The overall efficiency and the efficiency of electricity storage are 48.37% and 81.50%, respectively. Furthermore, the exergy analysis is then derived and forecasted, and the exergy efficiency of the proposed system is 47.22%. The results show that the proposed CAES has more performance advantages than Huntorf CAES (the first CAES plant in the world). Techno-economic analysis of the coal-fired CAES shows that the cost of electricity (COE) is $106.33/MWh, which is relatively high in the rapidly developing power market. However, CAES will be more likely to be competitive if the power grid is improved and suitable geographical conditions for storage caverns are satisfied. This research provides a new approach for developing CAES in China.Entropy2014-11-131611Article10.3390/e16115935593559531099-43002014-11-13doi: 10.3390/e16115935Wenyi LiuQing LiFeifei LiangLinzhi LiuGang XuYongping Yang<![CDATA[Entropy, Vol. 16, Pages 5919-5934: Effect of an Internal Heat Exchanger on Performance of the Transcritical Carbon Dioxide Refrigeration Cycle with an Expander]]>
http://www.mdpi.com/1099-4300/16/11/5919
The effect of the internal heat exchanger (IHE) on the performance of the transcritical carbon dioxide refrigeration cycle with an expander is analyzed theoretically on the basis of the first and second laws of thermodynamics. The possible parameters affecting system efficiency such as heat rejection pressure, gas cooler outlet temperature, evaporating temperature, expander isentropic efficiency and IHE effectiveness are investigated. It is found that the IHE addition in the carbon dioxide refrigeration cycle with an expander increases the specific cooling capacity and compression work, and decreases the optimum heat rejection pressure and the expander output power. An IHE addition does not always improve the system performance in the refrigeration cycle with an expander. The throttle valve cycle with IHE provides a 5.6% to 17% increase in maximum COP compared to that of the basic cycle. For the ideal expander cycle with IHE, the maximum COP is approximately 12.3% to 16.1% lower than the maximum COP of the cycle without IHE. Whether the energy efficiency of the cycle by IHE can be improved depends on the isentropic efficiency level of the expander. The use of IHE is only applicable in the cases of lower expander isentropic efficiencies or higher gas cooler exit temperatures for the refrigeration cycle with an expander from the view of energy efficiency.Entropy2014-11-101611Article10.3390/e16115919591959341099-43002014-11-10doi: 10.3390/e16115919Zhenying ZhangLili TianYanhua ChenLirui Tong<![CDATA[Entropy, Vol. 16, Pages 5901-5918: Comparative Study of Entropy Sensitivity to Missing Biosignal Data]]>
http://www.mdpi.com/1099-4300/16/11/5901
Entropy estimation metrics have become a widely used method to identify subtle changes or hidden features in biomedical records. These methods have been more effective than conventional linear techniques in a number of signal classification applications, specially the healthy–pathological segmentation dichotomy. Nevertheless, a thorough characterization of these measures, namely, how to match metric and signal features, is still lacking. This paper studies a specific characterization problem: the influence of missing samples in biomedical records. The assessment is conducted using four of the most popular entropy metrics: Approximate Entropy, Sample Entropy, Fuzzy Entropy, and Detrended Fluctuation Analysis. The rationale of this study is that missing samples are a signal disturbance that can arise in many cases: signal compression, non-uniform sampling, or data transmission stages. It is of great interest to determine if these real situations can impair the capability of segmenting signal classes using such metrics. The experiments employed several biosignals: electroencephalograms, gait records, and RR time series. Samples of these signals were systematically removed, and the entropy computed for each case. The results showed that these metrics are robust against missing samples: With a data loss percentage of 50% or even higher, the methods were still able to distinguish among signal classes.Entropy2014-11-101611Article10.3390/e16115901590159181099-43002014-11-10doi: 10.3390/e16115901Eva Cirugeda-RoldanDavid Cuesta-FrauPau Miro-MartinezSandra Oltra-Crespo<![CDATA[Entropy, Vol. 16, Pages 5891-5900: Heat Transfer Characteristics of a Speaker Using Nano-Sized Ferrofluid]]>
http://www.mdpi.com/1099-4300/16/11/5891
The purpose of this article is to study the heat transfer characteristics of a voice-coil and permanent magnet for a speaker using nano-sized ferrofluid. In order to investigate the temperature characteristics of the speaker, the speaker power ratings, ambient temperatures of the test chamber, chamber sizes and input signals were tested. As a result, the temperatures of the voice-coil and magnet for the speaker increased with time due to the thermal linearity. The temperature of the voice-coil increased with the decrease of the input signals, but with the increase of the nominal power rating. The voice-coil temperature of Speaker 1 using ferrofluid of an amount of 650 μL at an elapsed time of 10,000 s was 24.5% lower than that of general Speaker 1. In addition, the proper size selection of the enclosure is an important design factor to ensure the sound quality and effective heat transfer of the speaker.Entropy2014-11-101611Article10.3390/e16115891589159001099-43002014-11-10doi: 10.3390/e16115891Moo-Yeon LeeHyung-Jin Kim<![CDATA[Entropy, Vol. 16, Pages 5876-5890: J.J. Thomson and Duhem’s Lagrangian Approaches to Thermodynamics]]>
http://www.mdpi.com/1099-4300/16/11/5876
In the last decades of the nineteenth century, different attitudes towards mechanics led to two main theoretical approaches to thermodynamics: an abstract and phenomenological approach, and a very different approach in terms of microscopic models. In reality some intermediate solutions were also put forward. Helmholtz and Planck relied on a mere complementarity between mechanical and thermal variables in the expressions of state functions, and Oettingen explored the possibility of a more demanding symmetry between mechanical and thermal capacities. Planck refused microscopic interpretations of heat, whereas Helmholtz made also recourse to a Lagrangian approach involving fast hidden motions. J.J. Thomson incorporated the two mechanical attitudes in his theoretical framework, and put forward a very general theory for physical and chemical processes. He made use of two sets of Lagrangian coordinates that corresponded to two components of kinetic energy: alongside macroscopic energy, there was a microscopic energy, which was associated with the absolute temperature. Duhem put forward a bold design of unification between physics and chemistry, which was based on the two principles of thermodynamics. From the mathematical point of view, his thermodynamics or energetics consisted of a Lagrangian generalization of mechanics that could potentially describe every kind of irreversible process, explosive chemical reactions included.Entropy2014-11-061611Article10.3390/e16115876587658901099-43002014-11-06doi: 10.3390/e16115876Stefano Bordoni<![CDATA[Entropy, Vol. 16, Pages 5853-5875: A New Quantum f-Divergence for Trace Class Operators in Hilbert Spaces]]>
http://www.mdpi.com/1099-4300/16/11/5853
A new quantum f-divergence for trace class operators in Hilbert Spaces is introduced. It is shown that for normalised convex functions it is nonnegative. Some upper bounds are provided. Applications for some classes of convex functions of interest are also given.Entropy2014-11-061611Article10.3390/e16115853585358751099-43002014-11-06doi: 10.3390/e16115853Silvestru Dragomir<![CDATA[Entropy, Vol. 16, Pages 5838-5852: New Insights into the Fractional Order Diffusion Equation Using Entropy and Kurtosis]]>
http://www.mdpi.com/1099-4300/16/11/5838
Fractional order derivative operators offer a concise description to model multi-scale, heterogeneous and non-local systems. Specifically, in magnetic resonance imaging, there has been recent work to apply fractional order derivatives to model the non-Gaussian diffusion signal, which is ubiquitous in the movement of water protons within biological tissue. To provide a new perspective for establishing the utility of fractional order models, we apply entropy for the case of anomalous diffusion governed by a fractional order diffusion equation generalized in space and in time. This fractional order representation, in the form of the Mittag–Leffler function, gives an entropy minimum for the integer case of Gaussian diffusion and greater values of spectral entropy for non-integer values of the space and time derivatives. Furthermore, we consider kurtosis, defined as the normalized fourth moment, as another probabilistic description of the fractional time derivative. Finally, we demonstrate the implementation of anomalous diffusion, entropy and kurtosis measurements in diffusion weighted magnetic resonance imaging in the brain of a chronic ischemic stroke patient.Entropy2014-11-061611Article10.3390/e16115838583858521099-43002014-11-06doi: 10.3390/e16115838Carson IngoRichard MaginTodd Parrish<![CDATA[Entropy, Vol. 16, Pages 5822-5837: Plant Friendly Input Design for Parameter Estimation in an Inertial System with Respect to D-Efficiency Constraints]]>
http://www.mdpi.com/1099-4300/16/11/5822
System identification, in practice, is carried out by perturbing processes or plants under operation. That is why in many industrial applications a plant-friendly input signal would be preferred for system identification. The goal of the study is to design the optimal input signal which is then employed in the identification experiment and to examine the relationships between the index of friendliness of this input signal and the accuracy of parameter estimation when the measured output signal is significantly affected by noise. In this case, the objective function was formulated through maximisation of the Fisher information matrix determinant (D-optimality) expressed in conventional Bolza form. As setting such conditions of the identification experiment we can only talk about the D-suboptimality, we quantify the plant trajectories using the D-efficiency measure. An additional constraint, imposed on D-efficiency of the solution, should allow one to attain the most adequate information content from the plant which operating point is perturbed in the least invasive (most friendly) way. A simple numerical example, which clearly demonstrates the idea presented in the paper, is included and discussed.Entropy2014-11-061611Article10.3390/e16115822582258371099-43002014-11-06doi: 10.3390/e16115822Wiktor Jakowluk<![CDATA[Entropy, Vol. 16, Pages 5810-5821: Choked Flow Characteristics of Subcritical Refrigerant Flowing Through Converging-Diverging Nozzles]]>
http://www.mdpi.com/1099-4300/16/11/5810
This paper presents the experimental results the choked flow characteristics of a subcritical refrigerant through a converging-diverging nozzle. A test nozzle with a throat diameter of 2 mm was designed and developed. The influence of operating conditions on the choked flow characteristics, i.e., the pressure profile and mass flow rate under choked flow conditions are investigated. The results indicate that the choked flow occurs in the flow of subcritical refrigerant through nozzles under the normal working conditions of air-conditioners or heat pumps. The pressure drop near the throat is about 80% of the total pressure drop through the nozzle. The critical mass flux is about 19,800 ~ 24,000 kg/(s·m2). The critical mass flow rate increases with increasing the upstream pressure and subcooling. Furthermore, the relative errors between the model predictions and the experimental results for the critical mass flux are also presented. It is found that the deviations of the predictions for homogeneous equilibrium model and Henry-Fauske model from the experimental values are −35% ~ 5% and 15% ~ 35%, respectivelyEntropy2014-11-041611Article10.3390/e16115810581058211099-43002014-11-04doi: 10.3390/e16115810Zhenying ZhangLili TianLirui TongYanhua Chen<![CDATA[Entropy, Vol. 16, Pages 5796-5809: Global Stability Analysis of a Curzon–Ahlborn Heat Engine under Different Regimes of Performance]]>
http://www.mdpi.com/1099-4300/16/11/5796
We present a global stability analysis of a Curzon–Ahlborn heat engine considering different regimes of performance. The stability theory is used to construct the Lyapunov functions to prove the asymptotic stability behavior around the steady state of internal temperatures. We provide a general analytic procedure for the description of the global stability by considering internal irreversibilities and a linear heat transfer law at the thermal couplings. The conditions of the global stability are explored for three regimes of performance: maximum power (MP), efficient power (EP) and the so-called ecological function (EF). Moreover, the analytical results were corroborated by means of numerical integrations, which fully validate the properties of the global asymptotic stability.Entropy2014-11-041611Article10.3390/e16115796579658091099-43002014-11-04doi: 10.3390/e16115796Israel Reyes-RamírezMarco Barranco-JiménezAdolfo Rojas-PachecoLev Guzmán-Vargas<![CDATA[Entropy, Vol. 16, Pages 5777-5795: Multiscale Compression Entropy of Microvascular Blood FlowSignals: Comparison of Results from Laser Speckle Contrastand Laser Doppler Flowmetry Data in Healthy Subjects]]>
http://www.mdpi.com/1099-4300/16/11/5777
Microvascular perfusion is commonly used to study the peripheral cardiovascular system. Microvascular blood flow can be continuously and non-invasively monitored with laser speckle contrast imaging (LSCI) or with laser Doppler flowmetry (LDF). These two optical-based techniques give perfusion values in arbitrary units. Our goal is to better understand the perfusion time series given by each technique. For this purpose, we propose a nonlinear complexity analysis of LSCI and LDF time series recorded simultaneously in nine healthy subjects. This is performed through the computation of their multiscale compression entropy. The results obtained with LSCI time series computed from different regions of interest (ROI) sizes are examined. Our findings show that, for LSCI and LDF time series, compression entropy values are less than one for all of the scales analyzed. This suggests that, for all scales, there are repetitive structures within the data fluctuations. Moreover, at the largest scales studied, LDF signals seem to have structures that are different from those Entropy 2014, 16 5778 of Gaussian white noise. By opposition, this is not observed for LSCI time series computed from small ROI sizesEntropy2014-11-041611Article10.3390/e16115777577757951099-43002014-11-04doi: 10.3390/e16115777Anne Humeau-HeurtierMathias BaumertGuillaume MahéPierre Abraham<![CDATA[Entropy, Vol. 16, Pages 5753-5776: Inferring a Drive-Response Network from Time Series of Topological Measures in Complex Networks with Transfer Entropy]]>
http://www.mdpi.com/1099-4300/16/11/5753
Topological measures are crucial to describe, classify and understand complex networks. Lots of measures are proposed to characterize specific features of specific networks, but the relationships among these measures remain unclear. Taking into account that pulling networks from different domains together for statistical analysis might provide incorrect conclusions, we conduct our investigation with data observed from the same network in the form of simultaneously measured time series. We synthesize a transfer entropy-based framework to quantify the relationships among topological measures, and then to provide a holistic scenario of these measures by inferring a drive-response network. Techniques from Symbolic Transfer Entropy, Effective Transfer Entropy, and Partial Transfer Entropy are synthesized to deal with challenges such as time series being non-stationary, finite sample effects and indirect effects. We resort to kernel density estimation to assess significance of the results based on surrogate data. The framework is applied to study 20 measures across 2779 records in the Technology Exchange Network, and the results are consistent with some existing knowledge. With the drive-response network, we evaluate the influence of each measure by calculating its strength, and cluster them into three classes, i.e., driving measures, responding measures and standalone measures, according to the network communities.Entropy2014-11-031611Article10.3390/e16115753575357761099-43002014-11-03doi: 10.3390/e16115753Xinbo Ai<![CDATA[Entropy, Vol. 16, Pages 5738-5752: Sensitivity Analysis for Urban Drainage Modeling Using Mutual Information]]>
http://www.mdpi.com/1099-4300/16/11/5738
The intention of this paper is to evaluate the sensitivity of the Storm Water Management Model (SWMM) output to its input parameters. A global parameter sensitivity analysis is conducted in order to determine which parameters mostly affect the model simulation results. Two different methods of sensitivity analysis are applied in this study. The first one is the partial rank correlation coefficient (PRCC) which measures nonlinear but monotonic relationships between model inputs and outputs. The second one is based on the mutual information which provides a general measure of the strength of the non-monotonic association between two variables. Both methods are based on the Latin Hypercube Sampling (LHS) of the parameter space, and thus the same datasets can be used to obtain both measures of sensitivity. The utility of the PRCC and the mutual information analysis methods are illustrated by analyzing a complex SWMM model. The sensitivity analysis revealed that only a few key input variables are contributing significantly to the model outputs; PRCCs and mutual information are calculated and used to determine and rank the importance of these key parameters. This study shows that the partial rank correlation coefficient and mutual information analysis can be considered effective methods for assessing the sensitivity of the SWMM model to the uncertainty in its input parameters.Entropy2014-11-031611Article10.3390/e16115738573857521099-43002014-11-03doi: 10.3390/e16115738Chuanqi LiWei WangJianzhi XiongPengyu Chen<![CDATA[Entropy, Vol. 16, Pages 5721-5737: Applying Information Theory to Neuronal Networks: From Theory to Experiments]]>
http://www.mdpi.com/1099-4300/16/11/5721
Information-theory is being increasingly used to analyze complex, self-organizing processes on networks, predominantly in analytical and numerical studies. Perhaps one of the most paradigmatic complex systems is a network of neurons, in which cognition arises from the information storage, transfer, and processing among individual neurons. In this article we review experimental techniques suitable for validating information-theoretical predictions in simple neural networks, as well as generating new hypotheses. Specifically, we focus on techniques that may be used to measure both network (microcircuit) anatomy as well as neuronal activity simultaneously. This is needed to study the role of the network structure on the emergent collective dynamics, which is one of the reasons to study the characteristics of information processing. We discuss in detail two suitable techniques, namely calcium imaging and the application of multi-electrode arrays to simple neural networks in culture, and discuss their advantages and limitations in an accessible manner for non-experts. In particular, we show that each technique induces a qualitatively different type of error on the measured mutual information. The ultimate goal of this work is to bridge the gap between theorists and experimentalists in their shared goal of understanding the behavior of networks of neurons.Entropy2014-11-031611Review10.3390/e16115721572157371099-43002014-11-03doi: 10.3390/e16115721Thijs JungFilippos VogiatzianOmri Har-ShemeshCarlos FitzsimonsRick Quax<![CDATA[Entropy, Vol. 16, Pages 5712-5720: The Case for Tetrahedral Oxy-subhydride (TOSH) Structures in the Exclusion Zones of Anchored Polar Solvents Including Water]]>
http://www.mdpi.com/1099-4300/16/11/5712
We hypothesize a mechanistic model of how negatively-charged exclusion zones (EZs) are created. While the growth of EZs is known to be associated with the absorption of ambient photonic energy, the molecular dynamics giving rise to this process need greater elucidation. We believe they arise due to the formation of oxy-subhydride structures (OH−)(H2O)4 with a tetrahedral (sp3) (OH−)(H2O)3 core. Five experimental data sets derived by previous researchers were assessed in this regard: (1) water-derived EZ light absorbance at specific infrared wavelengths, (2) EZ negative potential in water and ethanol, (3) maximum EZ light absorbance at 270 nm ultraviolet wavelength, (4) ability of dimethyl sulphoxide but not ether to form an EZ, and (5) transitory nature of melting ice derived EZs. The proposed tetrahedral oxy-subhydride structures (TOSH) appear to adequately account for all of the experimental evidence derived from water or other polar solvents.Entropy2014-11-031611Article10.3390/e16115712571257201099-43002014-11-03doi: 10.3390/e16115712Klaus OehrPaul LeMay<![CDATA[Entropy, Vol. 16, Pages 5698-5711: Sample Entropy and Traditional Measures of Heart Rate Dynamics Reveal Different Modes of Cardiovascular Control During Low Intensity Exercise]]>
http://www.mdpi.com/1099-4300/16/11/5698
Nonlinear parameters of heart rate variability (HRV) have proven their prognostic value in clinical settings, but their physiological background is not very well established. We assessed the effects of low intensity isometric (ISO) and dynamic (DYN) exercise of the lower limbs on heart rate matched intensity on traditional and entropy measures of HRV. Due to changes of afferent feedback under DYN and ISO a distinct autonomic response, mirrored by HRV measures, was hypothesized. Five-minute inter-beat interval measurements of 43 healthy males (26.0 ± 3.1 years) were performed during rest, DYN and ISO in a randomized order. Blood pressures and rate pressure product were higher during ISO vs. DYN (p &lt; 0.001). HRV indicators SDNN as well as low and high frequency power were significantly higher during ISO (p &lt; 0.001 for all measures). Compared to DYN, sample entropy (SampEn) was lower during ISO (p &lt; 0.001). Concluding, contraction mode itself is a significant modulator of the autonomic cardiovascular response to exercise. Compared to DYN, ISO evokes a stronger blood pressure response and an enhanced interplay between both autonomic branches. Non-linear HRV measures indicate a more regular behavior under ISO. Results support the view of the reciprocal antagonism being only one of many modes of autonomic heart rate control. Under different conditions; the identical “end product” heart rate might be achieved by other modes such as sympathovagal co-activation as well.Entropy2014-10-311611Article10.3390/e16115698569857111099-43002014-10-31doi: 10.3390/e16115698Matthias WeippertMartin BehrensAnnika RiegerKristin Behrens<![CDATA[Entropy, Vol. 16, Pages 5677-5697: A Load Balancing Algorithm Based on Maximum Entropy Methods in Homogeneous Clusters]]>
http://www.mdpi.com/1099-4300/16/11/5677
In order to solve the problems of ill-balanced task allocation, long response time, low throughput rate and poor performance when the cluster system is assigning tasks, we introduce the concept of entropy in thermodynamics into load balancing algorithms. This paper proposes a new load balancing algorithm for homogeneous clusters based on the Maximum Entropy Method (MEM). By calculating the entropy of the system and using the maximum entropy principle to ensure that each scheduling and migration is performed following the increasing tendency of the entropy, the system can achieve the load balancing status as soon as possible, shorten the task execution time and enable high performance. The result of simulation experiments show that this algorithm is more advanced when it comes to the time and extent of the load balance of the homogeneous cluster system compared with traditional algorithms. It also provides novel thoughts of solutions for the load balancing problem of the homogeneous cluster system.Entropy2014-10-301611Article10.3390/e16115677567756971099-43002014-10-30doi: 10.3390/e16115677Long ChenKehe WuYi Li<![CDATA[Entropy, Vol. 16, Pages 5668-5676: Permutation Entropy Applied to the Characterization of the Clinical Evolution of Epileptic Patients under PharmacologicalTreatment]]>
http://www.mdpi.com/1099-4300/16/11/5668
Different techniques originated in information theory and tools from nonlinear systems theory have been applied to the analysis of electro-physiological time series. Several clinically relevant results have emerged from the use of concepts, such as entropy, chaos and complexity, in analyzing electrocardiograms and electroencephalographic (EEG) records. In this work, we develop a method based on permutation entropy (PE) to characterize EEG records from different stages in the treatment of a chronic epileptic patient. Our results show that the PE is useful for clearly quantifying the evolution of the patient along a certain lapse of time and allows visualizing in a very convenient way the effects of the pharmacotherapy.Entropy2014-10-291611Article10.3390/e16115668566856761099-43002014-10-29doi: 10.3390/e16115668Diego MateosJuan DiazPedro Lamberti<![CDATA[Entropy, Vol. 16, Pages 5654-5667: Characterizing Motif Dynamics of Electric Brain Activity Using Symbolic Analysis]]>
http://www.mdpi.com/1099-4300/16/11/5654
Motifs are small recurring circuits of interactions which constitute the backbone of networked systems. Characterizing motif dynamics is therefore key to understanding the functioning of such systems. Here we propose a method to define and quantify the temporal variability and time scales of electroencephalogram (EEG) motifs of resting brain activity. Given a triplet of EEG sensors, links between them are calculated by means of linear correlation; each pattern of links (i.e., each motif) is then associated to a symbol, and its appearance frequency is analyzed by means of Shannon entropy. Our results show that each motif becomes observable with different coupling thresholds and evolves at its own time scale, with fronto-temporal sensors emerging at high thresholds and changing at fast time scales, and parietal ones at low thresholds and changing at slower rates. Finally, while motif dynamics differed across individuals, for each subject, it showed robustness across experimental conditions, indicating that it could represent an individual dynamical signature.Entropy2014-10-271611Article10.3390/e16115654565456671099-43002014-10-27doi: 10.3390/e16115654Massimiliano ZaninDavid Papo<![CDATA[Entropy, Vol. 16, Pages 5633-5653: Energy Analysis and Multi-Objective Optimization of an Internal Combustion Engine-Based CHP System for Heat Recovery]]>
http://www.mdpi.com/1099-4300/16/11/5633
A comprehensive thermodynamic study is conducted of a diesel based Combined Heat and Power (CHP) system, based on a diesel engine and an Organic Rankine Cycle (ORC). Present research covers both energy and exergy analyses along with a multi-objective optimization. In order to determine the irreversibilities in each component of the CHP system and assess the system performance, a complete parametric study is performed to investigate the effects of major design parameters and operating conditions on the system’s performance. The main contribution of the current research study is to conduct both exergy and multi-objective optimization of a system using different working fluid for low-grade heat recovery. In order to conduct the evolutionary based optimization, two objective functions are considered in the optimization; namely the system exergy efficiency, and the total cost rate of the system, which is a combination of the cost associated with environmental impact and the purchase cost of each component. Therefore, in the optimization approach, the overall cycle exergy efficiency is maximized satisfying several constraints while the total cost rate of the system is minimized. To provide a better understanding of the system under study, the Pareto frontier is shown for multi-objective optimization and also an equation is derived to fit the optimized point. In addition, a closed form relationship between exergy efficiency and total cost rate is derived.Entropy2014-10-271611Article10.3390/e16115633563356531099-43002014-10-27doi: 10.3390/e16115633Abdolsaeid GanjehkaviriMohammad Jaafar<![CDATA[Entropy, Vol. 16, Pages 5618-5632: The Property of Chaotic Orbits with Lower Positions of Numerical Solutions in the Logistic Map]]>
http://www.mdpi.com/1099-4300/16/11/5618
In this paper, we introduce an iterative method with lower positions of true numerical solutions located in the real orbit in order to investigate the property of the logistic map. The basic structure of the logistic map is presented, which consists of the root gene position, the common gene position and the individual gene position. The ergodicity and randomness of the logistic map are dependent on the individual gene position. We find that the lower positions of the true numerical solutions in the real orbits have the property of a half-life.Entropy2014-10-271611Article10.3390/e16115618561856321099-43002014-10-27doi: 10.3390/e16115618Jiahui LiuHongli ZhangDahua Song<![CDATA[Entropy, Vol. 16, Pages 5601-5617: On One-Sided, D-Chaotic CA Without Fixed Points, Having Continuum of Periodic Points With Period 2 and Topological Entropy log(p) for Any Prime p]]>
http://www.mdpi.com/1099-4300/16/11/5601
A method is known by which any integer \(\, n\geq2\,\) in a metric Cantor space of right-infinite words \(\,\tilde{A}_{n}^{\,\mathbb N}\,\) gives a construction of a non-injective cellular automaton \(\,(\tilde{A}_{n}^{\,\mathbb N},\,\tilde{F}_{n}),\,\) which is chaotic in Devaney sense, has a radius \(\, r=1,\,\) continuum of fixed points and topological entropy \(\, log(n).\,\) As a generalization of this method we present for any integer \(\, n\geq2,\,\) a construction of a cellular automaton \(\,(A_{n}^{\,\mathbb{N}},\, F_{n}),\,\) which has the listed properties of \(\,(\tilde{A}_{n}^{\,\mathbb N},\,\tilde{F}_{n}),\,\) but has no fixed points and has continuum of periodic points with the period 2. The construction is based on properties of cellular automaton introduced here \(\,(B^{\,\mathbb N},\, F)\,\) with radius \(1\) defined for any prime number \(\, p.\,\) We prove that \(\,(B^{\,\mathbb N},\, F)\,\) is non-injective, chaotic in Devaney sense, has no fixed points, has continuum of periodic points with the period \(2\) and topological entropy \(\, log(p).\,\)Entropy2014-10-241611Article10.3390/e16115601560156171099-43002014-10-24doi: 10.3390/e16115601Wit ForysJanusz Matyja<![CDATA[Entropy, Vol. 16, Pages 5575-5600: Partial Encryption of Entropy-Coded Video Compression Using Coupled Chaotic Maps]]>
http://www.mdpi.com/1099-4300/16/10/5575
Due to pervasive communication infrastructures, a plethora of enabling technologies is being developed over mobile and wired networks. Among these, video streaming services over IP are the most challenging in terms of quality, real-time requirements and security. In this paper, we propose a novel scheme to efficiently secure variable length coded (VLC) multimedia bit streams, such as H.264. It is based on code word error diffusion and variable size segment shuffling. The codeword diffusion and the shuffling mechanisms are based on random operations from a secure and computationally efficient chaos-based pseudo-random number generator. The proposed scheme is ubiquitous to the end users and can be deployed at any node in the network. It provides different levels of security, with encrypted data volume fluctuating between 5.5–17%. It works on the compressed bit stream without requiring any decoding. It provides excellent encryption speeds on different platforms, including mobile devices. It is 200% faster and 150% more power efficient when compared with AES software-based full encryption schemes. Regarding security, the scheme is robust to well-known attacks in the literature, such as brute force and known/chosen plain text attacks.Entropy2014-10-231610Article10.3390/e16105575557556001099-43002014-10-23doi: 10.3390/e16105575Fadi AlmasalhaRogelio Hasimoto-BeltranAshfaq Khokhar<![CDATA[Entropy, Vol. 16, Pages 5560-5574: Contributions to the Transformation Entropy Change and Influencing Factors in Metamagnetic Ni-Co-Mn-Ga Shape Memory Alloys]]>
http://www.mdpi.com/1099-4300/16/10/5560
Ni-Co-Mn-Ga ferromagnetic shape memory alloys show metamagnetic transition from ferromagnetic austenite to paramagnetic (or weak-magnetic) martensite for a limited range of Co contents. The temperatures of the structural and magnetic transitions depend strongly on composition and atomic order degree, in such a way that combined composition and thermal treatment allows obtaining martensitic transformation (MT) between any magnetic state of austenite and martensite. The entropy change ΔS measured in the magnetostructural transition comprises a magnetic contribution which depends on the type and degree of magnetic order of the related phases. Consequently, both the magnetization jump across the MT (ΔM) and ΔS are composition and atomic order dependent. Both ΔS and ΔM determine the effect of applied magnetic fields on the MT, hence knowledge and understanding of their behavior can help to approach the best conditions for magnetic field induced MT and related effects. In previous papers, we have reported findings regarding the behavior of the transformation entropy in relation to composition and atomic order in Ni50−xCoxMn25+yGa25−y (x = 3–8, y = 5–7) alloys. In the present paper we will review our recent results, summarizing the key findings and drawing general conclusions regarding the magnetic contribution to ΔS and the effect of different factors on the magnetic and structural properties of these metamagnetic alloys.Entropy2014-10-221610Article10.3390/e16105560556055741099-43002014-10-22doi: 10.3390/e16105560Concepció SeguíEduard Cesari<![CDATA[Entropy, Vol. 16, Pages 5546-5559: Conventional Point-Velocity Records and Surface Velocity Observations for Estimating High Flow Discharge]]>
http://www.mdpi.com/1099-4300/16/10/5546
Flow velocity measurements using point-velocity meters are normally obtained by sampling one, two or three velocity points per vertical profile. During high floods their use is inhibited due to the difficulty of sampling in lower portions of the flow area. Nevertheless, the application of standard methods allows estimation of a parameter, α, which depends on the energy slope and the Manning roughness coefficient. During high floods, monitoring of velocity can be accomplished by sampling the maximum velocity, umax, only, which can be used to estimate the mean flow velocity, um, by applying the linear entropy relationship depending on the parameter, M, estimated on the basis of historical observed pairs (um, umax). In this context, this work attempts to analyze if a correlation between α and M holds, so that the monitoring for high flows can be addressed by exploiting information from standard methods. A methodology is proposed to estimate M from α, by coupling the “historical” information derived by standard methods, and “new” information from the measurement of umax surmised at later times. Results from four gauged river sites of different hydraulic and geometric characteristics have shown the robust estimation of M based on α.Entropy2014-10-211610Article10.3390/e16105546554655591099-43002014-10-21doi: 10.3390/e16105546Giovanni CoratoAbdelhadi AmmariTommaso Moramarco<![CDATA[Entropy, Vol. 16, Pages 5537-5545: The Q-Exponential Decay of Subjective Probability for Future Reward: A Psychophysical Time Approach]]>
http://www.mdpi.com/1099-4300/16/10/5537
This study experimentally examined why subjective probability for delayed reward decays non-exponentially (“hyperbolically”, i.e., q ˂ 1 in the q-exponential discount function) in humans. Our results indicate that nonlinear psychophysical time causes hyperbolic time-decay of subjective probability for delayed reward. Implications for econophysics and neuroeconomics are discussed.Entropy2014-10-211610Article10.3390/e16105537553755451099-43002014-10-21doi: 10.3390/e16105537Taiki TakahashiShinsuke TokudaMasato NishimuraRyo Kimura<![CDATA[Entropy, Vol. 16, Pages 5523-5536: Extreme Value Laws for Superstatistics]]>
http://www.mdpi.com/1099-4300/16/10/5523
We study the extreme value distribution of stochastic processes modeled by superstatistics. Classical extreme value theory asserts that (under mild asymptotic independence assumptions) only three possible limit distributions are possible, namely: Gumbel, Fréchet and Weibull distribution. On the other hand, superstatistics contains three important universality classes, namely χ2-superstatistics, inverse χ2 -superstatistics, and lognormal superstatistics, all maximizing different effective entropy measures. We investigate how the three classes of extreme value theory are related to the three classes of superstatistics. We show that for any superstatistical process whose local equilibrium distribution does not live on a finite support, the Weibull distribution cannot occur. Under the above mild asymptotic independence assumptions, we also show that χ2-superstatistics generally leads an extreme value statistics described by a Fréchet distribution, whereas inverse χ2 -superstatistics, as well as lognormal superstatistics, lead to an extreme value statistics associated with the Gumbel distribution.Entropy2014-10-201610Article10.3390/e16105523552355361099-43002014-10-20doi: 10.3390/e16105523Pau RabassaChristian Beck<![CDATA[Entropy, Vol. 16, Pages 5428-5522: Directionality Theory and the Entropic Principle of Natural Selection]]>
http://www.mdpi.com/1099-4300/16/10/5428
Darwinian fitness describes the capacity of an organism to appropriate resources from the environment and to convert these resources into net-offspring production. Studies of competition between related types indicate that fitness is analytically described by entropy, a statistical measure which is positively correlated with population stability, and describes the number of accessible pathways of energy flow between the individuals in the population. Directionality theory is a mathematical model of the evolutionary process based on the concept evolutionary entropy as the measure of fitness. The theory predicts that the changes which occur as a population evolves from one non-equilibrium steady state to another are described by the following directionality principle–fundamental theorem of evolution: (a) an increase in evolutionary entropy when resource composition is diverse, and resource abundance constant; (b) a decrease in evolutionary entropy when resource composition is singular, and resource abundance variable. Evolutionary entropy characterizes the dynamics of energy flow between the individual elements in various classes of biological networks: (a) where the units are individuals parameterized by age, and their age-specific fecundity and mortality; where the units are metabolites, and the transitions are the biochemical reactions that convert substrates to products; (c) where the units are social groups, and the forces are the cooperative and competitive interactions between the individual groups. % This article reviews the analytical basis of the evolutionary entropic principle, and describes applications of directionality theory to the study of evolutionary dynamics in two biological systems; (i) social networks–the evolution of cooperation; (ii) metabolic networks–the evolution of body size. Statistical thermodynamics is a mathematical model of macroscopic behavior in inanimate matter based on entropy, a statistical measure which describes the number of ways the molecules that compose the a material aggregate can be arranged to attain the same total energy. This theory predicts an increase in thermodynamic entropy as the system evolves towards its equilibrium state. We will delineate the relation between directionality theory and statistical thermodynamics, and review the claim that the entropic principle for thermodynamic systems is the limit, as the resource production rate tends to zero, and population size tends to infinity, of the entropic principle for evolutionary systems.Entropy2014-10-201610Article10.3390/e16105428542855221099-43002014-10-20doi: 10.3390/e16105428Lloyd DemetriusVolker Gundlach<![CDATA[Entropy, Vol. 16, Pages 5416-5427: A Note on Distance-based Graph Entropies]]>
http://www.mdpi.com/1099-4300/16/10/5416
A variety of problems in, e.g., discrete mathematics, computer science, information theory, statistics, chemistry, biology, etc., deal with inferring and characterizing relational structures by using graph measures. In this sense, it has been proven that information-theoretic quantities representing graph entropies possess useful properties such as a meaningful structural interpretation and uniqueness. As classical work, many distance-based graph entropies, e.g., the ones due to Bonchev et al. and related quantities have been proposed and studied. Our contribution is to explore graph entropies that are based on a novel information functional, which is the number of vertices with distance \(k\) to a given vertex. In particular, we investigate some properties thereof leading to a better understanding of this new information-theoretic quantity.Entropy2014-10-201610Article10.3390/e16105416541654271099-43002014-10-20doi: 10.3390/e16105416Zengqiang ChenMatthias DehmerYongtang Shi<![CDATA[Entropy, Vol. 16, Pages 5400-5415: Performance Degradation Assessment of Rolling Element Bearings Based on an Index Combining SVD and Information Exergy]]>
http://www.mdpi.com/1099-4300/16/10/5400
Performance degradation assessment of rolling element bearings is vital for the reliable and cost-efficient operation and maintenance of rotating machines, especially for the implementation of condition-based maintenance (CBM). For robust degradation assessment of rolling element bearings, uncertainties such as those induced from usage variations or sensor errors must be taken into account. This paper presents an information exergy index for bearing performance degradation assessment that combines singular value decomposition (SVD) and the information exergy method. Information exergy integrates condition monitoring information of multiple instants and multiple sensors, and thus performance degradation assessment uncertainties are reduced and robust degradation assessment results can be obtained using the proposed index. The effectiveness and robustness of the proposed information exergy index are validated through experimental case studies.Entropy2014-10-161610Article10.3390/e16105400540054151099-43002014-10-16doi: 10.3390/e16105400Bin ZhangLijun ZhangJinwu XuPingfeng Wang<![CDATA[Entropy, Vol. 16, Pages 5377-5399: On Some Properties of Tsallis Hypoentropies and Hypodivergences]]>
http://www.mdpi.com/1099-4300/16/10/5377
Both the Kullback–Leibler and the Tsallis divergence have a strong limitation: if the value zero appears in probability distributions (p1, ··· , pn) and (q1, ··· , qn), it must appear in the same positions for the sake of significance. In order to avoid that limitation in the framework of Shannon statistics, Ferreri introduced in 1980 hypoentropy: “such conditions rarely occur in practice”. The aim of the present paper is to extend Ferreri’s hypoentropy to the Tsallis statistics. We introduce the Tsallis hypoentropy and the Tsallis hypodivergence and describe their mathematical behavior. Fundamental properties, like nonnegativity, monotonicity, the chain rule and subadditivity, are established.Entropy2014-10-151610Article10.3390/e16105377537753991099-43002014-10-15doi: 10.3390/e16105377Shigeru FuruichiFlavia-Corina Mitroi-SymeonidisEleutherius Symeonidis<![CDATA[Entropy, Vol. 16, Pages 5358-5376: Research and Development of a Chaotic Signal Synchronization Error Dynamics-Based Ball Bearing Fault Diagnostor]]>
http://www.mdpi.com/1099-4300/16/10/5358
This paper describes the fault diagnosis in the operation of industrial ball bearings. In order to cluster the very small differential signals of the four classic fault types of the ball bearing system, the chaos synchronization (CS) concept is used in this study as the chaos system is very sensitive to a system’s variation such as initial conditions or system parameters. In this study, the Chen-Lee chaotic system was used to load the normal and fault signals of the bearings into the chaos synchronization error dynamics system. The fractal theory was applied to determine the fractal dimension and lacunarity from the CS error dynamics. Extenics theory was then applied to distinguish the state of the bearing faults. This study also compared the proposed method with discrete Fourier transform and wavelet packet analysis. According to the results, it is shown that the proposed chaos synchronization method combined with extenics theory can separate the characteristics (fractal dimension vs. lacunarity) completely. Therefore, it has a better fault diagnosis rate than the two traditional signal processing methods, i.e., Fourier transform and wavelet packet analysis combined with extenics theory.Entropy2014-10-151610Article10.3390/e16105358535853761099-43002014-10-15doi: 10.3390/e16105358Ying-Che KuoChin-Tsung HsiehHer-Terng YauYu-Chung Li<![CDATA[Entropy, Vol. 16, Pages 5339-5357: Redundancy of Exchangeable Estimators]]>
http://www.mdpi.com/1099-4300/16/10/5339
Exchangeable random partition processes are the basis for Bayesian approaches to statistical inference in large alphabet settings. On the other hand, the notion of the pattern of a sequence provides an information-theoretic framework for data compression in large alphabet scenarios. Because data compression and parameter estimation are intimately related, we study the redundancy of Bayes estimators coming from Poisson–Dirichlet priors (or “Chinese restaurant processes”) and the Pitman–Yor prior. This provides an understanding of these estimators in the setting of unknown discrete alphabets from the perspective of universal compression. In particular, we identify relations between alphabet sizes and sample sizes where the redundancy is small, thereby characterizing useful regimes for these estimators.Entropy2014-10-131610Article10.3390/e16105339533953571099-43002014-10-13doi: 10.3390/e16105339Narayana SanthanamAnand SarwateJae Woo<![CDATA[Entropy, Vol. 16, Pages 5290-5338: Quantum Computation-Based Image Representation, Processing Operations and Their Applications]]>
http://www.mdpi.com/1099-4300/16/10/5290
A flexible representation of quantum images (FRQI) was proposed to facilitate the extension of classical (non-quantum)-like image processing applications to the quantum computing domain. The representation encodes a quantum image in the form of a normalized state, which captures information about colors and their corresponding positions in the images. Since its conception, a handful of processing transformations have been formulated, among which are the geometric transformations on quantum images (GTQI) and the CTQI that are focused on the color information of the images. In addition, extensions and applications of FRQI representation, such as multi-channel representation for quantum images (MCQI), quantum image data searching, watermarking strategies for quantum images, a framework to produce movies on quantum computers and a blueprint for quantum video encryption and decryption have also been suggested. These proposals extend classical-like image and video processing applications to the quantum computing domain and offer a significant speed-up with low computational resources in comparison to performing the same tasks on traditional computing devices. Each of the algorithms and the mathematical foundations for their execution were simulated using classical computing resources, and their results were analyzed alongside other classical computing equivalents. The work presented in this review is intended to serve as the epitome of advances made in FRQI quantum image processing over the past five years and to simulate further interest geared towards the realization of some secure and efficient image and video processing applications on quantum computers.Entropy2014-10-101610Review10.3390/e16105290529053381099-43002014-10-10doi: 10.3390/e16105290Fei YanAbdullah IliyasuZhengang Jiang<![CDATA[Entropy, Vol. 16, Pages 5263-5289: Cross-Scale Interactions and Information Transfer]]>
http://www.mdpi.com/1099-4300/16/10/5263
An information-theoretic approach for detecting interactions and informationtransfer between two systems is extended to interactions between dynamical phenomenaevolving on different time scales of a complex, multiscale process. The approach isdemonstrated in the detection of an information transfer from larger to smaller time scales ina model multifractal process and applied in a study of cross-scale interactions in atmosphericdynamics. Applying a form of the conditional mutual information and a statistical test basedon the Fourier transform and multifractal surrogate data to about a century long recordsof daily mean surface air temperature from various European locations, an informationtransfer from larger to smaller time scales has been observed as the influence of the phaseof slow oscillatory phenomena with the periods around 6–11 years on the amplitudes of thevariability characterized by the smaller temporal scales from a few months to 4–5 years.These directed cross-scale interactions have a non-negligible effect on interannual airtemperature variability in a large area of Europe.Entropy2014-10-101610Article10.3390/e16105263526352891099-43002014-10-10doi: 10.3390/e16105263Milan Paluš<![CDATA[Entropy, Vol. 16, Pages 5242-5262: How to Mine Information from Each Instance to Extract an Abbreviated and Credible Logical Rule]]>
http://www.mdpi.com/1099-4300/16/10/5242
Decision trees are particularly promising in symbolic representation and reasoning due to their comprehensible nature, which resembles the hierarchical process of human decision making. However, their drawbacks, caused by the single-tree structure,cannot be ignored. A rigid decision path may cause the majority class to overwhelm otherclass when dealing with imbalanced data sets, and pruning removes not only superfluousnodes, but also subtrees. The proposed learning algorithm, flexible hybrid decision forest(FHDF), mines information implicated in each instance to form logical rules on the basis of a chain rule of local mutual information, then forms different decision tree structures and decision forests later. The most credible decision path from the decision forest can be selected to make a prediction. Furthermore, functional dependencies (FDs), which are extracted from the whole data set based on association rule analysis, perform embedded attribute selection to remove nodes rather than subtrees, thus helping to achieve different levels of knowledge representation and improve model comprehension in the framework of semi-supervised learning. Naive Bayes replaces the leaf nodes at the bottom of the tree hierarchy, where the conditional independence assumption may hold. This technique reduces the potential for overfitting and overtraining and improves the prediction quality and generalization. Experimental results on UCI data sets demonstrate the efficacy of the proposed approach.Entropy2014-10-091610Article10.3390/e16105242524252621099-43002014-10-09doi: 10.3390/e16105242Limin WangMinghui SunChunhong Cao<![CDATA[Entropy, Vol. 16, Pages 5232-5241: Entropy Methods in Guided Self-Organisation]]>
http://www.mdpi.com/1099-4300/16/10/5232
Self-organisation occurs in natural phenomena when a spontaneous increase in order is produced by the interactions of elements of a complex system. Thermodynamically, this increase must be offset by production of entropy which, broadly speaking, can be understood as a decrease in order. Ideally, self-organisation can be used to guide the system towards a desired regime or state, while "exporting" the entropy to the system's exterior. Thus, Guided Self-Organisation (GSO) attempts to harness the order-inducing potential of self-organisation for specific purposes. Not surprisingly, general methods developed to study entropy can also be applied to guided self-organisation. This special issue covers abroad diversity of GSO approaches which can be classified in three categories: information theory, intelligent agents, and collective behavior. The proposals make another step towards a unifying theory of GSO which promises to impact numerous research fields.Entropy2014-10-091610Editorial10.3390/e16105232523252411099-43002014-10-09doi: 10.3390/e16105232Mikhail ProkopenkoCarlos Gershenson<![CDATA[Entropy, Vol. 16, Pages 5223-5231: Elimination of a Second-Law-Attack, and All Cable-Resistance-Based Attacks, in the Kirchhoff-Law-Johnson-Noise (KLJN) Secure Key Exchange System]]>
http://www.mdpi.com/1099-4300/16/10/5223
We introduce the so far most efficient attack against the Kirchhoff-law-Johnson-noise (KLJN) secure key exchange system. This attack utilizes the lack of exact thermal equilibrium in practical applications and is based on cable resistance losses and the fact that the Second Law of Thermodynamics cannot provide full security when such losses are present. The new attack does not challenge the unconditional security of the KLJN scheme, but it puts more stringent demands on the security/privacy enhancing protocol than for any earlier attack. In this paper we present a simple defense protocol to fully eliminate this new attack by increasing the noise-temperature at the side of the smaller resistance value over the noise-temperature at the side with the greater resistance. It is shown that this simple protocol totally removes Eve’s information not only for the new attack but also for the old Bergou-Scheuer-Yariv attack. The presently most efficient attacks against the KLJN scheme are thereby completely nullified.Entropy2014-10-071610Article10.3390/e16105223522352311099-43002014-10-07doi: 10.3390/e16105223Laszlo KishClaes-Göran Granqvist<![CDATA[Entropy, Vol. 16, Pages 5211-5222: A Further Indication of the Self-Ordering Capacity of Water Via the Droplet Evaporation Method]]>
http://www.mdpi.com/1099-4300/16/10/5211
The droplet evaporation method (DEM) is increasingly used for assessing various characteristics of water. In our research we tried to use DEM to detect a possible self-ordering capability of (spring) water that would be similar to the already found and described autothixotropic phenomenon, namely increasing order of non-distilled water subject to aging. The output of DEM is a droplet remnant pattern (DRP). For analysis of DRP images we used a specially developed computer program that does the frequency distribution analysis of certain parameters of the images. The results of experiments demonstrated statistically significant differences in both aging of water as well as in the glass exposed surface/volume ratio of the aged water. The most important result supporting the self-ordering character of water was found in an increasing dependence between two analyzed parameters: distance and frequency, at the peak frequency. As the result concerns mostly aging and shows increasing order it further corroborates other findings concerning increasing order by aging. Such further confirmation of self-ordering capacity of water is not important only for physical chemistry, but also for biology.Entropy2014-10-071610Article10.3390/e16105211521152221099-43002014-10-07doi: 10.3390/e16105211Igor JermanPetra Ratajc<![CDATA[Entropy, Vol. 16, Pages 5198-5210: Exact Probability Distribution versus Entropy]]>
http://www.mdpi.com/1099-4300/16/10/5198
The problem addressed concerns the determination of the average number of successive attempts of guessing a word of a certain length consisting of letters with given probabilities of occurrence. Both first- and second-order approximations to a natural language are considered. The guessing strategy used is guessing words in decreasing order of probability. When word and alphabet sizes are large, approximations are necessary in order to estimate the number of guesses. Several kinds of approximations are discussed demonstrating moderate requirements regarding both memory and central processing unit (CPU) time. When considering realistic sizes of alphabets and words (100), the number of guesses can be estimated within minutes with reasonable accuracy (a few percent) and may therefore constitute an alternative to, e.g., various entropy expressions. For many probability distributions, the density of the logarithm of probability products is close to a normal distribution. For those cases, it is possible to derive an analytical expression for the average number of guesses. The proportion of guesses needed on average compared to the total number decreases almost exponentially with the word length. The leading term in an asymptotic expansion can be used to estimate the number of guesses for large word lengths. Comparisons with analytical lower bounds and entropy expressions are also provided.Entropy2014-10-071610Article10.3390/e16105198519852101099-43002014-10-07doi: 10.3390/e16105198Kerstin Andersson<![CDATA[Entropy, Vol. 16, Pages 5178-5197: Entropy Generation in Flow of Highly Concentrated Non-Newtonian Emulsions in Smooth Tubes]]>
http://www.mdpi.com/1099-4300/16/10/5178
Entropy generation in adiabatic flow of highly concentrated non-Newtonian emulsions in smooth tubes of five different diameters (7.15–26.54 mm) was investigated experimentally. The emulsions were of oil-in-water type with dispersed-phase concentration (Φ) ranging from 59.61–72.21% vol. The emulsions exhibited shear-thinning behavior in that the viscosity decreased with the increase in shear rate. The shear-stress (τ) versus shear rate (˙γ) data of emulsions could be described well by the power-law model: τ=K˙γn. The flow behavior index n was less than 1 and it decreased sharply with the increase in Φ whereas the consistency index K increased rapidly with the increase in Φ . For a given emulsion and tube diameter, the entropy generation rate per unit tube length increased linearly with the increase in the generalized Reynolds number ( Re_n ) on a log-log scale. For emulsions with Φ ≤65.15 % vol., the entropy generation rate decreased with the increase in tube diameter. A reverse trend in diameter-dependence was observed for the emulsion with Φ of 72.21% vol. New models are developed for the prediction of entropy generation rate in flow of power-law emulsions in smooth tubes. The experimental data shows good agreement with the proposed models.Entropy2014-10-071610Article10.3390/e16105178517851971099-43002014-10-07doi: 10.3390/e16105178Rajinder Pal<![CDATA[Entropy, Vol. 16, Pages 5159-5177: Progress in the Prediction of Entropy Generation in Turbulent Reacting Flows Using Large Eddy Simulation]]>
http://www.mdpi.com/1099-4300/16/10/5159
An overview is presented of the recent developments in the application of large eddy simulation (LES) for prediction and analysis of local entropy generation in turbulent reacting flows. A challenging issue in such LES is subgrid-scale (SGS) modeling of filtered entropy generation terms. An effective closure strategy, recently developed, is based on the filtered density function (FDF) methodology with inclusion of entropy variations. This methodology, titled entropy FDF (En-FDF), is the main focus of this article. The En-FDF has been introduced as the joint velocity-scalar-turbulent frequency-entropy FDF and the marginal scalar-entropy FDF. Both formulations contain the chemical reaction and its entropy generation effects in closed forms. The former constitutes the most comprehensive form of the En-FDF and provides closure for all of the unclosed terms in LES transport equations. The latter is the marginal En-FDF and accounts for entropy generation effects, as well as scalar-entropy statistics. The En-FDF methodologies are described, and some of their recent predictions of entropy statistics and entropy generation in turbulent shear flows are presented.Entropy2014-09-261610Article10.3390/e16105159515951771099-43002014-09-26doi: 10.3390/e16105159Mehdi SafariFatemeh HadiM. Sheikhi<![CDATA[Entropy, Vol. 16, Pages 5144-5158: Nonlinearities in Elliptic Curve Authentication]]>
http://www.mdpi.com/1099-4300/16/9/5144
In order to construct the border solutions for nonsupersingular elliptic curve equations, some common used models need to be adapted from linear treated cases for use in particular nonlinear cases. There are some approaches that conclude with these solutions. Optimization in this area means finding the majority of points on the elliptic curve and minimizing the time to compute the solution in contrast with the necessary time to compute the inverse solution. We can compute the positive solution of PDE (partial differential equation) like oscillations of f(s)/s around the principal eigenvalue λ1 of -Δ in H 0 1 (Ω).Translating mathematics into cryptographic applications will be relevant in everyday life, where in there are situations in which two parts that communicate need a third part to confirm this process. For example, if two persons want to agree on something they need an impartial person to confirm this agreement, like a notary. This third part does not influence in anyway the communication process. It is just a witness to the agreement. We present a system where the communicating parties do not authenticate one another. Each party authenticates itself to a third part who also sends the keys for the encryption/decryption process. Another advantage of such a system is that if someone (sender) wants to transmit messages to more than one person (receivers), he needs only one authentication, unlike the classic systems where he would need to authenticate himself to each receiver. We propose an authentication method based on zero-knowledge and elliptic curves.Entropy2014-09-25169Article10.3390/e16095144514451581099-43002014-09-25doi: 10.3390/e16095144Ramzi AlsaediNicolae ConstantinescuVicenţiu Rādulescu<![CDATA[Entropy, Vol. 16, Pages 5122-5143: Entropy of Closure Operators and Network Coding Solvability]]>
http://www.mdpi.com/1099-4300/16/9/5122
The entropy of a closure operator has been recently proposed for the study of network coding and secret sharing. In this paper, we study closure operators in relation to their entropy. We first introduce four different kinds of rank functions for a given closure operator, which determine bounds on the entropy of that operator. This yields new axioms for matroids based on their closure operators. We also determine necessary conditions for a large class of closure operators to be solvable. We then define the Shannon entropy of a closure operator and use it to prove that the set of closure entropies is dense. Finally, we justify why we focus on the solvability of closure operators only.Entropy2014-09-25169Article10.3390/e16095122512251431099-43002014-09-25doi: 10.3390/e16095122Maximilien Gadouleau<![CDATA[Entropy, Vol. 16, Pages 5102-5121: Strategic Islands in Economic Games: Isolating Economies From Better Outcomes]]>
http://www.mdpi.com/1099-4300/16/9/5102
Many of the issues we face as a society are made more problematic by the rapidly changing context in which important decisions are made. For example buying a petrol powered car is most advantageous when there are many petrol pumps providing cheap petrol whereas buying an electric car is most advantageous when there are many electrical recharge points or high capacity batteries available. Such collective decision-making is often studied using economic game theory where the focus is on how individuals might reach an agreement regarding the supply and demand for the different energy types. But even if the two parties find a mutually agreeable strategy, as technology and costs change over time, for example through cheaper and more efficient batteries and a more accurate pricing of the total cost of oil consumption, so too do the incentives for the choices buyers and sellers make, the result of which can be the stranding of an industry or even a whole economy on an island of inefficient outcomes. In this article we consider the issue of how changes in the underlying incentives can move us from an optimal economy to a sub-optimal economy while at the same time making it impossible to collectively navigate our way to a better strategy without forcing us to pass through a socially undesirable “tipping point”. We show that different perturbations to underlying incentives results in the creation or destruction of “strategic islands” isolated by disruptive transitions between strategies. The significant result in this work is the illustration that an economy that remains strategically stationary can over time become stranded in a suboptimal outcome from which there is no easy way to put the economy on a path to better outcomes without going through an economic tipping point.Entropy2014-09-24169Article10.3390/e16095102510251211099-43002014-09-24doi: 10.3390/e16095102Michael HarréTerry Bossomaier<![CDATA[Entropy, Vol. 16, Pages 5078-5101: Hierarchical Sensor Placement Using Joint Entropy and the Effect of Modeling Error]]>
http://www.mdpi.com/1099-4300/16/9/5078
Good prediction of the behavior of wind around buildings improves designs for natural ventilation in warm climates. However wind modeling is complex, predictions are often inaccurate due to the large uncertainties in parameter values. The goal of this work is to enhance wind prediction around buildings using measurements through implementing a multiple-model system-identification approach. The success of system-identification approaches depends directly upon the location and number of sensors. Therefore, this research proposes a methodology for optimal sensor configuration based on hierarchical sensor placement involving calculations of prediction-value joint entropy. Computational Fluid Dynamics (CFD) models are generated to create a discrete population of possible wind-flow predictions, which are then used to identify optimal sensor locations. Optimal sensor configurations are revealed using the proposed methodology and considering the effect of systematic and spatially distributed modeling errors, as well as the common information between sensor locations. The methodology is applied to a full-scale case study and optimum configurations are evaluated for their ability to falsify models and improve predictions at locations where no measurements have been taken. It is concluded that a sensor placement strategy using joint entropy is able to lead to predictions of wind characteristics around buildings and capture short-term wind variability more effectively than sequential strategies, which maximize entropy.Entropy2014-09-23169Article10.3390/e16095078507851011099-43002014-09-23doi: 10.3390/e16095078Maria PapadopoulouBenny RaphaelIan SmithChandra Sekhar<![CDATA[Entropy, Vol. 16, Pages 5068-5077: Editorial Comment on the Special Issue of “Information in Dynamical Systems and Complex Systems”]]>
http://www.mdpi.com/1099-4300/16/9/5068
This special issue collects contributions from the participants of the “Information in Dynamical Systems and Complex Systems” workshop, which cover a wide range of important problems and new approaches that lie in the intersection of information theory and dynamical systems. The contributions include theoretical characterization and understanding of the different types of information flow and causality in general stochastic processes, inference and identification of coupling structure and parameters of system dynamics, rigorous coarse-grain modeling of network dynamical systems, and exact statistical testing of fundamental information-theoretic quantities such as the mutual information. The collective efforts reported here in reflect a modern perspective of the intimate connection between dynamical systems and information flow, leading to the promise of better understanding and modeling of natural complex systems and better/optimal design of engineering systems.Entropy2014-09-23169Editorial10.3390/e16095068506850771099-43002014-09-23doi: 10.3390/e16095068Erik BolltJie Sun<![CDATA[Entropy, Vol. 16, Pages 5032-5067: An Entropy-Based Upper Bound Methodology for Robust Predictive Multi-Mode RCPSP Schedules]]>
http://www.mdpi.com/1099-4300/16/9/5032
Projects are an important part of our activities and regardless of their magnitude, scheduling is at the very core of every project. In an ideal world makespan minimization, which is the most commonly sought objective, would give us an advantage. However, every time we execute a project we have to deal with uncertainty; part of it coming from known sources and part remaining unknown until it affects us. For this reason, it is much more practical to focus on making our schedules robust, capable of handling uncertainty, and even to determine a range in which the project could be completed. In this paper we focus on an approach to determine such a range for the Multi-mode Resource Constrained Project Scheduling Problem (MRCPSP), a widely researched, NP-complete problem, but without adding any subjective considerations to its estimation. We do this by using a concept well known in the domain of thermodynamics, entropy and a three-stage approach. First we use Artificial Bee Colony (ABC)—an effective and powerful meta-heuristic—to determine a schedule with minimized makespan which serves as a lower bound. The second stage defines buffer times and creates an upper bound makespan using an entropy function, with the advantage over other methods that it only considers elements which are inherent to the schedule itself and does not introduce any subjectivity to the buffer time generation. In the last stage, we use the ABC algorithm with an objective function that seeks to maximize robustness while staying within the makespan boundaries defined previously and in some cases even below the lower boundary. We evaluate our approach with two different benchmarks sets: when using the PSPLIB for the MRCPSP benchmark set, the computational results indicate that it is possible to generate robust schedules which generally result in an increase of less than 10% of the best known solutions while increasing the robustness in at least 20% for practically every benchmark set. And, in an attempt to solve larger instances with 50 or 100 activities, we also used the MRCPSP/max benchmark sets, where the increase of the makespan is approximately 35% with respect to the best known solutions at the same time as with a 20% increase in robustness.Entropy2014-09-22169Article10.3390/e16095032503250671099-43002014-09-22doi: 10.3390/e16095032Angela ChenYun-Chia LiangJose Padilla<![CDATA[Entropy, Vol. 16, Pages 5020-5031: Adaptive Leader-Following Consensus of Multi-Agent Systems with Unknown Nonlinear Dynamics]]>
http://www.mdpi.com/1099-4300/16/9/5020
This paper deals with the leader-following consensus of multi-agent systems with matched nonlinear dynamics. Compared with previous works, the major difficulty here is caused by the simultaneous existence of nonidentical agent dynamics and unknown system parameters, which are more practical in real-world applications. To tackle this difficulty, a distributed adaptive control law for each follower is proposed based on algebraic graph theory and algebraic Riccati equation. By a Lyapunov function method, we show that the designed control law guarantees that each follower asymptotically converges to the leader under connected communication graphs. A simulation example demonstrates the effectiveness of the proposed scheme.Entropy2014-09-22169Article10.3390/e16095020502050311099-43002014-09-22doi: 10.3390/e16095020Junwei WangKairui ChenQinghua Ma<![CDATA[Entropy, Vol. 16, Pages 4992-5019: Ab Initio and Monte Carlo Approaches For the Magnetocaloric Effect in Co- and In-Doped Ni-Mn-Ga Heusler Alloys]]>
http://www.mdpi.com/1099-4300/16/9/4992
The complex magnetic and structural properties of Co-doped Ni-Mn-Ga Heusler alloys have been investigated by using a combination of first-principles calculations and classical Monte Carlo simulations. We have restricted the investigations to systems with 0, 5 and 9 at% Co. Ab initio calculations show the presence of the ferrimagnetic order of austenite and martensite depending on the composition, where the excess Mn atoms on Ga sites show reversed spin configurations. Stable ferrimagnetic martensite is found for systems with 0 (5) at% Co and a c=a ratio of 1.31 (1.28), respectively, leading to a strong competition of ferro- and antiferro-magnetic exchange interactions between nearest neighbor Mn atoms. The Monte Carlo simulations with ab initio exchange coupling constants as input parameters allow one to discuss the behavior at finite temperatures and to determine magnetic transition temperatures. The Curie temperature of austenite is found to increase with Co, while the Curie temperature of martensite decreases with increasing Co content. This behavior can be attributed to the stronger Co-Mn, Mn-Mn and Mn-Ni exchange coupling constants in austenite compared to the corresponding ones in martensite. The crossover from a direct to inverse magnetocaloric effect in Ni-Mn-Ga due to the substitution of Ni by Co leads to the appearance of a “paramagnetic gap” in the martensitic phase. Doping with In increases the magnetic jump at the martensitic transition temperature. The simulated magnetic and magnetocaloric properties of Co- and In-doped Ni-Mn-Ga alloys are in good qualitative agreement with the available experimental data.Entropy2014-09-19169Article10.3390/e16094992499250191099-43002014-09-19doi: 10.3390/e16094992Vladimir SokolovskiyAnna GrünebohmVasiliy BuchelnikovPeter Entel<![CDATA[Entropy, Vol. 16, Pages 4974-4991: Simultaneous State and Parameter Estimation Using Maximum Relative Entropy with Nonhomogenous Differential Equation Constraints]]>
http://www.mdpi.com/1099-4300/16/9/4974
In this paper, we continue our efforts to show how maximum relative entropy (MrE) can be used as a universal updating algorithm. Here, our purpose is to tackle a joint state and parameter estimation problem where our system is nonlinear and in a non-equilibrium state, i.e., perturbed by varying external forces. Traditional parameter estimation can be performed by using filters, such as the extended Kalman filter (EKF). However, as shown with a toy example of a system with first order non-homogeneous ordinary differential equations, assumptions made by the EKF algorithm (such as the Markov assumption) may not be valid. The problem can be solved with exponential smoothing, e.g., exponentially weighted moving average (EWMA). Although this has been shown to produce acceptable filtering results in real exponential systems, it still cannot simultaneously estimate both the state and its parameters and has its own assumptions that are not always valid, for example when jump discontinuities exist. We show that by applying MrE as a filter, we can not only develop the closed form solutions, but we can also infer the parameters of the differential equation simultaneously with the means. This is useful in real, physical systems, where we want to not only filter the noise from our measurements, but we also want to simultaneously infer the parameters of the dynamics of a nonlinear and non-equilibrium system. Although there were many assumptions made throughout the paper to illustrate that EKF and exponential smoothing are special cases ofMrE, we are not “constrained”, by these assumptions. In other words, MrE is completely general and can be used in broader ways.Entropy2014-09-17169Article10.3390/e16094974497449911099-43002014-09-17doi: 10.3390/e16094974Adom GiffinRenaldas Urniezius<![CDATA[Entropy, Vol. 16, Pages 4960-4973: The Character of Entropy Production in Rayleigh–Bénard Convection]]>
http://www.mdpi.com/1099-4300/16/9/4960
In this study; the Rayleigh–Bénard convection model was established; and a great number of Bénard cells with different numbered vortexes were acquired by numerical simulation. Additionally; the Bénard cell with two vortexes; which appeared in the steady Bénard fluid with a different Rayleigh number (abbreviated Ra); was found to display the primary characteristics of the system’s entropy production. It was found that two entropy productions; which are calculated using either linear theory or classical thermodynamic theory; are all basically consistent when the system can form a steady Bénard flow in the proper range of the Rayleigh number’s parameters. Furthermore; in a steady Bénard flow; the entropy productions of the system increase alongside the Ra parameters. It was also found that the difference between the two entropy productions is the driving force to drive the system to a steady state. Otherwise; through the distribution of the local entropy production of the Bénard cell; two vortexes are clearly located where there is minimum local entropy production and in the borders around the cell’s areas of larger local entropy production.Entropy2014-09-17169Article10.3390/e16094960496049731099-43002014-09-17doi: 10.3390/e16094960Chenxia JiaChengjun JingJian Liu<![CDATA[Entropy, Vol. 16, Pages 4937-4959: Distributed Control of Heat Conduction in Thermal Inductive Materials with 2D Geometrical Isomorphism]]>
http://www.mdpi.com/1099-4300/16/9/4937
In a previous study we provided analytical and experimental evidence that some materials are able to store entropy-flow, of which the heat-conduction behaves as standing waves in a bounded region small enough in practice. In this paper we continue to develop distributed control of heat conduction in these thermal-inductive materials. The control objective is to achieve subtle temperature distribution in space and simultaneously to suppress its transient overshoots in time. This technology concerns safe and accurate heating/cooling treatments in medical operations, polymer processing, and other prevailing modern day practices. Serving for distributed feedback, spatiotemporal H ∞ /μ control is developed by expansion of the conventional 1D-H ∞ /μ control to a 2D version. Therein 2D geometrical isomorphism is constructed with the Laplace-Galerkin transform, which extends the small-gain theorem into the mode-frequency domain, wherein 2D transfer-function controllers are synthesized with graphical methods. Finally, 2D digital-signal processing is programmed to implement 2D transfer-function controllers, possibly of spatial fraction-orders, into DSP-engine embedded microcontrollers.Entropy2014-09-15169Article10.3390/e16094937493749591099-43002014-09-15doi: 10.3390/e16094937Chia-Yu ChouBoe-Shong HongPei-Ju ChiangWen-Teng WangLiang-Kuang ChenChia-Yen Lee<![CDATA[Entropy, Vol. 16, Pages 4923-4936: Effect of Conformational Entropy on the Nanomechanics of Microcantilever-Based Single-Stranded DNA Sensors]]>
http://www.mdpi.com/1099-4300/16/9/4923
An entropy-controlled bending mechanism is presented to study the nanomechanics of microcantilever-based single-stranded DNA (ssDNA) sensors. First; the conformational free energy of the ssDNA layer is given with an improved scaling theory of thermal blobs considering the curvature effect; and the mechanical energy of the non-biological layer is described by Zhang’s two-variable method for laminated beams. Then; an analytical model for static deflections of ssDNA microcantilevers is formulated by the principle of minimum energy. The comparisons of deflections predicted by the proposed model; Utz–Begley’s model and Hagan’s model are also examined. Numerical results show that the conformational entropy effect on microcantilever deflections cannot be ignored; especially at the conditions of high packing density or long chain systems; and the variation of deflection predicted by the proposed analytical model not only accords with that observed in the related experiments qualitatively; but also appears quantitatively closer to the experimental values than that by the preexisting models. In order to improve the sensitivity of static-mode biosensors; it should be as small as possible to reduce the substrate stiffness.Entropy2014-09-15169Article10.3390/e16094923492349361099-43002014-09-15doi: 10.3390/e16094923Zou-Qing TanNeng-Hui Zhang<![CDATA[Entropy, Vol. 16, Pages 4911-4922: Existence of Entropy Solutions for Nonsymmetric Fractional Systems]]>
http://www.mdpi.com/1099-4300/16/9/4911
The present work focuses on entropy solutions for the fractional Cauchy problem of nonsymmetric systems. We impose sufficient conditions on the parameters to obtain bounded solutions of L∞ . The solutions attained are unique and exclusive. Performance is established by utilizing the maximum principle for certain generalized time and space-fractional diffusion equations. The fractional differential operator is inspected based on the interpretation of the Riemann–Liouville differential operator. Fractional entropy inequalities are imposed.Entropy2014-09-12169Article10.3390/e16094911491149221099-43002014-09-12doi: 10.3390/e16094911Rabha IbrahimHamid Jalab<![CDATA[Entropy, Vol. 16, Pages 4892-4910: On Shannon’s Formula and Hartley’s Rule: Beyond the Mathematical Coincidence]]>
http://www.mdpi.com/1099-4300/16/9/4892
In the information theory community, the following “historical” statements are generally well accepted: (1) Hartley did put forth his rule twenty years before Shannon; (2) Shannon’s formula as a fundamental tradeoff between transmission rate, bandwidth, and signal-to-noise ratio came out unexpected in 1948; (3) Hartley’s rule is inexact while Shannon’s formula is characteristic of the additive white Gaussian noise channel; (4) Hartley’s rule is an imprecise relation that is not an appropriate formula for the capacity of a communication channel. We show that all these four statements are somewhat wrong. In fact, a careful calculation shows that “Hartley’s rule” in fact coincides with Shannon’s formula. We explain this mathematical coincidence by deriving the necessary and sufficient conditions on an additive noise channel such that its capacity is given by Shannon’s formula and construct a sequence of such channels that makes the link between the uniform (Hartley) and Gaussian (Shannon) channels.Entropy2014-09-10169Article10.3390/e16094892489249101099-43002014-09-10doi: 10.3390/e16094892Olivier RioulJosé Magossi<![CDATA[Entropy, Vol. 16, Pages 4874-4891: Illuminating Water and Life]]>
http://www.mdpi.com/1099-4300/16/9/4874
This paper reviews the quantum electrodynamics theory of water put forward by Del Giudice and colleagues and how it may provide a useful foundation for a new science of water for life. The interaction of light with liquid water generates quantum coherent domains in which the water molecules oscillate between the ground state and an excited state close to the ionizing potential of water. This produces a plasma of almost free electrons favouring redox reactions, the basis of energy metabolism in living organisms. Coherent domains stabilized by surfaces, such as membranes and macromolecules, provide the excited interfacial water that enables photosynthesis to take place, on which most of life on Earth depends. Excited water is the source of superconducting protons for rapid intercommunication within the body that may be associated with the acupuncture meridians. Coherent domains can also trap electromagnetic frequencies from the environment to orchestrate and activate specific biochemical reactions through resonance, a mechanism for the most precise regulation of gene function.Entropy2014-09-10169Review10.3390/e16094874487448911099-43002014-09-10doi: 10.3390/e16094874Mae-Wan Ho<![CDATA[Entropy, Vol. 16, Pages 4855-4873: Entropy Evaluation Based on Value Validity]]>
http://www.mdpi.com/1099-4300/16/9/4855
Besides its importance in statistical physics and information theory, the Boltzmann-Shannon entropy S has become one of the most widely used and misused summary measures of various attributes (characteristics) in diverse fields of study. It has also been the subject of extensive and perhaps excessive generalizations. This paper introduces the concept and criteria for value validity as a means of determining if an entropy takes on values that reasonably reflect the attribute being measured and that permit different types of comparisons to be made for different probability distributions. While neither S nor its relative entropy equivalent S* meet the value-validity conditions, certain power functions of S and S* do to a considerable extent. No parametric generalization offers any advantage over S in this regard. A measure based on Euclidean distances between probability distributions is introduced as a potential entropy that does comply fully with the value-validity requirements and its statistical inference procedure is discussed.Entropy2014-09-05169Article10.3390/e16094855485548731099-43002014-09-05doi: 10.3390/e16094855Tarald Kvålseth<![CDATA[Entropy, Vol. 16, Pages 4839-4854: Low-Pass Filtering Approach via Empirical Mode Decomposition Improves Short-Scale Entropy-Based Complexity Estimation of QT Interval Variability in Long QT Syndrome Type 1 Patients]]>
http://www.mdpi.com/1099-4300/16/9/4839
Entropy-based complexity of cardiovascular variability at short time scales is largely dependent on the noise and/or action of neural circuits operating at high frequencies. This study proposes a technique for canceling fast variations from cardiovascular variability, thus limiting the effect of these overwhelming influences on entropy-based complexity. The low-pass filtering approach is based on the computation of the fastest intrinsic mode function via empirical mode decomposition (EMD) and its subtraction from the original variability. Sample entropy was exploited to estimate complexity. The procedure was applied to heart period (HP) and QT (interval from Q-wave onset to T-wave end) variability derived from 24-hour Holter recordings in 14 non-mutation carriers (NMCs) and 34 mutation carriers (MCs) subdivided into 11 asymptomatic MCs (AMCs) and 23 symptomatic MCs (SMCs). All individuals belonged to the same family developing long QT syndrome type 1 (LQT1) via KCNQ1-A341V mutation. We found that complexity indexes computed over EMD-filtered QT variability differentiated AMCs from NMCs and detected the effect of beta-blocker therapy, while complexity indexes calculated over EMD-filtered HP variability separated AMCs from SMCs. The EMD-based filtering method enhanced features of the cardiovascular control that otherwise would have remained hidden by the dominant presence of noise and/or fast physiological variations, thus improving classification in LQT1.Entropy2014-09-05169Article10.3390/e16094839483948541099-43002014-09-05doi: 10.3390/e16094839Vlasta BariAndrea MarchiBeatrice De MariaGiulia GirardengoAlfred GeorgePaul BrinkSergio CeruttiLia CrottiPeter SchwartzAlberto Porta<![CDATA[Entropy, Vol. 16, Pages 4818-4838: A Trustworthiness Evaluation Method for Software Architectures Based on the Principle of Maximum Entropy (POME) and the Grey Decision-Making Method (GDMM)]]>
http://www.mdpi.com/1099-4300/16/9/4818
As the early design decision-making structure, a software architecture plays a key role in the final software product quality and the whole project. In the software design and development process, an effective evaluation of the trustworthiness of a software architecture can help making scientific and reasonable decisions on the architecture, which are necessary for the construction of highly trustworthy software. In consideration of lacking the trustworthiness evaluation and measurement studies for software architecture, this paper provides one trustworthy attribute model of software architecture. Based on this model, the paper proposes to use the Principle of Maximum Entropy (POME) and Grey Decision-making Method (GDMM) as the trustworthiness evaluation method of a software architecture and proves the scientificity and rationality of this method, as well as verifies the feasibility through case analysis.Entropy2014-09-03169Article10.3390/e16094818481848381099-43002014-09-03doi: 10.3390/e16094818Rong Jiang<![CDATA[Entropy, Vol. 16, Pages 4801-4817: Pneumatic Performance Study of a High Pressure Ejection Device Based on Real Specific Energy and Specific Enthalpy]]>
http://www.mdpi.com/1099-4300/16/9/4801
In high-pressure dynamic thermodynamic processes, the pressure is much higher than the air critical pressure, and the temperature can deviate significantly from the Boyle temperature. In such situations, the thermo-physical properties and pneumatic performance can’t be described accurately by the ideal gas law. This paper proposes an approach to evaluate the pneumatic performance of a high-pressure air catapult launch system, in which esidual functions are used to compensate the thermal physical property uncertainties of caused by real gas effects. Compared with the Nelson-Obert generalized compressibility charts, the precision of the improved virial equation of state is better than Soave-Redlich-Kwong (S-R-K) and Peng-Robinson (P-R) equations for high pressure air. In this paper, the improved virial equation of state is further used to establish a compressibility factor database which is applied to evaluate real gas effects. The specific residual thermodynamic energy and specific residual enthalpy of the high-pressure air are also derived using the modified corresponding state equation and improved virial equation of state which are truncated to the third virial coefficient. The pneumatic equations are established on the basis of the derived residual functions. The comparison of the numerical results shows that the real gas effects are strong, and the pneumatic performance analysis indicates that the real dynamic thermodynamic process is obviously different from the ideal one.Entropy2014-09-03169Article10.3390/e16094801480148171099-43002014-09-03doi: 10.3390/e16094801Jie RenFengbo YangDawei MaGuigao LeJianlin Zhong<![CDATA[Entropy, Vol. 16, Pages 4788-4800: Application of Entropy-Based Attribute Reduction and an Artificial Neural Network in Medicine: A Case Study of Estimating Medical Care Costs Associated with Myocardial Infarction]]>
http://www.mdpi.com/1099-4300/16/9/4788
In medicine, artificial neural networks (ANN) have been extensively applied in many fields to model the nonlinear relationship of multivariate data. Due to the difficulty of selecting input variables, attribute reduction techniques were widely used to reduce data to get a smaller set of attributes. However, to compute reductions from heterogeneous data, a discretizing algorithm was often introduced in dimensionality reduction methods, which may cause information loss. In this study, we developed an integrated method for estimating the medical care costs, obtained from 798 cases, associated with myocardial infarction disease. The subset of attributes was selected as the input variables of ANN by using an entropy-based information measure, fuzzy information entropy, which can deal with both categorical attributes and numerical attributes without discretization. Then, we applied a correction for the Akaike information criterion (ΑICc) to compare the networks. The results revealed that fuzzy information entropy was capable of selecting input variables from heterogeneous data for ANN, and the proposed procedure of this study provided a reasonable estimation of medical care costs, which can be adopted in other fields of medical science.Entropy2014-08-29169Article10.3390/e16094788478848001099-43002014-08-29doi: 10.3390/e16094788Qingyun DuKe NieZhensheng Wang<![CDATA[Entropy, Vol. 16, Pages 4769-4787: Study on Mixed Working Fluids with Different Compositions in Organic Rankine Cycle (ORC) Systems for Vehicle Diesel Engines]]>
http://www.mdpi.com/1099-4300/16/9/4769
One way to increase the thermal efficiency of vehicle diesel engines is to recover waste heat by using an organic Rankine cycle (ORC) system. Tests were conducted to study the running performances of diesel engines in the whole operating range. The law of variation of the exhaust energy rate under various engine operating conditions was also analyzed. A diesel engine-ORC combined system was designed, and relevant evaluation indexes proposed. The variation of the running performances of the combined system under various engine operating conditions was investigated. R245fa and R152a were selected as the components of the mixed working fluid. Thereafter, six kinds of mixed working fluids with different compositions were presented. The effects of mixed working fluids with different compositions on the running performances of the combined system were revealed. Results show that the running performances of the combined system can be improved effectively when mass fraction R152a in the mixed working fluid is high and the engine operates with high power. For the mixed working fluid M1 (R245fa/R152a, 0.1/0.9, by mass fraction), the net power output of the combined system reaches the maximum of 34.61 kW. Output energy density of working fluid (OEDWF), waste heat recovery efficiency (WHRE), and engine thermal efficiency increasing ratio (ETEIR) all reach their maximum values at 42.7 kJ/kg, 10.90%, and 11.29%, respectively.Entropy2014-08-27169Article10.3390/e16094769476947871099-43002014-08-27doi: 10.3390/e16094769Kai YangHongguang ZhangEnhua WangSongsong SongChen BeiYing ChangHongjin WangBaofeng Yao<![CDATA[Entropy, Vol. 16, Pages 4749-4768: Multicomponent and High Entropy Alloys]]>
http://www.mdpi.com/1099-4300/16/9/4749
This paper describes some underlying principles of multicomponent and high entropy alloys, and gives some examples of these materials. Different types of multicomponent alloy and different methods of accessing multicomponent phase space are discussed. The alloys were manufactured by conventional and high speed solidification techniques, and their macroscopic, microscopic and nanoscale structures were studied by optical, X-ray and electron microscope methods. They exhibit a variety of amorphous, quasicrystalline, dendritic and eutectic structures.Entropy2014-08-26169Review10.3390/e16094749474947681099-43002014-08-26doi: 10.3390/e16094749Brian Cantor<![CDATA[Entropy, Vol. 16, Pages 4713-4748: Information Anatomy of Stochastic Equilibria]]>
http://www.mdpi.com/1099-4300/16/9/4713
A stochastic nonlinear dynamical system generates information, as measured by its entropy rate. Some—the ephemeral information—is dissipated and some—the bound information—is actively stored and so affects future behavior. We derive analytic expressions for the ephemeral and bound information in the limit of infinitesimal time discretization for two classical systems that exhibit dynamical equilibria: first-order Langevin equations (i) where the drift is the gradient of an analytic potential function and the diffusion matrix is invertible and (ii) with a linear drift term (Ornstein–Uhlenbeck), but a noninvertible diffusion matrix. In both cases, the bound information is sensitive to the drift and diffusion, while the ephemeral information is sensitive only to the diffusion matrix and not to the drift. Notably, this information anatomy changes discontinuously as any of the diffusion coefficients vanishes, indicating that it is very sensitive to the noise structure. We then calculate the information anatomy of the stochastic cusp catastrophe and of particles diffusing in a heat bath in the overdamped limit, both examples of stochastic gradient descent on a potential landscape. Finally, we use our methods to calculate and compare approximations for the time-local predictive information for adaptive agents.Entropy2014-08-25169Article10.3390/e16094713471347481099-43002014-08-25doi: 10.3390/e16094713Sarah MarzenJames Crutchfield<![CDATA[Entropy, Vol. 16, Pages 4693-4712: Some New Results on the Multiple-AccessWiretap Channel]]>
http://www.mdpi.com/1099-4300/16/8/4693
In this paper, some new results on the multiple-access wiretap channel (MAC-WT) are provided. Specifically, first, we investigate the degraded MAC-WT, where two users transmit their corresponding confidential messages (no common message) to a legitimate receiver via a multiple-access channel (MAC), while a wiretapper wishes to obtain the messages via a physically degraded wiretap channel. The secrecy capacity region of this model is determined for both the discrete memoryless and Gaussian cases. For the Gaussian case, we find that this secrecy capacity region is exactly the same as the achievable secrecy rate region provided by Tekin and Yener, i.e., Tekin–Yener’s achievable region is exactly the secrecy capacity region of the degraded Gaussian MAC-WT. Second, we study a special Gaussian MAC-WT, and find the power control for two kinds of optimal points (max-min point and single user point) on the secrecy rate region of this special Gaussian model.Entropy2014-08-21168Article10.3390/e16084693469347121099-43002014-08-21doi: 10.3390/e16084693Bin DaiZheng Ma<![CDATA[Entropy, Vol. 16, Pages 4677-4692: Entropy-Complexity Characterization of Brain Development in Chickens]]>
http://www.mdpi.com/1099-4300/16/8/4677
Electroencephalography (EEG) reflects the electrical activity of the brain, which can be considered chaotic and ruled by a nonlinear dynamics. Chickens exhibit a protracted period of maturation, and this temporal separation of the synapse formation and maturation phases is analogous to human neural development, though the changes in chickens occur in weeks compared to years in humans. The development of synaptic networks in the chicken brain can be regarded as occurring in two broadly defined phases. We specifically describe the chicken brain development phases in the causality entropy-complexity plane H × C, showing that the complexity of the electrical activity can be characterized by estimating the intrinsic correlational structure of the EEG signal. This allows us to identify the dynamics of the developing chicken brain within the zone of a chaotic dissipative behavior in the plane H × C.Entropy2014-08-21168Article10.3390/e16084677467746921099-43002014-08-21doi: 10.3390/e16084677Fernando MontaniOsvaldo Rosso<![CDATA[Entropy, Vol. 16, Pages 4662-4676: Information-Theoretic Bounded Rationality and ε-Optimality]]>
http://www.mdpi.com/1099-4300/16/8/4662
Bounded rationality concerns the study of decision makers with limited information processing resources. Previously, the free energy difference functional has been suggested to model bounded rational decision making, as it provides a natural trade-off between an energy or utility function that is to be optimized and information processing costs that are measured by entropic search costs. The main question of this article is how the information-theoretic free energy model relates to simple ε-optimality models of bounded rational decision making, where the decision maker is satisfied with any action in an ε-neighborhood of the optimal utility. We find that the stochastic policies that optimize the free energy trade-off comply with the notion of ε-optimality. Moreover, this optimality criterion even holds when the environment is adversarial. We conclude that the study of bounded rationality based on ε-optimality criteria that abstract away from the particulars of the information processing constraints is compatible with the information-theoretic free energy model of bounded rationality.Entropy2014-08-21168Article10.3390/e16084662466246761099-43002014-08-21doi: 10.3390/e16084662Daniel BraunPedro Ortega<![CDATA[Entropy, Vol. 16, Pages 4648-4661: Entropy Production in Pipeline Flow of Dispersions of Water in Oil]]>
http://www.mdpi.com/1099-4300/16/8/4648
Entropy production in pipeline adiabatic flow of water-in-oil emulsions is investigated experimentally in three different diameter pipes. The dispersed-phase (water droplets) concentration of emulsion is varied from 0 to 41% vol. The entropy production rates in emulsion flow are compared with the values expected in single-phase flow of Newtonian fluids with the same properties (viscosity and density). While in the laminar regime the entropy production rates in emulsion flow can be described adequately by the single-phase Newtonian equations, a significant deviation from single-phase flow behavior is observed in the turbulent regime. In the turbulent regime, the entropy production rates in emulsion flow are found to be substantially smaller than those expected on the basis of single-phase equations. For example, the entropy production rate in water-in-oil emulsion flow at a dispersed-phase volume fraction of 0.41 is only 38.4% of that observed in flow of a single-phase Newtonian fluid with the same viscosity and density, when comparison is made at a Reynolds number of 4000. Thus emulsion flow in pipelines is more efficient thermodynamically than single-phase Newtonian flow.Entropy2014-08-19168Article10.3390/e16084648464846611099-43002014-08-19doi: 10.3390/e16084648Rajinder Pal<![CDATA[Entropy, Vol. 16, Pages 4626-4647: Spatiotemporal Scaling Effect on Rainfall Network Design Using Entropy]]>
http://www.mdpi.com/1099-4300/16/8/4626
Because of high variation in mountainous areas, rainfall data at different spatiotemporal scales may yield potential uncertainty for network design. However, few studies focus on the scaling effect on both the spatial and the temporal scale. By calculating the maximum joint entropy of hourly typhoon events, monthly, six dry and wet months and annual rainfall between 1992 and 2012 for 1-, 3-, and 5-km grids, the relocated candidate rain gauges in the National Taiwan University Experimental Forest of Central Taiwan are prioritized. The results show: (1) the network exhibits different locations for first prioritized candidate rain gauges for different spatiotemporal scales; (2) the effect of spatial scales is insignificant compared to temporal scales; and (3) a smaller number and a lower percentage of required stations (PRS) reach stable joint entropy for a long duration at finer spatial scale. Prioritized candidate rain gauges provide key reference points for adjusting the network to capture more accurate information and minimize redundancy.Entropy2014-08-18168Article10.3390/e16084626462646471099-43002014-08-18doi: 10.3390/e16084626Chiang WeiHui-Chung YehYen-Chang Chen<![CDATA[Entropy, Vol. 16, Pages 4612-4625: Exergetic and Thermoeconomic Analyses of Solar Air Heating Processes Using a Parabolic Trough Collector]]>
http://www.mdpi.com/1099-4300/16/8/4612
This paper presents a theoretical and practical analysis of the application of the thermoeconomic method. A furnace for heating air is evaluated using the methodology. The furnace works with solar energy, received from a parabolic trough collector and with electricity supplied by an electric power utility. The methodology evaluates the process by the first and second law of thermodynamics as the first step then the cost analysis is applied for getting the thermoeconomic cost. For this study, the climatic conditions of the city of Queretaro (Mexico) are considered. Two periods were taken into account: from July 2006 to June 2007 and on 6 January 2011. The prototype, located at CICATA-IPN, Qro, was analyzed in two different scenarios i.e., with 100% of electricity and 100% of solar energy. The results showed that thermoeconomic costs for the heating process with electricity, inside the chamber, are less than those using solar heating. This may be ascribed to the high cost of the materials, fittings, and manufacturing of the solar equipment. Also, the influence of the mass flow, aperture area, length and diameter of the receiver of the solar prototype is a parameter for increasing the efficiency of the prototype in addition to the price of manufacturing. The optimum design parameters are: length is 3 to 5 m, mass flow rate is 0.03 kg/s, diameter of the receiver is around 10 to 30 mm and aperture area is 3 m2.Entropy2014-08-18168Article10.3390/e16084612461246251099-43002014-08-18doi: 10.3390/e16084612Miguel Hernández-RománAlejandro Manzano-RamírezJorge Pineda-PiñónJorge Ortega-Moody<![CDATA[Entropy, Vol. 16, Pages 4603-4611: A Maximum Entropy Approach for Predicting Epileptic Tonic-Clonic Seizure]]>
http://www.mdpi.com/1099-4300/16/8/4603
The development of methods for time series analysis and prediction has always been and continues to be an active area of research. In this work, we develop a technique for modelling chaotic time series in parametric fashion. In the case of tonic-clonic epileptic electroencephalographic (EEG) analysis, we show that appropriate information theory tools provide valuable insights into the dynamics of neural activity. Our purpose is to demonstrate the feasibility of the maximum entropy principle to anticipate tonic-clonic seizure in patients with epilepsy.Entropy2014-08-18168Article10.3390/e16084603460346111099-43002014-08-18doi: 10.3390/e16084603Maria MartínAngelo PlastinoVictoria Vampa<![CDATA[Entropy, Vol. 16, Pages 4583-4602: Information Entropy-Based Metrics for Measuring Emergences in Artificial Societies]]>
http://www.mdpi.com/1099-4300/16/8/4583
Emergence is a common phenomenon, and it is also a general and important concept in complex dynamic systems like artificial societies. Usually, artificial societies are used for assisting in resolving several complex social issues (e.g., emergency management, intelligent transportation system) with the aid of computer science. The levels of an emergence may have an effect on decisions making, and the occurrence and degree of an emergence are generally perceived by human observers. However, due to the ambiguity and inaccuracy of human observers, to propose a quantitative method to measure emergences in artificial societies is a meaningful and challenging task. This article mainly concentrates upon three kinds of emergences in artificial societies, including emergence of attribution, emergence of behavior, and emergence of structure. Based on information entropy, three metrics have been proposed to measure emergences in a quantitative way. Meanwhile, the correctness of these metrics has been verified through three case studies (the spread of an infectious influenza, a dynamic microblog network, and a flock of birds) with several experimental simulations on the Netlogo platform. These experimental results confirm that these metrics increase with the rising degree of emergences. In addition, this article also has discussed the limitations and extended applications of these metrics.Entropy2014-08-15168Article10.3390/e16084583458346021099-43002014-08-15doi: 10.3390/e16084583Mingsheng TangXinjun Mao<![CDATA[Entropy, Vol. 16, Pages 4566-4582: Chaos Synchronization Error Technique-Based Defect Pattern Recognition for GIS through Partial Discharge Signal Analysis]]>
http://www.mdpi.com/1099-4300/16/8/4566
The work is aimed at using the chaos synchronization error dynamics (CSED) technique for defect pattern recognition in gas insulated switchgear (GIS). The radiated electromagnetic waves generated due to internal defects were measured by the self-made ultrahigh frequency (UHF) micro-strip antenna, so as to determine whether partial discharge will occur. Firstly, a data pretreatment is performed on the measured raw data for the purpose of computational burden reduction. A characteristic matrix is then constructed according to dynamic error trajectories in a chaos synchronization system, subsequent to which characteristics are extracted. A comparison with the existing Hilbert-Huang Transform (HHT) method reveals that the two characteristics extracted from the CSED results presented herein using the fractal theory were recognized at a higher rate pattern.Entropy2014-08-13168Article10.3390/e16084566456645821099-43002014-08-13doi: 10.3390/e16084566Hung-Cheng ChenHer-Terng YauPo-Yan Chen<![CDATA[Entropy, Vol. 16, Pages 4521-4565: Koszul Information Geometry and Souriau Geometric Temperature/Capacity of Lie Group Thermodynamics]]>
http://www.mdpi.com/1099-4300/16/8/4521
The François Massieu 1869 idea to derive some mechanical and thermal properties of physical systems from “Characteristic Functions”, was developed by Gibbs and Duhem in thermodynamics with the concept of potentials, and introduced by Poincaré in probability. This paper deals with generalization of this Characteristic Function concept by Jean-Louis Koszul in Mathematics and by Jean-Marie Souriau in Statistical Physics. The Koszul-Vinberg Characteristic Function (KVCF) on convex cones will be presented as cornerstone of “Information Geometry” theory, defining Koszul Entropy as Legendre transform of minus the logarithm of KVCF, and Fisher Information Metrics as hessian of these dual functions, invariant by their automorphisms. In parallel, Souriau has extended the Characteristic Function in Statistical Physics looking for other kinds of invariances through co-adjoint action of a group on its momentum space, defining physical observables like energy, heat and momentum as pure geometrical objects. In covariant Souriau model, Gibbs equilibriums states are indexed by a geometric parameter, the Geometric (Planck) Temperature, with values in the Lie algebra of the dynamical Galileo/Poincaré groups, interpreted as a space-time vector, giving to the metric tensor a null Lie derivative. Fisher Information metric appears as the opposite of the derivative of Mean “Moment map” by geometric temperature, equivalent to a Geometric Capacity or Specific Heat. We will synthetize the analogies between both Koszul and Souriau models, and will reduce their definitions to the exclusive Cartan “Inner Product”. Interpreting Legendre transform as Fourier transform in (Min,+) algebra, we conclude with a definition of Entropy given by a relation mixing Fourier/Laplace transforms: Entropy = (minus) Fourier(Min,+) o Log o Laplace(+,X).Entropy2014-08-12168Article10.3390/e16084521452145651099-43002014-08-12doi: 10.3390/e16084521Frédéric Barbaresco<![CDATA[Entropy, Vol. 16, Pages 4497-4520: Fractal Structure and Entropy Production within the Central Nervous System]]>
http://www.mdpi.com/1099-4300/16/8/4497
Our goal is to explore the relationship between two traditionally unrelated concepts, fractal structure and entropy production, evaluating both within the central nervous system (CNS). Fractals are temporal or spatial structures with self-similarity across scales of measurement; whereas entropy production represents the necessary exportation of entropy to our environment that comes with metabolism and life. Fractals may be measured by their fractal dimension; and human entropy production may be estimated by oxygen and glucose metabolism. In this paper, we observe fractal structures ubiquitously present in the CNS, and explore a hypothetical and unexplored link between fractal structure and entropy production, as measured by oxygen and glucose metabolism. Rapid increase in both fractal structures and metabolism occur with childhood and adolescent growth, followed by slow decrease during aging. Concomitant increases and decreases in fractal structure and metabolism occur with cancer vs. Alzheimer’s and multiple sclerosis, respectively. In addition to fractals being related to entropy production, we hypothesize that the emergence of fractal structures spontaneously occurs because a fractal is more efficient at dissipating energy gradients, thus maximizing entropy production. Experimental evaluation and further understanding of limitations and necessary conditions are indicated to address broad scientific and clinical implications of this work.Entropy2014-08-12168Article10.3390/e16084497449745201099-43002014-08-12doi: 10.3390/e16084497Andrew SeelyKimberley NewmanChristophe Herry<![CDATA[Entropy, Vol. 16, Pages 4489-4496: Complexity and the Emergence of Physical Properties]]>
http://www.mdpi.com/1099-4300/16/8/4489
Using the effective complexity measure, proposed by M. Gell-Mann and S. Lloyd, we give a quantitative definition of an emergent property. We use several previous results and properties of this particular information measure closely related to the random features of the entity and its regularities.Entropy2014-08-11168Article10.3390/e16084489448944961099-43002014-08-11doi: 10.3390/e16084489Miguel Fuentes<![CDATA[Entropy, Vol. 16, Pages 4483-4488: Is Gravity Entropic Force?]]>
http://www.mdpi.com/1099-4300/16/8/4483
If we assume that the source of thermodynamic system, ρ and p, are also the source of gravity, then either thermal quantities, such as entropy, temperature, and chemical potential, can induce gravitational effects, or gravity can induce thermal effects. We find that gravity can be seen as entropic force only for systems with constant temperature and zero chemical potential. The case for Newtonian approximation is discussed.Entropy2014-08-11168Article10.3390/e16084483448344881099-43002014-08-11doi: 10.3390/e16084483Rongjia Yang<![CDATA[Entropy, Vol. 16, Pages 4443-4482: Structure of a Global Network of Financial Companies Based on Transfer Entropy]]>
http://www.mdpi.com/1099-4300/16/8/4443
This work uses the stocks of the 197 largest companies in the world, in terms of market capitalization, in the financial area, from 2003 to 2012. We study the causal relationships between them using Transfer Entropy, which is calculated using the stocks of those companies and their counterparts lagged by one day. With this, we can assess which companies influence others according to sub-areas of the financial sector, which are banks, diversified financial services, savings and loans, insurance, private equity funds, real estate investment companies, and real estate trust funds. We also analyze the exchange of information between those stocks as seen by Transfer Entropy and the network formed by them based on this measure, verifying that they cluster mainly according to countries of origin, and then by industry and sub-industry. Then we use data on the stocks of companies in the financial sector of some countries that are suffering the most with the current credit crisis, namely Greece, Cyprus, Ireland, Spain, Portugal, and Italy, and assess, also using Transfer Entropy, which companies from the largest 197 are most affected by the stocks of these countries in crisis. The aim is to map a network of influences that may be used in the study of possible contagions originating in those countries in financial crisis.Entropy2014-08-07168Article10.3390/e16084443444344821099-43002014-08-07doi: 10.3390/e16084443Leonidas Sandoval<![CDATA[Entropy, Vol. 16, Pages 4420-4442: Historical and Physical Account on Entropy and Perspectives on the Second Law of Thermodynamics for Astrophysical and Cosmological Systems]]>
http://www.mdpi.com/1099-4300/16/8/4420
We performed an in depth analysis of the subjects of entropy and the second law of thermodynamics and how they are treated in astrophysical systems. These subjects are retraced historically from the early works on thermodynamics to the modern statistical mechanical approach and analyzed in view of specific practices within the field of astrophysics. As often happens in discussions regarding cosmology, the implications of this analysis range from physics to philosophy of science. We argue that the difficult question regarding entropy and the second law in the scope of cosmology is a consequence of the dominating paradigm. We further demonstrate this point by assuming an alternative paradigm, not related to thermodynamics of horizons, and successfully describing entropic behavior of astrophysical systems.Entropy2014-08-05168Article10.3390/e16084420442044421099-43002014-08-05doi: 10.3390/e16084420Jeroen Schoenmaker<![CDATA[Entropy, Vol. 16, Pages 4408-4419: Information Entropy Evolution for Groundwater Flow System: A Case Study of Artificial Recharge in Shijiazhuang City, China]]>
http://www.mdpi.com/1099-4300/16/8/4408
The groundwater flow system is typical dissipative structure system, and its evolution can be described with system information entropies. The information entropies of groundwater in Shijiazhuang City had been calculated between 1960 and 2005, and the results show that the entropies have a decreasing trend throughout the research period, and they can be divided into our stages based on the groundwater flow system entropy variation as follows: entropy steady period (1960–1965), entropy decreasing period (1965–1980), entropy increasing period (1980–1995) and secondary entropy decreasing period (1995–2005); understanding the major and significant driving the pattern changing forces of groundwater levels is essential to groundwater management,. A new method of grey correlation analysis has been presented, and the results show that, the grey correlation grade between groundwater flow system information entropies and precipitation series is γ01 = 0.749, the grey correlation grade between groundwater flow system information entropies and groundwater withdrawal series is γ02 = 0.814, as the groundwater withdrawal is the main driving force of groundwater flow system entropy variation; based on the numerical simulation results, information entropy increased with artificial recharge, and a smaller recharge water volume would enhance the information entropy drastically, but then doubled water would not increase the information correspondingly, which could be useful to assess the health state of groundwater flow systems.Entropy2014-08-05168Article10.3390/e16084408440844191099-43002014-08-05doi: 10.3390/e16084408Wei XuShanghai Du<![CDATA[Entropy, Vol. 16, Pages 4392-4407: Exergy Analysis of a Subcritical Refrigeration Cycle with an Improved Impulse Turbo Expander]]>
http://www.mdpi.com/1099-4300/16/8/4392
The impulse turbo expander (ITE) is employed to replace the throttling valve in the vapor compression refrigeration cycle to improve the system performance. An improved ITE and the corresponding cycle are presented. In the new cycle, the ITE not only acts as an expansion device with work extraction, but also serves as an economizer with vapor injection. An increase of 20% in the isentropic efficiency can be attained for the improved ITE compared with the conventional ITE owing to the reduction of the friction losses of the rotor. The performance of the novel cycle is investigated based on energy and exergy analysis. A correlation of the optimum intermediate pressure in terms of ITE efficiency is developed. The improved ITE cycle increases the exergy efficiency by 1.4%–6.1% over the conventional ITE cycle, 4.6%–8.3% over the economizer cycle and 7.2%–21.6% over the base cycle. Furthermore, the improved ITE cycle is also preferred due to its lower exergy loss.Entropy2014-08-04168Article10.3390/e16084392439244071099-43002014-08-04doi: 10.3390/e16084392Zhenying ZhangLili Tian<![CDATA[Entropy, Vol. 16, Pages 4375-4391: An Energetic Analysis of the Phase Separation in Non-Ionic Surfactant Mixtures: The Role of the Headgroup Structure]]>
http://www.mdpi.com/1099-4300/16/8/4375
The main goal of this paper was to examine the effect of the hydrophilic surfactant headgroup on the phase behavior of non-ionic surfactant mixtures. Four mixed systems composed of an ethoxylated plus sugar-based surfactants, each having the same hydrophobic tail, were investigated. We found that the hydrophilicity of the surfactant inhibits the tendency of the system to phase separate, which is sensitive to the presence of NaCl. Applying a classical phase separation thermodynamic model, the corresponding energy parameters were evaluated. In all cases, the parameters were found to depend on the type of nonionic surfactant, its concentration in the micellar solution and the presence of NaCl in the medium. The experimental results can be explained by assuming the phase separation process takes place as a result of reduced hydration of the surfactant headgroup caused by a temperature increase. The enthalpy-entropy compensation plot exhibits excellent linearity. We found that all the mixed surfactant systems coincided on the same straight line, the compensation temperature being lower in the presence of NaCl.Entropy2014-08-04168Article10.3390/e16084375437543911099-43002014-08-04doi: 10.3390/e16084375José HierrezueloJosé Molina-BolívarCristóbal Ruiz