Entropy
http://www.mdpi.com/journal/entropy
Latest open access articles published in Entropy at http://www.mdpi.com/journal/entropy<![CDATA[Entropy, Vol. 19, Pages 182: Carnot-Like Heat Engines Versus Low-Dissipation Models]]>
http://www.mdpi.com/1099-4300/19/4/182
In this paper, a comparison between two well-known finite time heat engine models is presented: the Carnot-like heat engine based on specific heat transfer laws between the cyclic system and the external heat baths and the Low-Dissipation model where irreversibilities are taken into account by explicit entropy generation laws. We analyze the mathematical relation between the natural variables of both models and from this the resulting thermodynamic implications. Among them, particular emphasis has been placed on the physical consistency between the heat leak and time evolution on the one side, and between parabolic and loop-like behaviors of the parametric power-efficiency plots. A detailed analysis for different heat transfer laws in the Carnot-like model in terms of the maximum power efficiencies given by the Low-Dissipation model is also presented.Entropy2017-04-23194Article10.3390/e190401821821099-43002017-04-23doi: 10.3390/e19040182Julian Gonzalez-AyalaJosé RocoAlejandro MedinaAntonio Calvo Hernández<![CDATA[Entropy, Vol. 19, Pages 180: Using Measured Values in Bell’s Inequalities Entails at Least One Hypothesis in Addition to Local Realism]]>
http://www.mdpi.com/1099-4300/19/4/180
The recent loophole-free experiments have confirmed the violation of Bell’s inequalities in nature. Yet, in order to insert measured values in Bell’s inequalities, it is unavoidable to make a hypothesis similar to “ergodicity at the hidden variables level”. This possibility opens a promising way out from the old controversy between quantum mechanics and local realism. Here, I review the reason why such a hypothesis (actually, it is one of a set of related hypotheses) in addition to local realism is necessary, and present a simple example, related to Bell’s inequalities, where the hypothesis is violated. This example shows that the violation of the additional hypothesis is necessary, but not sufficient, to violate Bell’s inequalities without violating local realism. The example also provides some clues that may reveal the violation of the additional hypothesis in an experiment.Entropy2017-04-22194Article10.3390/e190401801801099-43002017-04-22doi: 10.3390/e19040180Alejandro Hnilo<![CDATA[Entropy, Vol. 19, Pages 181: Citizen Science and Topology of Mind: Complexity, Computation and Criticality in Data-Driven Exploration of Open Complex Systems]]>
http://www.mdpi.com/1099-4300/19/4/181
Recently emerging data-driven citizen sciences need to harness an increasing amount of massive data with varying quality. This paper develops essential theoretical frameworks, example models, and a general definition of complexity measure, and examines its computational complexity for an interactive data-driven citizen science within the context of guided self-organization. We first define a conceptual model that incorporates the quality of observation in terms of accuracy and reproducibility, ranging between subjectivity, inter-subjectivity, and objectivity. Next, we examine the database’s algebraic and topological structure in relation to informational complexity measures, and evaluate its computational complexities with respect to an exhaustive optimization. Conjectures of criticality are obtained on the self-organizing processes of observation and dynamical model development. Example analysis is demonstrated with the use of biodiversity assessment database—the process that inevitably involves human subjectivity for management within open complex systems.Entropy2017-04-22194Article10.3390/e190401811811099-43002017-04-22doi: 10.3390/e19040181Masatoshi Funabashi<![CDATA[Entropy, Vol. 19, Pages 179: On the Definition of Diversity Order Based on Renyi Entropy for Frequency Selective Fading Channels]]>
http://www.mdpi.com/1099-4300/19/4/179
Outage probabilities are important measures of the performance of wireless communication systems, but to obtain outage probabilities it is necessary to first determine detailed system parameters, followed by complicated calculations. When there are multiple candidates of diversity techniques applicable for a system, the diversity order can be used to roughly but quickly compare the techniques for a wide range of operating environments. For a system transmitting over frequency selective fading channels, the diversity order can be defined as the number of multi-paths if multi-paths have all equal energy. However, diversity order may not be adequately defined when the energy values are different. In order to obtain a rough value of diversity order, one may use the number of multi-paths or the reciprocal value of the multi-path energy variance. Such definitions are not very useful for evaluating the performance of diversity techniques since the former is meaningful only when the target outage probability is extremely small, while the latter is reasonable when the target outage probability is very large. In this paper, we propose a new definition of diversity order for frequency selective fading channels. The proposed scheme is based on Renyi entropy, which is widely used in biology and many other fields. We provide various simulation results to show that the diversity order using the proposed definition is tightly correlated with the corresponding outage probability, and thus the proposed scheme can be used for quickly selecting the best diversity technique among multiple candidates.Entropy2017-04-20194Article10.3390/e190401791791099-43002017-04-20doi: 10.3390/e19040179Seungyeob ChaeMinjoong Rim<![CDATA[Entropy, Vol. 19, Pages 177: Entropy in Natural Time and the Associated Complexity Measures]]>
http://www.mdpi.com/1099-4300/19/4/177
Natural time is a new time domain introduced in 2001. The analysis of time series associated with a complex system in natural time may provide useful information and may reveal properties that are usually hidden when studying the system in conventional time. In this new time domain, an entropy has been defined, and complexity measures based on this entropy, as well as its value under time-reversal have been introduced and found applications in various complex systems. Here, we review these applications in the electric signals that precede rupture, e.g., earthquakes, in the analysis of electrocardiograms, as well as in global atmospheric phenomena, like the El Niño/La Niña Southern Oscillation.Entropy2017-04-20194Article10.3390/e190401771771099-43002017-04-20doi: 10.3390/e19040177Nicholas Sarlis<![CDATA[Entropy, Vol. 19, Pages 178: Entropy “2”-Soft Classification of Objects]]>
http://www.mdpi.com/1099-4300/19/4/178
A proposal for a new method of classification of objects of various nature, named “2”-soft classification, which allows for referring objects to one of two types with optimal entropy probability for available collection of learning data with consideration of additive errors therein. A decision rule of randomized parameters and probability density function (PDF) is formed, which is determined by the solution of the problem of the functional entropy linear programming. A procedure for “2”-soft classification is developed, consisting of the computer simulation of the randomized decision rule with optimal entropy PDF parameters. Examples are provided.Entropy2017-04-20194Article10.3390/e190401781781099-43002017-04-20doi: 10.3390/e19040178Yuri PopkovZeev VolkovichYuri DubnovRenata AvrosElena Ravve<![CDATA[Entropy, Vol. 19, Pages 174: Leaks: Quantum, Classical, Intermediate and More]]>
http://www.mdpi.com/1099-4300/19/4/174
We introduce the notion of a leak for general process theories and identify quantum theory as a theory with minimal leakage, while classical theory has maximal leakage. We provide a construction that adjoins leaks to theories, an instance of which describes the emergence of classical theory by adjoining decoherence leaks to quantum theory. Finally, we show that defining a notion of purity for processes in general process theories has to make reference to the leaks of that theory, a feature missing in standard definitions; hence, we propose a refined definition and study the resulting notion of purity for quantum, classical and intermediate theories.Entropy2017-04-19194Article10.3390/e190401741741099-43002017-04-19doi: 10.3390/e19040174John SelbyBob Coecke<![CDATA[Entropy, Vol. 19, Pages 176: Multi-Scale Permutation Entropy Based on Improved LMD and HMM for Rolling Bearing Diagnosis]]>
http://www.mdpi.com/1099-4300/19/4/176
Based on the combination of improved Local Mean Decomposition (LMD), Multi-scale Permutation Entropy (MPE) and Hidden Markov Model (HMM), the fault types of bearings are diagnosed. Improved LMD is proposed based on the self-similarity of roller bearing vibration signal by extending the right and left side of the original signal to suppress its edge effect. First, the vibration signals of the rolling bearing are decomposed into several product function (PF) components by improved LMD respectively. Then, the phase space reconstruction of the PF1 is carried out by using the mutual information (MI) method and the false nearest neighbor (FNN) method to calculate the delay time and the embedding dimension, and then the scale is set to obtain the MPE of PF1. After that, the MPE features of rolling bearings are extracted. Finally, the features of MPE are used as HMM training and diagnosis. The experimental results show that the proposed method can effectively identify the different faults of the rolling bearing.Entropy2017-04-19194Article10.3390/e190401761761099-43002017-04-19doi: 10.3390/e19040176Yangde GaoFrancesco VilleccoMing LiWanqing Song<![CDATA[Entropy, Vol. 19, Pages 175: Second Law Analysis of a Mobile Air Conditioning System with Internal Heat Exchanger Using Low GWP Refrigerants]]>
http://www.mdpi.com/1099-4300/19/4/175
This paper investigates the results of a Second Law analysis applied to a mobile air conditioning system (MACs) integrated with an internal heat exchanger (IHX) by considering R152a, R1234yf and R1234ze as low global warming potential (GWP) refrigerants and establishing R134a as baseline. System simulation is performed considering the maximum value of entropy generated in the IHX. The maximum entropy production occurs at an effectiveness of 66% for both R152a and R134a, whereas for the cases of R1234yf and R1234ze occurs at 55%. Sub-cooling and superheating effects are evaluated for each one of the cases. It is also found that the sub-cooling effect shows the greatest impact on the cycle efficiency. The results also show the influence of isentropic efficiency on relative exergy destruction, resulting that the most affected components are the compressor and the condenser for all of the refrigerants studied herein. It is also found that the most efficient operation of the system resulted to be when using the R1234ze refrigerant.Entropy2017-04-19194Article10.3390/e190401751751099-43002017-04-19doi: 10.3390/e19040175Vicente Pérez-GarcíaJuan Belman-FloresJosé Rodríguez-MuñozVíctor. Rangel-HernándezArmando Gallegos-Muñoz<![CDATA[Entropy, Vol. 19, Pages 172: Multilevel Integration Entropies: The Case of Reconstruction of Structural Quasi-Stability in Building Complex Datasets]]>
http://www.mdpi.com/1099-4300/19/4/172
The emergence of complex datasets permeates versatile research disciplines leading to the necessity to develop methods for tackling complexity through finding the patterns inherent in datasets. The challenge lies in transforming the extracted patterns into pragmatic knowledge. In this paper, new information entropy measures for the characterization of the multidimensional structure extracted from complex datasets are proposed, complementing the conventionally-applied algebraic topology methods. Derived from topological relationships embedded in datasets, multilevel entropy measures are used to track transitions in building the high dimensional structure of datasets captured by the stratified partition of a simplicial complex. The proposed entropies are found suitable for defining and operationalizing the intuitive notions of structural relationships in a cumulative experience of a taxi driver’s cognitive map formed by origins and destinations. The comparison of multilevel integration entropies calculated after each new added ride to the data structure indicates slowing the pace of change over time in the origin-destination structure. The repetitiveness in taxi driver rides, and the stability of origin-destination structure, exhibits the relative invariance of rides in space and time. These results shed light on taxi driver’s ride habits, as well as on the commuting of persons whom he/she drove.Entropy2017-04-18194Article10.3390/e190401721721099-43002017-04-18doi: 10.3390/e19040172Slobodan MaletićYi Zhao<![CDATA[Entropy, Vol. 19, Pages 146: Design and Implementation of SOC Prediction for a Li-Ion Battery Pack in an Electric Car with an Embedded System]]>
http://www.mdpi.com/1099-4300/19/4/146
Li-Ion batteries are widely preferred in electric vehicles. The charge status of batteries is a critical evaluation issue, and many researchers are studying in this area. State of charge gives information about how much longer the battery can be used and when the charging process will be cut off. Incorrect predictions may cause overcharging or over-discharging of the battery. In this study, a low-cost embedded system is used to determine the state of charge of an electric car. A Li-Ion battery cell is trained using a feed-forward neural network via Matlab/Neural Network Toolbox. The trained cell is adapted to the whole battery pack of the electric car and embedded via Matlab/Simulink to a low-cost microcontroller that proposed a system in real-time. The experimental results indicated that accurate robust estimation results could be obtained by the proposed system.Entropy2017-04-17194Article10.3390/e190401461461099-43002017-04-17doi: 10.3390/e19040146Emel SoyluTuncay SoyluRaif Bayir<![CDATA[Entropy, Vol. 19, Pages 171: Entropy Generation of Double Diffusive Forced Convection in Porous Channels with Thick Walls and Soret Effect]]>
http://www.mdpi.com/1099-4300/19/4/171
The second law performance of double diffusive forced convection in a horizontal porous channel with thick walls was considered. The Soret effect is included in the concentration equation and the first order chemical reaction was chosen for the concentration boundary conditions at the porous-solid walls interfaces. This investigation is focused on two principal types of boundary conditions. The first assumes a constant temperature condition at the outer surfaces of the solid walls, and the second assumes a constant heat flux at the lower wall and convection heat transfer at the upper wall. After obtaining the velocity, temperature and concentration distributions, the local and total entropy generation formulations were used to visualize the second law performance of the two cases. The results indicate that the total entropy generation rate is directly related to the lower wall thickness. Interestingly, it was observed that the total entropy generation rate for the second case reaches a minimum value, if the upper and lower wall thicknesses are chosen correctly. However, this observation was not true for the first case. These analyses can be useful for the design of microreactors and microcombustor systems when the second law analysis is taken into account.Entropy2017-04-15194Article10.3390/e190401711711099-43002017-04-15doi: 10.3390/e19040171Mohsen TorabiMehrdad TorabiG.P. Peterson<![CDATA[Entropy, Vol. 19, Pages 170: Dynamic Rankings for Seed Selection in Complex Networks: Balancing Costs and Coverage]]>
http://www.mdpi.com/1099-4300/19/4/170
Information spreading processes within the complex networks are usually initiated by a selection of highly influential nodes in accordance with the used seeding strategy. The majority of earlier studies assumed the usage of selected seeds at the beginning of the process. Our previous research revealed the advantage of using a sequence of seeds instead of a single stage approach. The current study extends sequential seeding and further improves results with the use of dynamic rankings, which are created by recalculation of network measures used for additional seed selection during the process instead of static ranking computed only once at the beginning. For calculation of network centrality measures such as degree, only non-infected nodes are taken into account. Results showed increased coverage represented by a percentage of activated nodes dependent on intervals between recalculations as well as the trade-off between outcome and computational costs. For over 90% of simulation cases, dynamic rankings with a high frequency of recalculations delivered better coverage than approaches based on static rankings.Entropy2017-04-15194Article10.3390/e190401701701099-43002017-04-15doi: 10.3390/e19040170Jarosław Jankowski<![CDATA[Entropy, Vol. 19, Pages 169: Where There is Life There is Mind: In Support of a Strong Life-Mind Continuity Thesis]]>
http://www.mdpi.com/1099-4300/19/4/169
This paper considers questions about continuity and discontinuity between life and mind. It begins by examining such questions from the perspective of the free energy principle (FEP). The FEP is becoming increasingly influential in neuroscience and cognitive science. It says that organisms act to maintain themselves in their expected biological and cognitive states, and that they can do so only by minimizing their free energy given that the long-term average of free energy is entropy. The paper then argues that there is no singular interpretation of the FEP for thinking about the relation between life and mind. Some FEP formulations express what we call an independence view of life and mind. One independence view is a cognitivist view of the FEP. It turns on information processing with semantic content, thus restricting the range of systems capable of exhibiting mentality. Other independence views exemplify what we call an overly generous non-cognitivist view of the FEP, and these appear to go in the opposite direction. That is, they imply that mentality is nearly everywhere. The paper proceeds to argue that non-cognitivist FEP, and its implications for thinking about the relation between life and mind, can be usefully constrained by key ideas in recent enactive approaches to cognitive science. We conclude that the most compelling account of the relationship between life and mind treats them as strongly continuous, and that this continuity is based on particular concepts of life (autopoiesis and adaptivity) and mind (basic and non-semantic).Entropy2017-04-14194Article10.3390/e190401691691099-43002017-04-14doi: 10.3390/e19040169Michael D. KirchhoffTom Froese<![CDATA[Entropy, Vol. 19, Pages 167: Application of the Fuzzy Oil Drop Model Describes Amyloid as a Ribbonlike Micelle]]>
http://www.mdpi.com/1099-4300/19/4/167
We propose a mathematical model describing the formation of micellar forms—whether spherical, globular, cylindrical, or ribbonlike—as well as its adaptation to protein structure. Our model, based on the fuzzy oil drop paradigm, assumes that in a spherical micelle the distribution of hydrophobicity produced by the alignment of polar molecules with the external water environment can be modeled by a 3D Gaussian function. Perturbing this function by changing the values of its sigma parameters leads to a variety of conformations—the model is therefore applicable to globular, cylindrical, and ribbonlike micelles. In the context of protein structures ranging from globular to ribbonlike, our model can explain the emergence of fibrillar forms; particularly amyloids.Entropy2017-04-14194Article10.3390/e190401671671099-43002017-04-14doi: 10.3390/e19040167Irena RotermanMateusz BanachLeszek Konieczny<![CDATA[Entropy, Vol. 19, Pages 159: A Study of the Transfer Entropy Networks on Industrial Electricity Consumption]]>
http://www.mdpi.com/1099-4300/19/4/159
We study information transfer routes among cross-industry and cross-region electricity consumption data based on transfer entropy and the MST (Minimum Spanning Tree) model. First, we characterize the information transfer routes with transfer entropy matrixes, and find that the total entropy transfer of the relatively developed Guangdong Province is lower than others, with significant industrial cluster within the province. Furthermore, using a reshuffling method, we find that driven industries contain much more information flows than driving industries, and are more influential on the degree of order of regional industries. Finally, based on the Chu-Liu-Edmonds MST algorithm, we extract the minimum spanning trees of provincial industries. Individual MSTs show that the MSTs follow a chain-like formation in developed provinces and star-like structures in developing provinces. Additionally, all MSTs with the root of minimal information outflow industrial sector are of chain-form.Entropy2017-04-13194Article10.3390/e190401591591099-43002017-04-13doi: 10.3390/e19040159Can-Zhong YaoPeng-Cheng KuangQing-Wen LinBo-Yi Sun<![CDATA[Entropy, Vol. 19, Pages 166: Entropic Aspects of Nonlinear Partial Differential Equations: Classical and Quantum Mechanical Perspectives]]>
http://www.mdpi.com/1099-4300/19/4/166
There has been increasing research activity in recent years concerning the properties and the applications of nonlinear partial differential equations that are closely related to nonstandard entropic functionals, such as the Tsallis and Renyi entropies.[...]Entropy2017-04-12194Editorial10.3390/e190401661661099-43002017-04-12doi: 10.3390/e19040166Angelo Plastino<![CDATA[Entropy, Vol. 19, Pages 165: An Entropy-Based Approach for Evaluating Travel Time Predictability Based on Vehicle Trajectory Data]]>
http://www.mdpi.com/1099-4300/19/4/165
With the great development of intelligent transportation systems (ITS), travel time prediction has attracted the interest of many researchers, and a large number of prediction methods have been developed. However, as an unavoidable topic, the predictability of travel time series is the basic premise for travel time prediction, which has received less attention than the methodology. Based on the analysis of the complexity of the travel time series, this paper defines travel time predictability to express the probability of correct travel time prediction, and proposes an entropy-based method to measure the upper bound of travel time predictability. Multiscale entropy is employed to quantify the complexity of the travel time series, and the relationships between entropy and the upper bound of travel time predictability are presented. Empirical studies are made with vehicle trajectory data in an express road section to shape the features of travel time predictability. The effectiveness of time scales, tolerance, and series length to entropy and travel time predictability are analyzed, and some valuable suggestions about the accuracy of travel time predictability are discussed. Finally, comparisons between travel time predictability and actual prediction results from two prediction models, ARIMA and BPNN, are made. Experimental results demonstrate the validity and reliability of the proposed travel time predictability.Entropy2017-04-11194Article10.3390/e190401651651099-43002017-04-11doi: 10.3390/e19040165Tao XuXianrui XuYujie HuXiang Li<![CDATA[Entropy, Vol. 19, Pages 164: Heisenberg and Entropic Uncertainty Measures for Large-Dimensional Harmonic Systems]]>
http://www.mdpi.com/1099-4300/19/4/164
The D-dimensional harmonic system (i.e., a particle moving under the action of a quadratic potential) is, together with the hydrogenic system, the main prototype of the physics of multidimensional quantum systems. In this work, we rigorously determine the leading term of the Heisenberg-like and entropy-like uncertainty measures of this system as given by the radial expectation values and the Rényi entropies, respectively, at the limit of large D. The associated multidimensional position-momentum uncertainty relations are discussed, showing that they saturate the corresponding general ones. A conjecture about the Shannon-like uncertainty relation is given, and an interesting phenomenon is observed: the Heisenberg-like and Rényi-entropy-based equality-type uncertainty relations for all of the D-dimensional harmonic oscillator states in the pseudoclassical ( D → ∞ ) limit are the same as the corresponding ones for the hydrogenic systems, despite the so different character of the oscillator and Coulomb potentials.Entropy2017-04-09194Article10.3390/e190401641641099-43002017-04-09doi: 10.3390/e19040164David Puertas-CentenoIrene ToranzoJesús Dehesa<![CDATA[Entropy, Vol. 19, Pages 163: Modelling Urban Sprawl Using Remotely Sensed Data: A Case Study of Chennai City, Tamilnadu]]>
http://www.mdpi.com/1099-4300/19/4/163
Urban sprawl (US), propelled by rapid population growth leads to the shrinkage of productive agricultural lands and pristine forests in the suburban areas and, in turn, adversely affects the provision of ecosystem services. The quantification of US is thus crucial for effective urban planning and environmental management. Like many megacities in fast growing developing countries, Chennai, the capital of Tamilnadu and one of the business hubs in India, has experienced extensive US triggered by the doubling of total population over the past three decades. However, the extent and level of US has not yet been quantified and a prediction for future extent of US is lacking. We employed the Random Forest (RF) classification on Landsat imageries from 1991, 2003, and 2016, and computed six landscape metrics to delineate the extent of urban areas within a 10 km suburban buffer of Chennai. The level of US was then quantified using Renyi’s entropy. A land change model was subsequently used to project land cover for 2027. A 70.35% expansion in urban areas was observed mainly towards the suburban periphery of Chennai between 1991 and 2016. The Renyi’s entropy value for year 2016 was 0.9, exhibiting a two-fold level of US when compared to 1991. The spatial metrics values indicate that the existing urban areas became denser and the suburban agricultural, forests and particularly barren lands were transformed into fragmented urban settlements. The forecasted land cover for 2027 indicates a conversion of 13,670.33 ha (16.57% of the total landscape) of existing forests and agricultural lands into urban areas with an associated increase in the entropy value to 1.7, indicating a tremendous level of US. Our study provides useful metrics for urban planning authorities to address the social-ecological consequences of US and to protect ecosystem services.Entropy2017-04-07194Article10.3390/e190401631631099-43002017-04-07doi: 10.3390/e19040163Rajchandar PadmanabanAvit K. BhowmikPedro CabralAlexander ZamyatinOraib AlmegdadiShuangao Wang<![CDATA[Entropy, Vol. 19, Pages 162: Situatedness and Embodiment of Computational Systems]]>
http://www.mdpi.com/1099-4300/19/4/162
In this paper, the role of the environment and physical embodiment of computational systems for explanatory purposes will be analyzed. In particular, the focus will be on cognitive computational systems, understood in terms of mechanisms that manipulate semantic information. It will be argued that the role of the environment has long been appreciated, in particular in the work of Herbert A. Simon, which has inspired the mechanistic view on explanation. From Simon’s perspective, the embodied view on cognition seems natural but it is nowhere near as critical as its proponents suggest. The only point of difference between Simon and embodied cognition is the significance of body-based off-line cognition; however, it will be argued that it is notoriously over-appreciated in the current debate. The new mechanistic view on explanation suggests that even if it is critical to situate a mechanism in its environment and study its physical composition, or realization, it is also stressed that not all detail counts, and that some bodily features of cognitive systems should be left out from explanations.Entropy2017-04-07194Article10.3390/e190401621621099-43002017-04-07doi: 10.3390/e19040162Marcin Miłkowski<![CDATA[Entropy, Vol. 19, Pages 161: P-Adic Analog of Navier–Stokes Equations: Dynamics of Fluid’s Flow in Percolation Networks (from Discrete Dynamics with Hierarchic Interactions to Continuous Universal Scaling Model)]]>
http://www.mdpi.com/1099-4300/19/4/161
Recently p-adic (and, more generally, ultrametric) spaces representing tree-like networks of percolation, and as a special case of capillary patterns in porous media, started to be used to model the propagation of fluids (e.g., oil, water, oil-in-water, and water-in-oil emulsion). The aim of this note is to derive p-adic dynamics described by fractional differential operators (Vladimirov operators) starting with discrete dynamics based on hierarchically-structured interactions between the fluids’ volumes concentrated at different levels of the percolation tree and coming to the multiscale universal topology of the percolating nets. Similar systems of discrete hierarchic equations were widely applied to modeling of turbulence. However, in the present work this similarity is only formal since, in our model, the trees are real physical patterns with a tree-like topology of capillaries (or fractures) in random porous media (not cascade trees, as in the case of turbulence, which we will be discussed elsewhere for the spinner flowmeter commonly used in the petroleum industry). By going to the “continuous limit” (with respect to the p-adic topology) we represent the dynamics on the tree-like configuration space as an evolutionary nonlinear p-adic fractional (pseudo-) differential equation, the tree-like analog of the Navier–Stokes equation. We hope that our work helps to come closer to a nonlinear equation solution, taking into account the scaling, hierarchies, and formal derivations, imprinted from the similar properties of the real physical world. Once this coupling is resolved, the more problematic question of information scaling in industrial applications will be achieved.Entropy2017-04-07194Article10.3390/e190401611611099-43002017-04-07doi: 10.3390/e19040161Klaudia OleschkoAndrei KhrennikovMaría Correa López<![CDATA[Entropy, Vol. 19, Pages 160: Consistent Estimation of Partition Markov Models]]>
http://www.mdpi.com/1099-4300/19/4/160
The Partition Markov Model characterizes the process by a partition L of the state space, where the elements in each part of L share the same transition probability to an arbitrary element in the alphabet. This model aims to answer the following questions: what is the minimal number of parameters needed to specify a Markov chain and how to estimate these parameters. In order to answer these questions, we build a consistent strategy for model selection which consist of: giving a size n realization of the process, finding a model within the Partition Markov class, with a minimal number of parts to represent the process law. From the strategy, we derive a measure that establishes a metric in the state space. In addition, we show that if the law of the process is Markovian, then, eventually, when n goes to infinity, L will be retrieved. We show an application to model internet navigation patterns.Entropy2017-04-06194Article10.3390/e190401601601099-43002017-04-06doi: 10.3390/e19040160Jesús GarcíaVerónica González-López<![CDATA[Entropy, Vol. 19, Pages 152: An Approach to the Evaluation of the Quality of Accounting Information Based on Relative Entropy in Fuzzy Linguistic Environments]]>
http://www.mdpi.com/1099-4300/19/4/152
There is a risk when company stakeholders make decisions using accounting information with varied qualities in the same way. In order to evaluate the accounting information quality, this paper proposed an approach to the evaluation of the quality of accounting information based on relative entropy in fuzzy linguistic environments. Firstly, the accounting information quality evaluation criteria are constructed not only from the quality of the accounting information content but also from the accounting information generation environment. Considering that the rating values with respect to the criteria are in linguistic forms with different granularities, the method to deal with the linguistic rating values is given. In the method, the linguistic terms are modeled with the 2-tuple linguistic model. Relative entropy is used to calculate the information consistency, which is used to derive the weight of experts and criteria. Finally, the example is given to illustrate the feasibility and practicability of the proposed method.Entropy2017-04-05194Article10.3390/e190401521521099-43002017-04-05doi: 10.3390/e19040152Ming LiXiaoli NingMingzhu LiYingcheng Xu<![CDATA[Entropy, Vol. 19, Pages 158: Nonequilibrium Thermodynamics and Steady State Density Matrix for Quantum Open Systems]]>
http://www.mdpi.com/1099-4300/19/4/158
We consider the generic model of a finite-size quantum electron system connected to two (temperature and particle) reservoirs. The quantum open system is driven out of equilibrium by the presence of both potential temperature and chemical differences between the two reservoirs. The nonequilibrium (NE) thermodynamical properties of such a quantum open system are studied for the steady state regime. In such a regime, the corresponding NE density matrix is built on the so-called generalised Gibbs ensembles. From different expressions of the NE density matrix, we can identify the terms related to the entropy production in the system. We show, for a simple model, that the entropy production rate is always a positive quantity. Alternative expressions for the entropy production are also obtained from the Gibbs–von Neumann conventional formula and discussed in detail. Our results corroborate and expand earlier works found in the literature.Entropy2017-04-02194Article10.3390/e190401581581099-43002017-04-02doi: 10.3390/e19040158Hervé Ness<![CDATA[Entropy, Vol. 19, Pages 157: Quadratic Mutual Information Feature Selection]]>
http://www.mdpi.com/1099-4300/19/4/157
We propose a novel feature selection method based on quadratic mutual information which has its roots in Cauchy–Schwarz divergence and Renyi entropy. The method uses the direct estimation of quadratic mutual information from data samples using Gaussian kernel functions, and can detect second order non-linear relations. Its main advantages are: (i) unified analysis of discrete and continuous data, excluding any discretization; and (ii) its parameter-free design. The effectiveness of the proposed method is demonstrated through an extensive comparison with mutual information feature selection (MIFS), minimum redundancy maximum relevance (MRMR), and joint mutual information (JMI) on classification and regression problem domains. The experiments show that proposed method performs comparably to the other methods when applied to classification problems, except it is considerably faster. In the case of regression, it compares favourably to the others, but is slower.Entropy2017-04-01194Article10.3390/e190401571571099-43002017-04-01doi: 10.3390/e19040157Davor SlugaUroš Lotrič<![CDATA[Entropy, Vol. 19, Pages 156: Use of Exergy Analysis to Quantify the Effect of Lithium Bromide Concentration in an Absorption Chiller]]>
http://www.mdpi.com/1099-4300/19/4/156
Absorption chillers present opportunities to utilize sustainable fuels in the production of chilled water. An assessment of the steam driven absorption chiller at the University of Idaho, was performed to quantify the current exergy destruction rates. Measurements of external processes and flows were used to create a mathematical model. Using engineering equation solver to analyze and identify the major sources of exergy destruction within the chiller. It was determined that the absorber, generator and condenser are the largest contribution to the exergy destruction at 30%, 31% and 28% of the respectively. The exergetic efficiency is found to be 16% with a Coefficient of performance (COP) of 0.65. Impacts of weak solution concentration of lithium bromide on the exergy destruction rates were evaluated using parametric studies. The studies reveled an optimum concentration that could be obtained by increasing the weak solution concentration from 56% to 58.8% a net decrease in 0.4% of the exergy destruction caused by the absorption chiller can be obtained. The 2.8% increase in lithium-bromide concentration decreases the exergy destruction primarily within the absorber with a decrease of 5.1%. This increase in concentration is shown to also decrease the maximum cooling capacity by 3% and increase the exergy destruction of the generator by 4.9%. The study also shows that the increase in concentration will change the internal temperatures by 3 to 7 °C. Conversely, reducing the weak solution concentration results is also shown to increase the exergetic destruction rates while also potentially increasing the cooling capacity.Entropy2017-04-01194Article10.3390/e190401561561099-43002017-04-01doi: 10.3390/e19040156Andrew LakeBehanz RezaieSteven Beyerlein<![CDATA[Entropy, Vol. 19, Pages 155: Random Walks Associated with Nonlinear Fokker–Planck Equations]]>
http://www.mdpi.com/1099-4300/19/4/155
A nonlinear random walk related to the porous medium equation (nonlinear Fokker–Planck equation) is investigated. This random walk is such that when the number of steps is sufficiently large, the probability of finding the walker in a certain position after taking a determined number of steps approximates to a q-Gaussian distribution ( G q , β ( x ) ∝ [ 1 − ( 1 − q ) β x 2 ] 1 / ( 1 − q ) ), which is a solution of the porous medium equation. This can be seen as a verification of a generalized central limit theorem where the attractor is a q-Gaussian distribution, reducing to the Gaussian one when the linearity is recovered ( q → 1 ). In addition, motivated by this random walk, a nonlinear Markov chain is suggested.Entropy2017-04-01194Article10.3390/e190401551551099-43002017-04-01doi: 10.3390/e19040155Renio dos Santos MendesErvin LenziLuis MalacarneSergio PicoliMax Jauregui<![CDATA[Entropy, Vol. 19, Pages 153: Maxentropic Solutions to a Convex Interpolation Problem Motivated by Utility Theory]]>
http://www.mdpi.com/1099-4300/19/4/153
Here, we consider the following inverse problem: Determination of an increasing continuous function U ( x ) on an interval [ a , b ] from the knowledge of the integrals ∫ U ( x ) d F X i ( x ) = π i where the X i are random variables taking values on [ a , b ] and π i are given numbers. This is a linear integral equation with discrete data, which can be transformed into a generalized moment problem when U ( x ) is supposed to have a positive derivative, and it becomes a classical interpolation problem if the X i are deterministic. In some cases, e.g., in utility theory in economics, natural growth and convexity constraints are required on the function, which makes the inverse problem more interesting. Not only that, the data may be provided in intervals and/or measured up to an additive error. It is the purpose of this work to show how the standard method of maximum entropy, as well as the method of maximum entropy in the mean, provides an efficient method to deal with these problems.Entropy2017-04-01194Article10.3390/e190401531531099-43002017-04-01doi: 10.3390/e19040153Henryk GzylSilvia Mayoral<![CDATA[Entropy, Vol. 19, Pages 154: Is Turbulence a State of Maximum Energy Dissipation?]]>
http://www.mdpi.com/1099-4300/19/4/154
Turbulent flows are known to enhance turbulent transport. It has then even been suggested that turbulence is a state of maximum energy dissipation. In this paper, we re-examine critically this suggestion in light of several recent works around the Maximum Entropy Production principle (MEP) that has been used in several out-of-equilibrium systems. We provide a set of four different optimization principles, based on maximization of energy dissipation, entropy production, Kolmogorov–Sinai entropy and minimization of mixing time, and study the connection between these principles using simple out-of-equilibrium models describing mixing of a scalar quantity. We find that there is a chained-relationship between most probable stationary states of the system, and their ability to obey one of the four principles. This provides an empirical justification of the Maximum Entropy Production principle in this class of systems, including some turbulent flows, for special boundary conditions. Otherwise, we claim that the minimization of the mixing time would be a more appropriate principle. We stress that this principle might actually be limited to flows where symmetry or dynamics impose pure mixing of a quantity (like angular momentum, momentum or temperature). The claim that turbulence is a state of maximum energy dissipation, a quantity intimately related to entropy production, is therefore limited to special situations that nevertheless include classical systems such as shear flows, Rayleigh–Bénard convection and von Kármán flows, forced with constant velocity or temperature conditions.Entropy2017-03-31194Article10.3390/e190401541541099-43002017-03-31doi: 10.3390/e19040154Martin MihelichDavide FarandaDidier PaillardBérengère Dubrulle<![CDATA[Entropy, Vol. 19, Pages 151: A Combined Entropy/Phase-Field Approach to Gravity]]>
http://www.mdpi.com/1099-4300/19/4/151
Terms related to gradients of scalar fields are introduced as scalar products into the formulation of entropy. A Lagrange density is then formulated by adding constraints based on known conservation laws. Applying the Lagrange formalism to the resulting Lagrange density leads to the Poisson equation of gravitation and also includes terms which are related to the curvature of space. The formalism further leads to terms possibly explaining nonlinear extensions known from modified Newtonian dynamics approaches. The article concludes with a short discussion of the presented methodology and provides an outlook on other phenomena which might be dealt with using this new approach.Entropy2017-03-31194Article10.3390/e190401511511099-43002017-03-31doi: 10.3390/e19040151Georg J. Schmitz<![CDATA[Entropy, Vol. 19, Pages 149: A Distribution Family Bridging the Gaussian and the Laplace Laws, Gram–Charlier Expansions, Kurtosis Behaviour, and Entropy Features]]>
http://www.mdpi.com/1099-4300/19/4/149
The paper devises a family of leptokurtic bell-shaped distributions which is based on the hyperbolic secant raised to a positive power, and bridges the Laplace and Gaussian laws on asymptotic arguments. Moment and cumulant generating functions are then derived and represented in terms of polygamma functions. The behaviour of shape parameters, namely kurtosis and entropy, is investigated. In addition, Gram–Charlier-type (GCT) expansions, based on the aforementioned distributions and their orthogonal polynomials, are specified, and an operational criterion is provided to meet modelling requirements in a possibly severe kurtosis and skewness environment. The role played by entropy within the kurtosis ranges of GCT expansions is also examined.Entropy2017-03-31194Article10.3390/e190401491491099-43002017-03-31doi: 10.3390/e19040149Mario FalivaMaria Zoia<![CDATA[Entropy, Vol. 19, Pages 150: Minimum Sample Size for Reliable Causal Inference Using Transfer Entropy]]>
http://www.mdpi.com/1099-4300/19/4/150
Transfer Entropy has been applied to experimental datasets to unveil causality between variables. In particular, its application to non-stationary systems has posed a great challenge due to restrictions on the sample size. Here, we have investigated the minimum sample size that produces a reliable causal inference. The methodology has been applied to two prototypical models: the linear model autoregressive-moving average and the non-linear logistic map. The relationship between the Transfer Entropy value and the sample size has been systematically examined. Additionally, we have shown the dependence of the reliable sample size and the strength of coupling between the variables. Our methodology offers a realistic lower bound for the sample size to produce a reliable outcome.Entropy2017-03-31194Article10.3390/e190401501501099-43002017-03-31doi: 10.3390/e19040150Antônio RamosElbert Macau<![CDATA[Entropy, Vol. 19, Pages 148: Unsupervised Symbolization of Signal Time Series for Extraction of the Embedded Information]]>
http://www.mdpi.com/1099-4300/19/4/148
This paper formulates an unsupervised algorithm for symbolization of signal time series to capture the embedded dynamic behavior. The key idea is to convert time series of the digital signal into a string of (spatially discrete) symbols from which the embedded dynamic information can be extracted in an unsupervised manner (i.e., no requirement for labeling of time series). The main challenges here are: (1) definition of the symbol assignment for the time series; (2) identification of the partitioning segment locations in the signal space of time series; and (3) construction of probabilistic finite-state automata (PFSA) from the symbol strings that contain temporal patterns. The reported work addresses these challenges by maximizing the mutual information measures between symbol strings and PFSA states. The proposed symbolization method has been validated by numerical simulation as well as by experimentation in a laboratory environment. Performance of the proposed algorithm has been compared to that of two commonly used algorithms of time series partitioning.Entropy2017-03-31194Article10.3390/e190401481481099-43002017-03-31doi: 10.3390/e19040148Yue LiAsok Ray<![CDATA[Entropy, Vol. 19, Pages 145: Multiscale Cross-Approximate Entropy Analysis of Bilateral Fingertips Photoplethysmographic Pulse Amplitudes among Middle-to-Old Aged Individuals with or without Type 2 Diabetes]]>
http://www.mdpi.com/1099-4300/19/4/145
Multiscale cross-approximate entropy (MC-ApEn) between two different physiological signals could evaluate cardiovascular health in diabetes. Whether MC-ApEn analysis between two similar signals such as photoplethysmographic (PPG) pulse amplitudes of bilateral fingertips can reflect diabetes status is unknown. From a middle-to-old-aged population free of prior cardiovascular disease, we selected the unaffected (no type 2 diabetes, n = 36), the well-controlled diabetes (glycated hemoglobin (HbA1c) &lt; 8%, n = 30), and the poorly- controlled diabetes (HbA1c ≥ 8%, n = 26) groups. MC-ApEn indexes were calculated from simultaneous consecutive 1500 PPG pulse amplitudes signals of bilateral index fingertips. The average of scale factors 1–5 (MC-ApEnSS) and of scale factors 6–10 (MC-ApEnLS) were defined as the small- and large-scales MC-ApEn, respectively. The MC-ApEnLS index was highest in the unaffected, followed by the well-controlled diabetes, and then the poorly-controlled diabetes (0.70, 0.62, and 0.53; all paired p-values were &lt;0.05); in contrast, the MC-ApEnSS index did not differ between groups. Our findings suggested that the bilateral fingertips large-scale MC-ApEnLS index of PPG pulse amplitudes might be able to evaluate the glycemic status and detect subtle vascular disease in type 2 diabetes.Entropy2017-03-30194Article10.3390/e190401451451099-43002017-03-30doi: 10.3390/e19040145Hsien-Tsai WuCheng-Chan YangGen-Min LinBagus HaryadiShiao-Chiang ChuChieh-Ming YangCheuk-Kwan Sun<![CDATA[Entropy, Vol. 19, Pages 144: The Many Classical Faces of Quantum Structures]]>
http://www.mdpi.com/1099-4300/19/4/144
Interpretational problems with quantum mechanics can be phrased precisely by only talking about empirically accessible information. This prompts a mathematical reformulation of quantum mechanics in terms of classical mechanics. We survey this programme in terms of algebraic quantum theory.Entropy2017-03-29194Article10.3390/e190401441441099-43002017-03-29doi: 10.3390/e19040144Chris Heunen<![CDATA[Entropy, Vol. 19, Pages 143: Paradigms of Cognition]]>
http://www.mdpi.com/1099-4300/19/4/143
An abstract, quantitative theory which connects elements of information —key ingredients in the cognitive proces—is developed. Seemingly unrelated results are thereby unified. As an indication of this, consider results in classical probabilistic information theory involving information projections and so-called Pythagorean inequalities. This has a certain resemblance to classical results in geometry bearing Pythagoras’ name. By appealing to the abstract theory presented here, you have a common point of reference for these results. In fact, the new theory provides a general framework for the treatment of a multitude of global optimization problems across a range of disciplines such as geometry, statistics and statistical physics. Several applications are given, among them an “explanation” of Tsallis entropy is suggested. For this, as well as for the general development of the abstract underlying theory, emphasis is placed on interpretations and associated philosophical considerations. Technically, game theory is the key tool.Entropy2017-03-27194Article10.3390/e190401431431099-43002017-03-27doi: 10.3390/e19040143Flemming Topsøe<![CDATA[Entropy, Vol. 19, Pages 142: A Novel Framework for Shock Filter Using Partial Differential Equations]]>
http://www.mdpi.com/1099-4300/19/4/142
In dilation or erosion processes, a shock filter is widely used in signal enhancing or image deburring. Traditionally, sign function is employed in shock filtering for reweighting of edge-detection in images and decides whether a pixel should dilate to the local maximum or evolve to the local minimum. Some researchers replace sign function with tanh function or arctan function, trying to change the evolution tracks of the pixels when filtering is in progress. However, analysis here reveals that only function replacement does usually not work. This paper revisits first shock filters and their modifications. Then, a fuzzy shock filter is proposed after a membership function in a shock filter model is adopted to adjust the evolve rate of image pixels. The proposed filter is a parameter tuning system, which unites several formulations of shock filters into one fuzzy framework. Experimental results show that the new filter is flexible and robust and can converge fast.Entropy2017-03-26194Article10.3390/e190401421421099-43002017-03-26doi: 10.3390/e19040142Chunmei DuanHongqian Lu<![CDATA[Entropy, Vol. 19, Pages 141: Permutation Entropy for the Characterisation of Brain Activity Recorded with Magnetoencephalograms in Healthy Ageing]]>
http://www.mdpi.com/1099-4300/19/4/141
The characterisation of healthy ageing of the brain could help create a fingerprint of normal ageing that might assist in the early diagnosis of neurodegenerative conditions. This study examined changes in resting state magnetoencephalogram (MEG) permutation entropy due to age and gender in a sample of 220 healthy participants (98 males and 122 females, ages ranging between 7 and 84). Entropy was quantified using normalised permutation entropy and modified permutation entropy, with an embedding dimension of 5 and a lag of 1 as the input parameters for both algorithms. Effects of age were observed over the five regions of the brain, i.e., anterior, central, posterior, and left and right lateral, with the anterior and central regions containing the highest permutation entropy. Statistically significant differences due to age were observed in the different brain regions for both genders, with the evolutions described using the fitting of polynomial regressions. Nevertheless, no significant differences between the genders were observed across all ages. These results suggest that the evolution of entropy in the background brain activity, quantified with permutation entropy algorithms, might be considered an alternative illustration of a ‘nominal’ physiological rhythm.Entropy2017-03-25194Article10.3390/e190401411411099-43002017-03-25doi: 10.3390/e19040141Elizabeth ShumbayawondaAlberto FernándezMichael HughesDaniel Abásolo<![CDATA[Entropy, Vol. 19, Pages 137: Impact Location and Quantification on an Aluminum Sandwich Panel Using Principal Component Analysis and Linear Approximation with Maximum Entropy]]>
http://www.mdpi.com/1099-4300/19/4/137
To avoid structural failures it is of critical importance to detect, locate and quantify impact damage as soon as it occurs. This can be achieved by impact identification methodologies, which continuously monitor the structure, detecting, locating, and quantifying impacts as they occur. This article presents an improved impact identification algorithm that uses principal component analysis (PCA) to extract features from the monitored signals and an algorithm based on linear approximation with maximum entropy to estimate the impacts. The proposed methodology is validated with two experimental applications, which include an aluminum plate and an aluminum sandwich panel. The results are compared with those of other impact identification algorithms available in literature, demonstrating that the proposed method outperforms these algorithms.Entropy2017-03-25194Article10.3390/e190401371371099-43002017-03-25doi: 10.3390/e19040137Viviana MeruanePablo VélizEnrique López DroguettAlejandro Ortiz-Bernardin<![CDATA[Entropy, Vol. 19, Pages 140: Ionic Liquids Confined in Silica Ionogels: Structural, Thermal, and Dynamical Behaviors]]>
http://www.mdpi.com/1099-4300/19/4/140
Ionogels are porous monoliths providing nanometer-scale confinement of an ionic liquid within an oxide network. Various dynamic parameters and the detailed nature of phase transitions were investigated by using a neutron scattering technique, giving smaller time and space scales compared to earlier results from other techniques. By investigating the nature of the hydrogen mean square displacement (local mobility), qualitative information on diffusion and different phase transitions were obtained. The results presented herein show similar short-time molecular dynamics between pristine ionic liquids and confined ionic liquids through residence time and diffusion coefficient values, thus, explaining in depth the good ionic conductivity of ionogels.Entropy2017-03-24194Article10.3390/e190401401401099-43002017-03-24doi: 10.3390/e19040140Subhankur MitraCarole CerclierQuentin BerrodFilippo FerdeghiniRodrigo de Oliveira-SilvaPatrick JudeinsteinJean le BideauJean-Marc Zanotti<![CDATA[Entropy, Vol. 19, Pages 139: Tensor Singular Spectrum Decomposition Algorithm Based on Permutation Entropy for Rolling Bearing Fault Diagnosis]]>
http://www.mdpi.com/1099-4300/19/4/139
Mechanical vibration signal mapped into a high-dimensional space tends to exhibit a special distribution and movement characteristics, which can further reveal the dynamic behavior of the original time series. As the most natural representation of high-dimensional data, tensor can preserve the intrinsic structure of the data to the maximum extent. Thus, the tensor decomposition algorithm has broad application prospects in signal processing. High-dimensional tensor can be obtained from a one-dimensional vibration signal by using phase space reconstruction, which is called the tensorization of data. As a new signal decomposition method, tensor-based singular spectrum algorithm (TSSA) fully combines the advantages of phase space reconstruction and tensor decomposition. However, TSSA has some problems, mainly in estimating the rank of tensor and selecting the optimal reconstruction tensor. In this paper, the improved TSSA algorithm based on convex-optimization and permutation entropy (PE) is proposed. Firstly, aiming to accurately estimate the rank of tensor decomposition, this paper presents a convex optimization algorithm using non-convex penalty functions based on singular value decomposition (SVD). Then, PE is employed to evaluate the desired tensor and improve the denoising performance. In order to verify the effectiveness of proposed algorithm, both numerical simulation and experimental bearing failure data are analyzed.Entropy2017-03-23194Article10.3390/e190401391391099-43002017-03-23doi: 10.3390/e19040139Cancan YiYong LvMao GeHan XiaoXun Yu<![CDATA[Entropy, Vol. 19, Pages 136: The Quantum Harmonic Otto Cycle]]>
http://www.mdpi.com/1099-4300/19/4/136
The quantum Otto cycle serves as a bridge between the macroscopic world of heat engines and the quantum regime of thermal devices composed from a single element. We compile recent studies of the quantum Otto cycle with a harmonic oscillator as a working medium. This model has the advantage that it is analytically trackable. In addition, an experimental realization has been achieved, employing a single ion in a harmonic trap. The review is embedded in the field of quantum thermodynamics and quantum open systems. The basic principles of the theory are explained by a specific example illuminating the basic definitions of work and heat. The relation between quantum observables and the state of the system is emphasized. The dynamical description of the cycle is based on a completely positive map formulated as a propagator for each stroke of the engine. Explicit solutions for these propagators are described on a vector space of quantum thermodynamical observables. These solutions which employ different assumptions and techniques are compared. The tradeoff between power and efficiency is the focal point of finite-time-thermodynamics. The dynamical model enables the study of finite time cycles limiting time on the adiabatic and the thermalization times. Explicit finite time solutions are found which are frictionless (meaning that no coherence is generated), and are also known as shortcuts to adiabaticity.The transition from frictionless to sudden adiabats is characterized by a non-hermitian degeneracy in the propagator. In addition, the influence of noise on the control is illustrated. These results are used to close the cycles either as engines or as refrigerators. The properties of the limit cycle are described. Methods to optimize the power by controlling the thermalization time are also introduced. At high temperatures, the Novikov–Curzon–Ahlborn efficiency at maximum power is obtained. The sudden limit of the engine which allows finite power at zero cycle time is shown. The refrigerator cycle is described within the frictionless limit, with emphasis on the cooling rate when the cold bath temperature approaches zero.Entropy2017-03-23194Review10.3390/e190401361361099-43002017-03-23doi: 10.3390/e19040136Ronnie KosloffYair Rezek<![CDATA[Entropy, Vol. 19, Pages 138: Leveraging Receiver Message Side Information in Two-Receiver Broadcast Channels: A General Approach †]]>
http://www.mdpi.com/1099-4300/19/4/138
We consider two-receiver broadcast channels where each receiver may know a priori some of the messages requested by the other receiver as receiver message side information (RMSI). We devise a general approach to leverage RMSI in these channels. To this end, we first propose a pre-coding scheme considering the general message setup where each receiver requests both common and private messages and knows a priori part of the private message requested by the other receiver as RMSI. We then construct the transmission scheme of a two-receiver channel with RMSI by applying the proposed pre-coding scheme to the best transmission scheme for the channel without RMSI. To demonstrate the effectiveness of our approach, we apply our pre-coding scheme to three categories of the two-receiver discrete memoryless broadcast channel: (i) channel without state; (ii) channel with states known causally to the transmitter; and (iii) channel with states known non-causally to the transmitter. We then derive a unified inner bound for all three categories. We show that our inner bound is tight for some new cases in each of the three categories, as well as all cases whose capacity region was known previously.Entropy2017-03-23194Article10.3390/e190401381381099-43002017-03-23doi: 10.3390/e19040138Behzad AsadiLawrence OngSarah Johnson<![CDATA[Entropy, Vol. 19, Pages 119: Thermal Ratchet Effect in Confining Geometries]]>
http://www.mdpi.com/1099-4300/19/4/119
The stochastic model of the Feynman–Smoluchowski ratchet is proposed and solved using generalization of the Fick–Jacobs theory. The theory fully captures nonlinear response of the ratchet to the difference of heat bath temperatures. The ratchet performance is discussed using the mean velocity, the average heat flow between the two heat reservoirs and the figure of merit, which quantifies energetic cost for attaining a certain mean velocity. Limits of the theory are tested comparing its predictions to numerics. We also demonstrate connection between the ratchet effect emerging in the model and rotations of the probability current and explain direction of the mean velocity using simple discrete analogue of the model.Entropy2017-03-23194Article10.3390/e190401191191099-43002017-03-23doi: 10.3390/e19040119Viktor HolubecArtem RyabovMohammad YaghoubiMartin VargaAyub KhodaeeM. FoulaadvandPetr Chvosta<![CDATA[Entropy, Vol. 19, Pages 135: Structure and Dynamics of Water at Carbon-Based Interfaces]]>
http://www.mdpi.com/1099-4300/19/3/135
Water structure and dynamics are affected by the presence of a nearby interface. Here, first we review recent results by molecular dynamics simulations about the effect of different carbon-based materials, including armchair carbon nanotubes and a variety of graphene sheets—flat and with corrugation—on water structure and dynamics. We discuss the calculations of binding energies, hydrogen bond distributions, water’s diffusion coefficients and their relation with surface’s geometries at different thermodynamical conditions. Next, we present new results of the crystallization and dynamics of water in a rigid graphene sieve. In particular, we show that the diffusion of water confined between parallel walls depends on the plate distance in a non-monotonic way and is related to the water structuring, crystallization, re-melting and evaporation for decreasing inter-plate distance. Our results could be relevant in those applications where water is in contact with nanostructured carbon materials at ambient or cryogenic temperatures, as in man-made superhydrophobic materials or filtration membranes, or in techniques that take advantage of hydrated graphene interfaces, as in aqueous electron cryomicroscopy for the analysis of proteins adsorbed on graphene.Entropy2017-03-21193Article10.3390/e190301351351099-43002017-03-21doi: 10.3390/e19030135Jordi MartíCarles CaleroGiancarlo Franzese<![CDATA[Entropy, Vol. 19, Pages 134: Permutation Entropy: New Ideas and Challenges]]>
http://www.mdpi.com/1099-4300/19/3/134
Over recent years, some new variants of Permutation entropy have been introduced and applied to EEG analysis, including a conditional variant and variants using some additional metric information or being based on entropies that are different from the Shannon entropy. In some situations, it is not completely clear what kind of information the new measures and their algorithmic implementations provide. We discuss the new developments and illustrate them for EEG data.Entropy2017-03-21193Article10.3390/e190301341341099-43002017-03-21doi: 10.3390/e19030134Karsten KellerTeresa MangoldInga StolzJenna Werner<![CDATA[Entropy, Vol. 19, Pages 133: Spectral Entropy Parameters during Rapid Ventricular Pacing for Transcatheter Aortic Valve Implantation]]>
http://www.mdpi.com/1099-4300/19/3/133
The time-frequency balanced spectral entropy of the EEG is a monitoring technique measuring the level of hypnosis during general anesthesia. Two components of spectral entropy are calculated: state entropy (SE) and response entropy (RE). Transcatheter aortic valve implantation (TAVI) is a less invasive treatment for patients suffering from symptomatic aortic stenosis with contraindications for open heart surgery. The goal of hemodynamic management during the procedure is to achieve hemodynamic stability with exact blood pressure control and use of rapid ventricular pacing (RVP) that result in severe hypotension. The objective of this study was to examine how the spectral entropy values respond to RVP and other critical events during the TAVI procedure. Twenty one patients undergoing general anesthesia for TAVI were evaluated. The RVP was used twice during the procedure at a rate of 185 ± 9/min with durations of 16 ± 4 s (range 8–22 s) and 24 ± 6 s (range 18–39 s). The systolic blood pressure during RVP was under 50 ± 5 mmHg. Spectral entropy values SE were significantly declined during the RVP procedure, from 28 ± 13 to 23 ± 13 (p &lt; 0.003) and from 29 ± 12 to 24 ± 10 (p &lt; 0.001). The corresponding values for RE were 29 ± 13 vs. 24 ± 13 (p &lt; 0.006) and 30 ± 12 vs. 25 ± 10 (p &lt; 0.001). Both SE and RE values returned to the pre-RVP values after 1 min. Ultra-short hypotension during RVP changed the spectral entropy parameters, however these indices reverted rapidly to the same value before application of RVP.Entropy2017-03-20193Article10.3390/e190301331331099-43002017-03-20doi: 10.3390/e19030133Tadeusz MusialowiczAntti ValtolaMikko HippeläinenJari HalonenPasi Lahtinen<![CDATA[Entropy, Vol. 19, Pages 132: Discrepancies between Conventional Multiscale Entropy and Modified Short-Time Multiscale Entropy of Photoplethysmographic Pulse Signals in Middle- and Old- Aged Individuals with or without Diabetes]]>
http://www.mdpi.com/1099-4300/19/3/132
Multiscale entropy (MSE) of physiological signals may reflect cardiovascular health in diabetes. The classic MSE (cMSE) algorithm requires more than 750 signals for the calculations. The modified short-time MSE (sMSE) may have inconsistent outcomes compared with the cMSE at large time scales and in a disease status. Therefore, we compared the cMSE of 1500 (cMSE1500) consecutive and 1000 photoplethysmographic (PPG) pulse amplitudes with the sMSE of 500 PPG (sMSE500) pulse amplitudes of bilateral fingertips among middle- to old-aged individuals with or without type 2 diabetes. We discovered that cMSE1500 had the smallest value across scale factors 1–10, followed by cMSE1000, and then sMSE500 in both hands. The cMSE1500, cMSE1000 and sMSE500 did not differ at each scale factor in both hands of persons without diabetes and in the dominant hand of those with diabetes. In contrast, the sMSE500 differed at all scales 1–10 in the non-dominant hand with diabetes. In conclusion, autonomic dysfunction, prevalent in the non-dominant hand which had a low local physical activity in the person with diabetes, might be imprecisely evaluated by the sMSE; therefore, using more PPG signal numbers for the cMSE is preferred in such a situation.Entropy2017-03-18193Article10.3390/e190301321321099-43002017-03-18doi: 10.3390/e19030132Gen-Min LinBagus HaryadiChieh-Ming YangShiao-Chiang ChuCheng-Chan YangHsien-Tsai Wu<![CDATA[Entropy, Vol. 19, Pages 131: Information Submanifold Based on SPD Matrices and Its Applications to Sensor Networks]]>
http://www.mdpi.com/1099-4300/19/3/131
In this paper, firstly, manifoldPD(n)consisting of alln×nsymmetric positive-definite matrices is introduced based on matrix information geometry; Secondly, the geometrical structures of information submanifold ofPD(n)are presented including metric, geodesic and geodesic distance; Thirdly, the information resolution with sensor networks is presented by three classical measurement models based on information submanifold; Finally, the bearing-only tracking by single sensor is introduced by the Fisher information matrix. The preliminary analysis results introduced in this paper indicate that information submanifold is able to offer consistent and more comprehensive means to understand and solve sensor network problems for targets resolution and tracking, which are not easily handled by some conventional analysis methods.Entropy2017-03-17193Article10.3390/e190301311311099-43002017-03-17doi: 10.3390/e19030131Hao XuHuafei SunAung Win<![CDATA[Entropy, Vol. 19, Pages 130: Quantitative EEG Markers of Entropy and Auto Mutual Information in Relation to MMSE Scores of Probable Alzheimer’s Disease Patients]]>
http://www.mdpi.com/1099-4300/19/3/130
Analysis of nonlinear quantitative EEG (qEEG) markers describing complexity of signal in relation to severity of Alzheimer’s disease (AD) was the focal point of this study. In this study, 79 patients diagnosed with probable AD were recruited from the multi-centric Prospective Dementia Database Austria (PRODEM). EEG recordings were done with the subjects seated in an upright position in a resting state with their eyes closed. Models of linear regressions explaining disease severity, expressed in Mini Mental State Examination (MMSE) scores, were analyzed by the nonlinear qEEG markers of auto mutual information (AMI), Shannon entropy (ShE), Tsallis entropy (TsE), multiscale entropy (MsE), or spectral entropy (SpE), with age, duration of illness, and years of education as co-predictors. Linear regression models with AMI were significant for all electrode sites and clusters, where R 2 is 0.46 at the electrode site C3, 0.43 at Cz, F3, and central region, and 0.42 at the left region. MsE also had significant models at C3 with R 2 &gt; 0.40 at scales τ = 5 and τ = 6 . ShE and TsE also have significant models at T7 and F7 with R 2 &gt; 0.30 . Reductions in complexity, calculated by AMI, SpE, and MsE, were observed as the MMSE score decreased.Entropy2017-03-17193Article10.3390/e190301301301099-43002017-03-17doi: 10.3390/e19030130Carmina CoronelHeinrich GarnMarkus WaserManfred DeistlerThomas BenkePeter Dal-BiancoGerhard RansmayrStephan SeilerDieter GrosseggerReinhold Schmidt<![CDATA[Entropy, Vol. 19, Pages 129: Distance-Based Lempel–Ziv Complexity for the Analysis of Electroencephalograms in Patients with Alzheimer’s Disease]]>
http://www.mdpi.com/1099-4300/19/3/129
The analysis of electroencephalograms (EEGs) of patients with Alzheimer’s disease (AD) could contribute to the diagnosis of this dementia. In this study, a new non-linear signal processing metric, distance-based Lempel–Ziv complexity (dLZC), is introduced to characterise changes between pairs of electrodes in EEGs in AD. When complexity in each signal arises from different sub-sequences, dLZC would be greater than when similar sub-sequences are present in each signal. EEGs from 11 AD patients and 11 age-matched control subjects were analysed. The dLZC values for AD patients were lower than for control subjects for most electrode pairs, with statistically significant differences (p &lt; 0.01, Student’s t-test) in 17 electrode pairs in the distant left, local posterior left, and interhemispheric regions. Maximum diagnostic accuracies with leave-one-out cross-validation were 77.27% for subject-based classification and 78.25% for epoch-based classification. These findings suggest not only that EEGs from AD patients are less complex than those from controls, but also that the richness of the information contained in pairs of EEGs from patients is also lower than in age-matched controls. The analysis of EEGs in AD with dLZC may increase the insight into brain dysfunction, providing complementary information to that obtained with other complexity and synchrony methods.Entropy2017-03-17193Article10.3390/e190301291291099-43002017-03-17doi: 10.3390/e19030129Samantha SimonsDaniel Abásolo<![CDATA[Entropy, Vol. 19, Pages 127: Fractional Jensen–Shannon Analysis of the Scientific Output of Researchers in Fractional Calculus]]>
http://www.mdpi.com/1099-4300/19/3/127
This paper analyses the citation profiles of researchers in fractional calculus. Different metrics are used to quantify the dissimilarities between the data, namely the Canberra distance, and the classical and the generalized (fractional) Jensen–Shannon divergence. The information is then visualized by means of multidimensional scaling and hierarchical clustering. The mathematical tools and metrics allow for direct comparison and visualization of researchers based on their relative positioning and on patterns displayed in two- or three-dimensional maps.Entropy2017-03-17193Article10.3390/e190301271271099-43002017-03-17doi: 10.3390/e19030127José MachadoAntónio Mendes Lopes<![CDATA[Entropy, Vol. 19, Pages 128: Pairs Generating as a Consequence of the Fractal Entropy: Theory and Applications]]>
http://www.mdpi.com/1099-4300/19/3/128
In classical concepts, theoretical models are built assuming that the dynamics of the complex system’s stuctural units occur on continuous and differentiable motion variables. In reality, the dynamics of the natural complex systems are much more complicated. These difficulties can be overcome in a complementary approach, using the fractal concept and the corresponding non-differentiable theoretical model, such as the scale relativity theory or the extended scale relativity theory. Thus, using the last theory, fractal entropy through non-differentiable Lie groups was established and, moreover, the pairs generating mechanisms through fractal entanglement states were explained. Our model has implications in the dynamics of biological structures, in the form of the “chameleon-like” behavior of cholesterol.Entropy2017-03-17193Article10.3390/e190301281281099-43002017-03-17doi: 10.3390/e19030128Alexandru GrigoroviciElena BacaitaViorel PaunConstantin GreceaIrina ButucMaricel AgopOvidiu Popa<![CDATA[Entropy, Vol. 19, Pages 123: Friction, Free Axes of Rotation and Entropy]]>
http://www.mdpi.com/1099-4300/19/3/123
Friction forces acting on rotators may promote their alignment and therefore eliminate degrees of freedom in their movement. The alignment of rotators by friction force was shown by experiments performed with different spinners, demonstrating how friction generates negentropy in a system of rotators. A gas of rigid rotators influenced by friction force is considered. The orientational negentropy generated by a friction force was estimated with the Sackur-Tetrode equation. The minimal change in total entropy of a system of rotators, corresponding to their eventual alignment, decreases with temperature. The reported effect may be of primary importance for the phase equilibrium and motion of ubiquitous colloidal and granular systems.Entropy2017-03-17193Article10.3390/e190301231231099-43002017-03-17doi: 10.3390/e19030123Alexander KazachkovVictor MultanenViktor DanchukMark FrenkelEdward Bormashenko<![CDATA[Entropy, Vol. 19, Pages 121: Identity Based Generalized Signcryption Scheme in the Standard Model]]>
http://www.mdpi.com/1099-4300/19/3/121
Generalized signcryption (GSC) can adaptively work as an encryption scheme, a signature scheme or a signcryption scheme with only one algorithm. It is more suitable for the storage constrained setting. In this paper, motivated by Paterson–Schuldt’s scheme, based on bilinear pairing, we first proposed an identity based generalized signcryption (IDGSC) scheme in the standard model. To the best of our knowledge, it is the first scheme that is proven secure in the standard model.Entropy2017-03-17193Article10.3390/e190301211211099-43002017-03-17doi: 10.3390/e19030121Xiaoqin ShenYang MingJie Feng<![CDATA[Entropy, Vol. 19, Pages 126: Nonequilibrium Thermodynamics and Scale Invariance]]>
http://www.mdpi.com/1099-4300/19/3/126
A variant of continuous nonequilibrium thermodynamic theory based on the postulate of the scale invariance of the local relation between generalized fluxes and forces is proposed here. This single postulate replaces the assumptions on local equilibrium and on the known relation between thermodynamic fluxes and forces, which are widely used in classical nonequilibrium thermodynamics. It is shown here that such a modification not only makes it possible to deductively obtain the main results of classical linear nonequilibrium thermodynamics, but also provides evidence for a number of statements for a nonlinear case (the maximum entropy production principle, the macroscopic reversibility principle, and generalized reciprocity relations) that are under discussion in the literature.Entropy2017-03-16193Article10.3390/e190301261261099-43002017-03-16doi: 10.3390/e19030126Leonid M. MartyushevVladimir Celezneff<![CDATA[Entropy, Vol. 19, Pages 122: On Hölder Projective Divergences]]>
http://www.mdpi.com/1099-4300/19/3/122
We describe a framework to build distances by measuring the tightness of inequalities and introduce the notion of proper statistical divergences and improper pseudo-divergences. We then consider the Hölder ordinary and reverse inequalities and present two novel classes of Hölder divergences and pseudo-divergences that both encapsulate the special case of the Cauchy–Schwarz divergence. We report closed-form formulas for those statistical dissimilarities when considering distributions belonging to the same exponential family provided that the natural parameter space is a cone (e.g., multivariate Gaussians) or affine (e.g., categorical distributions). Those new classes of Hölder distances are invariant to rescaling and thus do not require distributions to be normalized. Finally, we show how to compute statistical Hölder centroids with respect to those divergences and carry out center-based clustering toy experiments on a set of Gaussian distributions which demonstrate empirically that symmetrized Hölder divergences outperform the symmetric Cauchy–Schwarz divergence.Entropy2017-03-16193Article10.3390/e190301221221099-43002017-03-16doi: 10.3390/e19030122Frank NielsenKe SunStéphane Marchand-Maillet<![CDATA[Entropy, Vol. 19, Pages 125: Packer Detection for Multi-Layer Executables Using Entropy Analysis]]>
http://www.mdpi.com/1099-4300/19/3/125
Packing algorithms are broadly used to avoid anti-malware systems, and the proportion of packed malware has been growing rapidly. However, just a few studies have been conducted on detection various types of packing algorithms in a systemic way. Following this understanding, we elaborate a method to classify packing algorithms of a given executable into three categories: single-layer packing, re-packing, or multi-layer packing. We convert entropy values of the executable file loaded into memory into symbolic representations, for which we used SAX (Symbolic Aggregate Approximation). Based on experiments of 2196 programs and 19 packing algorithms, we identify that precision (97.7%), accuracy (97.5%), and recall ( 96.8%) of our method are respectively high to confirm that entropy analysis is applicable in identifying packing algorithms.Entropy2017-03-16193Article10.3390/e190301251251099-43002017-03-16doi: 10.3390/e19030125Munkhbayar Bat-ErdeneTaebeom KimHyundo ParkHeejo Lee<![CDATA[Entropy, Vol. 19, Pages 124: Witnessing Multipartite Entanglement by Detecting Asymmetry]]>
http://www.mdpi.com/1099-4300/19/3/124
The characterization of quantum coherence in the context of quantum information theory and its interplay with quantum correlations is currently subject of intense study. Coherence in a Hamiltonian eigenbasis yields asymmetry, the ability of a quantum system to break a dynamical symmetry generated by the Hamiltonian. We here propose an experimental strategy to witness multipartite entanglement in many-body systems by evaluating the asymmetry with respect to an additive Hamiltonian. We test our scheme by simulating asymmetry and entanglement detection in a three-qubit Greenberger–Horne–Zeilinger (GHZ) diagonal state.Entropy2017-03-16193Article10.3390/e190301241241099-43002017-03-16doi: 10.3390/e19030124Davide GirolamiBenjamin Yadin<![CDATA[Entropy, Vol. 19, Pages 120: Variational Principle for Relative Tail Pressure]]>
http://www.mdpi.com/1099-4300/19/3/120
We introduce the relative tail pressure to establish a variational principle for continuous bundle random dynamical systems. We also show that the relative tail pressure is conserved by the principal extension.Entropy2017-03-15193Article10.3390/e190301201201099-43002017-03-15doi: 10.3390/e19030120Xianfeng MaErcai Chen<![CDATA[Entropy, Vol. 19, Pages 118: Thermoeconomic Optimization of an Irreversible Novikov Plant Model under Different Regimes of Performance]]>
http://www.mdpi.com/1099-4300/19/3/118
The so-called Novikov power plant model has been widely used to represent some actual power plants, such as nuclear electric power generators. In the present work, a thermo-economic study of a Novikov power plant model is presented under three different regimes of performance: maximum power (MP), maximum ecological function (ME) and maximum efficient power (EP). In this study, different heat transfer laws are used: The Newton’s law of cooling, the Stefan–Boltzmann radiation law, the Dulong–Petit’s law and another phenomenological heat transfer law. For the thermoeconomic optimization of power plant models, a benefit function defined as the quotient of an objective function and the total economical costs is commonly employed. Usually, the total costs take into account two contributions: a cost related to the investment and another stemming from the fuel consumption. In this work, a new cost associated to the maintenance of the power plant is also considered. With these new total costs, it is shown that under the maximum ecological function regime the plant improves its economic and energetic performance in comparison with the other two regimes. The methodology used in this paper is within the context of finite-time thermodynamics.Entropy2017-03-15193Article10.3390/e190301181181099-43002017-03-15doi: 10.3390/e19030118Juan Pacheco-PaezFernando Angulo-BrownMarco Barranco-Jiménez<![CDATA[Entropy, Vol. 19, Pages 117: Specific Emitter Identification Based on the Natural Measure]]>
http://www.mdpi.com/1099-4300/19/3/117
Specific emitter identification (SEI) techniques are often used in civilian and military spectrum-management operations, and they are also applied to support the security and authentication of wireless communication. In this letter, a new SEI method based on the natural measure of the one-dimensional component of the chaotic system is proposed. We find that the natural measures of the one-dimensional components of higher dimensional systems exist and that they are quite diverse for different systems. Based on this principle, the natural measure is used as an RF fingerprint in this letter. The natural measure can solve the problems caused by a small amount of data and a low sample rate. The Kullback–Leibler divergence is used to quantify the difference between the natural measures obtained from diverse emitters and classify them. The data obtained from real application are exploited to test the validity of the proposed method. Experimental results show that the proposed method is not only easy to operate, but also quite effective, even though the amount of data is small and the sample rate is low.Entropy2017-03-15193Letter10.3390/e190301171171099-43002017-03-15doi: 10.3390/e19030117Yongqiang JiaShengli ZhuLu Gan<![CDATA[Entropy, Vol. 19, Pages 115: A Model of Mechanothermodynamic Entropy in Tribology]]>
http://www.mdpi.com/1099-4300/19/3/115
A brief analysis of entropy concepts in continuum mechanics and thermodynamics is presented. The methods of accounting for friction, wear and fatigue processes in the calculation of the thermodynamic entropy are described. It is shown that these and other damage processes of solids are more adequately described by tribo-fatigue entropy. It was established that mechanothermodynamic entropy calculated as the sum of interacting thermodynamic and tribo-fatigue entropy components has the most general character. Examples of usage (application) of tribo-fatigue and mechanothermodynamic entropies for practical analysis of wear and fatigue processes are given.Entropy2017-03-14193Article10.3390/e190301151151099-43002017-03-14doi: 10.3390/e19030115Leonid SosnovskiySergei Sherbakov<![CDATA[Entropy, Vol. 19, Pages 116: Fluctuation-Driven Transport in Biological Nanopores. A 3D Poisson–Nernst–Planck Study]]>
http://www.mdpi.com/1099-4300/19/3/116
Living systems display a variety of situations in which non-equilibrium fluctuations couple to certain protein functions yielding astonishing results. Here we study the bacterial channel OmpF under conditions similar to those met in vivo, where acidic resistance mechanisms are known to yield oscillations in the electric potential across the cell membrane. We use a three-dimensional structure-based theoretical approach to assess the possibility of obtaining fluctuation-driven transport. Our calculations show that remarkably high voltages would be necessary to observe the actual transport of ions against their concentration gradient. The reasons behind this are the mild selectivity of this bacterial pore and the relatively low efficiencies of the oscillating signals characteristic of membrane cells (random telegraph noise and thermal noise).Entropy2017-03-14193Article10.3390/e190301161161099-43002017-03-14doi: 10.3390/e19030116Marcel Aguilella-ArzoMaría Queralt-MartínMaría-Lidón LopezAntonio Alcaraz<![CDATA[Entropy, Vol. 19, Pages 113: Recoverable Random Numbers in an Internet of Things Operating System]]>
http://www.mdpi.com/1099-4300/19/3/113
Over the past decade, several security issues with Linux Random Number Generator (LRNG) on PCs and Androids have emerged. The main problem involves the process of entropy harvesting, particularly at boot time. An entropy source in the input pool of LRNG is not transferred into the non-blocking output pool if the entropy counter of the input pool is less than 192 bits out of 4098 bits. Because the entropy estimation of LRNG is highly conservative, the process may require more than one minute for starting the transfer. Furthermore, the design principle of the estimation algorithm is not only heuristic but also unclear. Recently, Google released an Internet of Things (IoT) operating system called Brillo based on the Linux kernel. We analyze the behavior of the random number generator in Brillo, which inherits that of LRNG. In the results, we identify two features that enable recovery of random numbers. With these features, we demonstrate that random numbers of 700 bytes at boot time can be recovered with the success probability of 90% by using time complexity for 5.20 × 2 40 trials. Therefore, the entropy of random numbers of 700 bytes is merely about 43 bits. Since the initial random numbers are supposed to be used for sensitive security parameters, such as stack canary and key derivation, our observation can be applied to practical attacks against cryptosystem.Entropy2017-03-13193Article10.3390/e190301131131099-43002017-03-13doi: 10.3390/e19030113Taeill YooJu-Sung KangYongjin Yeom<![CDATA[Entropy, Vol. 19, Pages 112: Quantum Probabilities as Behavioral Probabilities]]>
http://www.mdpi.com/1099-4300/19/3/112
We demonstrate that behavioral probabilities of human decision makers share many common features with quantum probabilities. This does not imply that humans are some quantum objects, but just shows that the mathematics of quantum theory is applicable to the description of human decision making. The applicability of quantum rules for describing decision making is connected with the nontrivial process of making decisions in the case of composite prospects under uncertainty. Such a process involves deliberations of a decision maker when making a choice. In addition to the evaluation of the utilities of considered prospects, real decision makers also appreciate their respective attractiveness. Therefore, human choice is not based solely on the utility of prospects, but includes the necessity of resolving the utility-attraction duality. In order to justify that human consciousness really functions similarly to the rules of quantum theory, we develop an approach defining human behavioral probabilities as the probabilities determined by quantum rules. We show that quantum behavioral probabilities of humans do not merely explain qualitatively how human decisions are made, but they predict quantitative values of the behavioral probabilities. Analyzing a large set of empirical data, we find good quantitative agreement between theoretical predictions and observed experimental data.Entropy2017-03-13193Article10.3390/e190301121121099-43002017-03-13doi: 10.3390/e19030112Vyacheslav YukalovDidier Sornette<![CDATA[Entropy, Vol. 19, Pages 111: The Two-Time Interpretation and Macroscopic Time-Reversibility]]>
http://www.mdpi.com/1099-4300/19/3/111
The two-state vector formalism motivates a time-symmetric interpretation of quantum mechanics that entails a resolution of the measurement problem. We revisit a post-selection-assisted collapse model previously suggested by us, claiming that unlike the thermodynamic arrow of time, it can lead to reversible dynamics at the macroscopic level. In addition, the proposed scheme enables us to characterize the classical-quantum boundary. We discuss the limitations of this approach and its broad implications for other areas of physics.Entropy2017-03-12193Article10.3390/e190301111111099-43002017-03-12doi: 10.3390/e19030111Yakir AharonovEliahu CohenTomer Landsberger<![CDATA[Entropy, Vol. 19, Pages 110: The Gibbs Paradox, the Landauer Principle and the Irreversibility Associated with Tilted Observers]]>
http://www.mdpi.com/1099-4300/19/3/110
It is well known that, in the context of General Relativity, some spacetimes, when described by a congruence of comoving observers, may consist of a distribution of a perfect (non–dissipative) fluid, whereas the same spacetime as seen by a “tilted” (Lorentz–boosted) congruence of observers may exhibit the presence of dissipative processes. As we shall see, the appearance of entropy-producing processes are related to the high dependence of entropy on the specific congruence of observers. This fact is well illustrated by the Gibbs paradox. The appearance of such dissipative processes, as required by the Landauer principle, are necessary in order to erase the different amount of information stored by comoving observers, with respect to tilted ones.Entropy2017-03-11193Article10.3390/e190301101101099-43002017-03-11doi: 10.3390/e19030110Luis Herrera<![CDATA[Entropy, Vol. 19, Pages 108: Entropy Generation Analysis and Performance Evaluation of Turbulent Forced Convective Heat Transfer to Nanofluids]]>
http://www.mdpi.com/1099-4300/19/3/108
The entropy generation analysis of fully turbulent convective heat transfer to nanofluids in a circular tube is investigated numerically using the Reynolds Averaged Navier–Stokes (RANS) model. The nanofluids with particle concentration of 0%, 1%, 2%, 4% and 6% are treated as single phases of effective properties. The uniform heat flux is enforced at the tube wall. To confirm the validity of the numerical approach, the results have been compared with empirical correlations and analytical formula. The self-similarity profiles of local entropy generation are also studied, in which the peak values of entropy generation by direct dissipation, turbulent dissipation, mean temperature gradients and fluctuating temperature gradients for different Reynolds number as well as different particle concentration are observed. In addition, the effects of Reynolds number, volume fraction of nanoparticles and heat flux on total entropy generation and Bejan number are discussed. In the results, the intersection points of total entropy generation for water and four nanofluids are observed, when the entropy generation decrease before the intersection and increase after the intersection as the particle concentration increases. Finally, by definition of Ep, which combines the first law and second law of thermodynamics and attributed to evaluate the real performance of heat transfer processes, the optimal Reynolds number Reop corresponding to the best performance and the advisable Reynolds number Read providing the appropriate Reynolds number range for nanofluids in convective heat transfer can be determined.Entropy2017-03-11193Article10.3390/e190301081081099-43002017-03-11doi: 10.3390/e19030108Yu JiHao-Chun ZhangXie YangLei Shi<![CDATA[Entropy, Vol. 19, Pages 109: Formulation of Exergy Cost Analysis to Graph-Based Thermal Network Models]]>
http://www.mdpi.com/1099-4300/19/3/109
Information from exergy cost analysis can be effectively used in the design and management of modern district heating networks (DHNs) since it allows to properly account for the irreversibilities in energy conversion and distribution. Nevertheless, this requires the development of suitable graph-based approaches that are able to effectively consider the network topology and the variations of the physical properties of the heating fluid on a time-dependent basis. In this work, a formulation of exergetic costs suitable for large graph-based networks is proposed, which is consistent with the principles of exergetic costing. In particular, the approach is more compact in comparison to straightforward approaches of exergetic cost formulation available in the literature, especially when applied to fluid networks. Moreover, the proposed formulation is specifically considering transient operating conditions, which is a crucial feature and a necessity for the analysis of future DHNs. Results show that transient effects of the thermodynamic behavior are not negligible for exergy cost analysis, while this work offers a coherent approach to quantify them.Entropy2017-03-10193Article10.3390/e190301091091099-43002017-03-10doi: 10.3390/e19030109Stefano CossElisa GuelpaEtienne LetournelOlivier Le-CorreVittorio Verda<![CDATA[Entropy, Vol. 19, Pages 107: Physical Intelligence and Thermodynamic Computing]]>
http://www.mdpi.com/1099-4300/19/3/107
This paper proposes that intelligent processes can be completely explained by thermodynamic principles. They can equally be described by information-theoretic principles that, from the standpoint of the required optimizations, are functionally equivalent. The underlying theory arises from two axioms regarding distinguishability and causality. Their consequence is a theory of computation that applies to the only two kinds of physical processes possible—those that reconstruct the past and those that control the future. Dissipative physical processes fall into the first class, whereas intelligent ones comprise the second. The first kind of process is exothermic and the latter is endothermic. Similarly, the first process dumps entropy and energy to its environment, whereas the second reduces entropy while requiring energy to operate. It is shown that high intelligence efficiency and high energy efficiency are synonymous. The theory suggests the usefulness of developing a new computing paradigm called Thermodynamic Computing to engineer intelligent processes. The described engineering formalism for the design of thermodynamic computers is a hybrid combination of information theory and thermodynamics. Elements of the engineering formalism are introduced in the reverse-engineer of a cortical neuron. The cortical neuron provides perhaps the simplest and most insightful example of a thermodynamic computer possible. It can be seen as a basic building block for constructing more intelligent thermodynamic circuits.Entropy2017-03-09193Article10.3390/e190301071071099-43002017-03-09doi: 10.3390/e19030107Robert Fry<![CDATA[Entropy, Vol. 19, Pages 106: On Quantum Collapse as a Basis for the Second Law of Thermodynamics]]>
http://www.mdpi.com/1099-4300/19/3/106
It was first suggested by David Z. Albert that the existence of a real, physical non-unitary process (i.e., “collapse”) at the quantum level would yield a complete explanation for the Second Law of Thermodynamics (i.e., the increase in entropy over time). The contribution of such a process would be to provide a physical basis for the ontological indeterminacy needed to derive the irreversible Second Law against a backdrop of otherwise reversible, deterministic physical laws. An alternative understanding of the source of this possible quantum “collapse” or non-unitarity is presented herein, in terms of the Transactional Interpretation (TI). The present model provides a specific physical justification for Boltzmann’s often-criticized assumption of molecular randomness (Stosszahlansatz), thereby changing its status from an ad hoc postulate to a theoretically grounded result, without requiring any change to the basic quantum theory. In addition, it is argued that TI provides an elegant way of reconciling, via indeterministic collapse, the time-reversible Liouville evolution with the time-irreversible evolution inherent in so-called “master equations” that specify the changes in occupation of the various possible states in terms of the transition rates between them. The present model is contrasted with the Ghirardi–Rimini–Weber (GRW) “spontaneous collapse” theory previously suggested for this purpose by Albert.Entropy2017-03-09193Article10.3390/e190301061061099-43002017-03-09doi: 10.3390/e19030106Ruth Kastner<![CDATA[Entropy, Vol. 19, Pages 105: Brownian Dynamics Computational Model of Protein Diffusion in Crowded Media with Dextran Macromolecules as Obstacles]]>
http://www.mdpi.com/1099-4300/19/3/105
The high concentration of macromolecules (i.e., macromolecular crowding) in cellular environments leads to large quantitative effects on the dynamic and equilibrium biological properties. These effects have been experimentally studied using inert macromolecules to mimic a realistic cellular medium. In this paper, two different experimental in vitro systems of diffusing proteins which use dextran macromolecules as obstacles are computationally analyzed. A new model for dextran macromolecules based on effective radii accounting for macromolecular compression induced by crowding is proposed. The obtained results for the diffusion coefficient and the anomalous diffusion exponent exhibit good qualitative and generally good quantitative agreement with experiments. Volume fraction and hydrodynamic interactions are found to be crucial to describe the diffusion coefficient decrease in crowded media. However, no significant influence of the hydrodynamic interactions in the anomalous diffusion exponent is found.Entropy2017-03-09193Article10.3390/e190301051051099-43002017-03-09doi: 10.3390/e19030105Pablo BlancoMireia ViaJosep GarcésSergio MadurgaFrancesc Mas<![CDATA[Entropy, Vol. 19, Pages 101: “Over-Learning” Phenomenon of Wavelet Neural Networks in Remote Sensing Image Classifications with Different Entropy Error Functions]]>
http://www.mdpi.com/1099-4300/19/3/101
Artificial neural networks are widely applied for prediction, function simulation, and data classification. Among these applications, the wavelet neural network is widely used in image classification problems due to its advantages of high approximation capabilities, fault-tolerant capabilities, learning capacity, its ability to effectively overcome local minimization issues, and so on. The error function of a network is critical to determine the convergence, stability, and classification accuracy of a neural network. The selection of the error function directly determines the network’s performance. Different error functions will correspond with different minimum error values in training samples. With the decrease of network errors, the accuracy of the image classification is increased. However, if the image classification accuracy is difficult to improve upon, or is even decreased with the decreasing of the errors, then this indicates that the network has an “over-learning” phenomenon, which is closely related to the selection of the function errors. With regards to remote sensing data, it has not yet been reported whether there have been studies conducted regarding the “over-learning” phenomenon, as well as the relationship between the “over-learning” phenomenon and error functions. This study takes SAR, hyper-spectral, high-resolution, and multi-spectral images as data sources, in order to comprehensively and systematically analyze the possibility of an “over-learning” phenomenon in the remote sensing images from the aspects of image characteristics and neural network. Then, this study discusses the impact of three typical entropy error functions (NB, CE, and SH) on the “over-learning” phenomenon of a network. The experimental results show that the “over-learning” phenomenon may be caused only when there is a strong separability between the ground features, a low image complexity, a small image size, and a large number of hidden nodes. The SH entropy error function in that case will show a good “over-learning” resistance ability. However, for remote sensing image classification, the “over-learning” phenomenon will not be easily caused in most cases, due to the complexity of the image itself, and the diversity of the ground features. In that case, the NB and CE entropy error network mainly show a good stability. Therefore, a blind selection of a SH entropy error function with a high “over-learning” resistance ability from the wavelet neural network classification of the remote sensing image will only decrease the classification accuracy of the remote sensing image. It is therefore recommended to use an NB or CE entropy error function with a stable learning effect.Entropy2017-03-08193Article10.3390/e190301011011099-43002017-03-08doi: 10.3390/e19030101Dongmei SongYajie ZhangXinjian ShanJianyong CuiHuisheng Wu<![CDATA[Entropy, Vol. 19, Pages 104: Complexity and Vulnerability Analysis of the C. Elegans Gap Junction Connectome]]>
http://www.mdpi.com/1099-4300/19/3/104
We apply a network complexity measure to the gap junction network of the somatic nervous system of C. elegans and find that it possesses a much higher complexity than we might expect from its degree distribution alone. This “excess” complexity is seen to be caused by a relatively small set of connections involving command interneurons. We describe a method which progressively deletes these “complexity-causing” connections, and find that when these are eliminated, the network becomes significantly less complex than a random network. Furthermore, this result implicates the previously-identified set of neurons from the synaptic network’s “rich club” as the structural components encoding the network’s excess complexity. This study and our method thus support a view of the gap junction Connectome as consisting of a rather low-complexity network component whose symmetry is broken by the unique connectivities of singularly important rich club neurons, sharply increasing the complexity of the network.Entropy2017-03-08193Article10.3390/e190301041041099-43002017-03-08doi: 10.3390/e19030104James Kunert-GrafNikita SakhanenkoDavid Galas<![CDATA[Entropy, Vol. 19, Pages 103: Analysis of the Temporal Structure Evolution of Physical Systems with the Self-Organising Tree Algorithm (SOTA): Application for Validating Neural Network Systems on Adaptive Optics Data before On-Sky Implementation]]>
http://www.mdpi.com/1099-4300/19/3/103
Adaptive optics reconstructors are needed to remove the effects of atmospheric distortion in optical systems of large telescopes. The use of reconstructors based on neural networks has been proved successful in recent times. Some of their properties require a specific characterization. A procedure, based in time series clustering algorithms, is presented to characterize the relationship between temporal structure of inputs and outputs, through analyzing the data provided by the system. This procedure is used to compare the performance of a reconstructor based in Artificial Neural Networks, with one that shows promising results, but is still in development, in order to corroborate its suitability previously to its implementation in real applications. Also, this procedure could be applied with other physical systems that also have evolution in time.Entropy2017-03-07193Article10.3390/e190301031031099-43002017-03-07doi: 10.3390/e19030103Sergio Suárez GómezJesús Santos RodríguezFrancisco Iglesias RodríguezFrancisco de Cos Juez<![CDATA[Entropy, Vol. 19, Pages 102: Emergence of Distinct Spatial Patterns in Cellular Automata with Inertia: A Phase Transition-Like Behavior]]>
http://www.mdpi.com/1099-4300/19/3/102
We propose a Cellular Automata (CA) model in which three ubiquitous and relevant processes in nature are present, namely, spatial competition, distinction between dynamically stronger and weaker agents and the existence of an inner resistance to changes in the actual state S n (=−1,0,+1) of each CA lattice cell n (which we call inertia). Considering ensembles of initial lattices, we study the average properties of the CA final stationary configuration structures resulting from the system time evolution. Assuming the inertia a (proper) control parameter, we identify qualitative changes in the CA spatial patterns resembling usual phase transitions. Interestingly, some of the observed features may be associated with continuous transitions (critical phenomena). However, certain quantities seem to present jumps, typical of discontinuous transitions. We argue that these apparent contradictory findings can be attributed to the inertia parameter’s discrete character. Along the work, we also briefly discuss a few potential applications for the present CA formulation.Entropy2017-03-07193Article10.3390/e190301021021099-43002017-03-07doi: 10.3390/e19030102Klaus KramerMarlus KoehlerCarlos FioreMarcos da Luz<![CDATA[Entropy, Vol. 19, Pages 100: Normalized Unconditional ϵ-Security of Private-Key Encryption]]>
http://www.mdpi.com/1099-4300/19/3/100
In this paper we introduce two normalized versions of non-perfect security for private-key encryption: one version in the framework of Shannon entropy, another version in the framework of Kolmogorov complexity. We prove the lower bound on either key entropy or key size for these models and study the relations between these normalized security notions.Entropy2017-03-07193Article10.3390/e190301001001099-43002017-03-07doi: 10.3390/e19030100Lvqing BiSongsong DaiBo Hu<![CDATA[Entropy, Vol. 19, Pages 99: Tunable-Q Wavelet Transform Based Multivariate Sub-Band Fuzzy Entropy with Application to Focal EEG Signal Analysis]]>
http://www.mdpi.com/1099-4300/19/3/99
This paper analyses the complexity of multivariate electroencephalogram (EEG) signals in different frequency scales for the analysis and classification of focal and non-focal EEG signals. The proposed multivariate sub-band entropy measure has been built based on tunable-Q wavelet transform (TQWT). In the field of multivariate entropy analysis, recent studies have performed analysis of biomedical signals with a multi-level filtering approach. This approach has become a useful tool for measuring inherent complexity of the biomedical signals. However, these methods may not be well suited for quantifying the complexity of the individual multivariate sub-bands of the analysed signal. In this present study, we have tried to resolve this difficulty by employing TQWT for analysing the sub-band signals of the analysed multivariate signal. It should be noted that higher value of Q factor is suitable for analysing signals with oscillatory nature, whereas the lower value of Q factor is suitable for analysing signals with non-oscillatory transients in nature. Moreover, with an increased number of sub-bands and a higher value of Q-factor, a reasonably good resolution can be achieved simultaneously in high and low frequency regions of the considered signals. Finally, we have employed multivariate fuzzy entropy (mvFE) to the multivariate sub-band signals obtained from the analysed signal. The proposed Q-based multivariate sub-band entropy has been studied on the publicly available bivariate Bern Barcelona focal and non-focal EEG signals database to investigate the statistical significance of the proposed features in different time segmented signals. Finally, the features are fed to random forest and least squares support vector machine (LS-SVM) classifiers to select the best classifier. Our method has achieved the highest classification accuracy of 84.67% in classifying focal and non-focal EEG signals with LS-SVM classifier. The proposed multivariate sub-band fuzzy entropy can also be applied to measure complexity of other multivariate biomedical signals.Entropy2017-03-03193Article10.3390/e19030099991099-43002017-03-03doi: 10.3390/e19030099Abhijit BhattacharyyaRam PachoriU. Acharya<![CDATA[Entropy, Vol. 19, Pages 98: Quantum Theory from Rules on Information Acquisition]]>
http://www.mdpi.com/1099-4300/19/3/98
We summarize a recent reconstruction of the quantum theory of qubits from rules constraining an observer’s acquisition of information about physical systems. This review is accessible and fairly self-contained, focusing on the main ideas and results and not the technical details. The reconstruction offers an informational explanation for the architecture of the theory and speciﬁcally for its correlation structure. In particular, it explains entanglement, monogamy and non-locality compellingly from limited accessible information and complementarity. As a by-product, it also unravels new ‘conserved informational charges’ from complementarity relations that characterize the unitary group and the set of pure states.Entropy2017-03-03193Review10.3390/e19030098981099-43002017-03-03doi: 10.3390/e19030098Philipp Höhn<![CDATA[Entropy, Vol. 19, Pages 97: Taxis of Artificial Swimmers in a Spatio-Temporally Modulated Activation Medium]]>
http://www.mdpi.com/1099-4300/19/3/97
Contrary to microbial taxis, where a tactic response to external stimuli is controlled by complex chemical pathways acting like sensor-actuator loops, taxis of artificial microswimmers is a purely stochastic effect associated with a non-uniform activation of the particles’ self-propulsion. We study the tactic response of such swimmers in a spatio-temporally modulated activating medium by means of both numerical and analytical techniques. In the opposite limits of very fast and very slow rotational particle dynamics, we obtain analytic approximations that closely reproduce the numerical description. A swimmer drifts on average either parallel or anti-parallel to the propagation direction of the activating pulses, depending on their speed and width. The drift in line with the pulses is solely determined by the finite persistence length of the active Brownian motion performed by the swimmer, whereas the drift in the opposite direction results from the combination of the ballistic and diffusive properties of the swimmer’s dynamics.Entropy2017-03-03193Article10.3390/e19030097971099-43002017-03-03doi: 10.3390/e19030097Alexander GeiselerPeter HänggiFabio Marchesoni<![CDATA[Entropy, Vol. 19, Pages 96: Effect of a Magnetic Quadrupole Field on Entropy Generation in Thermomagnetic Convection of Paramagnetic Fluid with and without a Gravitational Field]]>
http://www.mdpi.com/1099-4300/19/3/96
Entropy generation for a paramagnetic fluid in a square enclosure with thermomagnetic convection is numerically investigated under the influence of a magnetic quadrupole field. The magnetic field is calculated using the scalar magnetic potential approach. The finite-volume method is applied to solve the coupled equation for flow, energy, and entropy generation. Simulations are conducted to obtain streamlines, isotherms, Nusselt numbers, entropy generation, and the Bejan number for various magnetic forces (1 ≤ γ ≤ 100) and Rayleigh numbers (104 ≤ Ra ≤ 106). In the absence of gravity, the total entropy generation increases with the increasing magnetic field number, but the average Bejan number decreases. In the gravitational field, the total entropy generation respects the insensitive trend to the change of the magnetic force for low Rayleigh numbers, while it changes significantly for high Rayleigh numbers. When the magnetic field enhances, the share of viscous dissipation in energy losses keeps growing.Entropy2017-03-03193Article10.3390/e19030096961099-43002017-03-03doi: 10.3390/e19030096Er ShiXiaoqin SunYecong HeChangwei Jiang<![CDATA[Entropy, Vol. 19, Pages 95: On the Complexity Reduction of Coding WSS Vector Processes by Using a Sequence of Block Circulant Matrices]]>
http://www.mdpi.com/1099-4300/19/3/95
In the present paper, we obtain a result on the rate-distortion function (RDF) of wide sense stationary (WSS) vector processes that allows us to reduce the complexity of coding those processes. To achieve this result, we propose a sequence of block circulant matrices. In addition, we use the proposed sequence to reduce the complexity of filtering WSS vector processes.Entropy2017-03-02193Article10.3390/e19030095951099-43002017-03-02doi: 10.3390/e19030095Jesús Gutiérrez-GutiérrezMarta Zárraga-RodríguezXabier InsaustiBjørn Hogstad<![CDATA[Entropy, Vol. 19, Pages 94: Numerical Study of the Magnetic Field Effects on the Heat Transfer and Entropy Generation Aspects of a Power Law Fluid over an Axisymmetric Stretching Plate Structure]]>
http://www.mdpi.com/1099-4300/19/3/94
Numerical investigation of the effects of magnetic field strength, thermal radiation, Joule heating, and viscous heating on a forced convective flow of a non-Newtonian, incompressible power law fluid in an axisymmetric stretching sheet with variable temperature wall is accomplished. The power law shear thinning viscosity-shear rate model for the anisotropic solutions and the Rosseland approximation for the thermal radiation through a highly absorbing medium are considered. The temperature dependent heat sources, Joule heating, and viscous heating are considered as the source terms in the energy balance. The non-dimensional boundary layer equations are solved numerically in terms of similarity variable. A parameter study on the Nusselt number, viscous components of entropy generation, and thermal components of entropy generation in fluid is performed as a function of thermal radiation parameter (0 to 2), Brinkman number (0 to 10), Prandtl number (0 to 10), Hartmann number (0 to 1), power law index (0 to 1), and heat source coefficient (0 to 0.1).Entropy2017-03-01193Article10.3390/e19030094941099-43002017-03-01doi: 10.3390/e19030094Payam HooshmandHamed GatabiNavid BagheriIsma’il PirzadehAshkan HesabiMohammad Abdollahzadeh JamalabadiMajid Oveisi<![CDATA[Entropy, Vol. 19, Pages 91: On the Entropy of Deformed Phase Space Black Hole and the Cosmological Constant]]>
http://www.mdpi.com/1099-4300/19/3/91
In this paper we study the effects of noncommutative phase space deformations on the Schwarzschild black hole. This idea has been previously studied in Friedmann–Robertson–Walker (FRW) cosmology, where this “noncommutativity” provides a simple mechanism that can explain the origin of the cosmological constant. In this paper, we obtain the same relationship between the cosmological constant and the deformation parameter that appears in deformed phase space cosmology, but in the context of the deformed phase space black holes. This was achieved by comparing the entropy of the deformed Schwarzschild black hole with the entropy of the Schwarzschild–de Sitter black hole.Entropy2017-02-28193Article10.3390/e19030091911099-43002017-02-28doi: 10.3390/e19030091Andrés Crespo-HernándezEri Mena-BarbozaMiguel Sabido<![CDATA[Entropy, Vol. 19, Pages 92: Use of Accumulated Entropies for Automated Detection of Congestive Heart Failure in Flexible Analytic Wavelet Transform Framework Based on Short-Term HRV Signals]]>
http://www.mdpi.com/1099-4300/19/3/92
In the present work, an automated method to diagnose Congestive Heart Failure (CHF) using Heart Rate Variability (HRV) signals is proposed. This method is based on Flexible Analytic Wavelet Transform (FAWT), which decomposes the HRV signals into different sub-band signals. Further, Accumulated Fuzzy Entropy (AFEnt) and Accumulated Permutation Entropy (APEnt) are computed over cumulative sums of these sub-band signals. This provides complexity analysis using fuzzy and permutation entropies at different frequency scales. We have extracted 20 features from these signals obtained at different frequency scales of HRV signals. The Bhattacharyya ranking method is used to rank the extracted features from the HRV signals of three different lengths (500, 1000 and 2000 samples). These ranked features are fed to the Least Squares Support Vector Machine (LS-SVM) classifier. Our proposed system has obtained a sensitivity of 98.07%, specificity of 98.33% and accuracy of 98.21% for the 500-sample length of HRV signals. Our system yielded a sensitivity of 97.95%, specificity of 98.07% and accuracy of 98.01% for HRV signals of a length of 1000 samples and a sensitivity of 97.76%, specificity of 97.67% and accuracy of 97.71% for signals corresponding to the 2000-sample length of HRV signals. Our automated system can aid clinicians in the accurate detection of CHF using HRV signals. It can be installed in hospitals, polyclinics and remote villages where there is no access to cardiologists.Entropy2017-02-27193Article10.3390/e19030092921099-43002017-02-27doi: 10.3390/e19030092Mohit KumarRam PachoriU. Acharya<![CDATA[Entropy, Vol. 19, Pages 93: An Entropy-Assisted Shielding Function in DDES Formulation for the SST Turbulence Model]]>
http://www.mdpi.com/1099-4300/19/3/93
The intent of shielding functions in delayed detached-eddy simulation methods (DDES) is to preserve the wall boundary layers as Reynolds-averaged Navier–Strokes (RANS) mode, avoiding possible modeled stress depletion (MSD) or even unphysical separation due to grid refinement. An entropy function fs is introduced to construct a DDES formulation for the k-ω shear stress transport (SST) model, whose performance is extensively examined on a range of attached and separated flows (flat-plate flow, circular cylinder flow, and supersonic cavity-ramp flow). Two more forms of shielding functions are also included for comparison: one that uses the blending function F2 of SST, the other which adopts the recalibrated shielding function fd_cor of the DDES version based on the Spalart-Allmaras (SA) model. In general, all of the shielding functions do not impair the vortex in fully separated flows. However, for flows including attached boundary layer, both F2 and the recalibrated fd_cor are found to be too conservative to resolve the unsteady flow content. On the other side, fs is proposed on the theory of energy dissipation and independent on from any particular turbulence model, showing the generic priority by properly balancing the need of reserving the RANS modeled regions for wall boundary layers and generating the unsteady turbulent structures in detached areas.Entropy2017-02-27193Article10.3390/e19030093931099-43002017-02-27doi: 10.3390/e19030093Ling ZhouRui ZhaoXiao-Pan Shi<![CDATA[Entropy, Vol. 19, Pages 90: A LiBr-H2O Absorption Refrigerator Incorporating a Thermally Activated Solution Pumping Mechanism]]>
http://www.mdpi.com/1099-4300/19/3/90
This paper provides an illustrated description of a proposed LiBr-H2O vapour absorption refrigerator which uses a thermally activated solution pumping mechanism that combines controlled variations in generator vapour pressure with changes it produces in static-head pressure difference to circulate the absorbent solution between the generator and absorber vessels. The proposed system is different and potentially more efficient than a bubble pump system previously proposed and avoids the need for an electrically powered circulation pump found in most conventional LiBr absorption refrigerators. The paper goes on to provide a sample set of calculations that show that the coefficient of performance values of the proposed cycle are similar to those found for conventional cycles. The theoretical results compare favourably with some preliminary experimental results, which are also presented for the first time in this paper. The paper ends by proposing an outline design for an innovative steam valve, which is a key component needed to control the solution pumping mechanism.Entropy2017-02-26193Article10.3390/e19030090901099-43002017-02-26doi: 10.3390/e19030090Ian Eames<![CDATA[Entropy, Vol. 19, Pages 89: Optimization of Alpha-Beta Log-Det Divergences and their Application in the Spatial Filtering of Two Class Motor Imagery Movements]]>
http://www.mdpi.com/1099-4300/19/3/89
The Alpha-Beta Log-Det divergences for positive definite matrices are flexible divergences that are parameterized by two real constants and are able to specialize several relevant classical cases like the squared Riemannian metric, the Steins loss, the S-divergence, etc. A novel classification criterion based on these divergences is optimized to address the problem of classification of the motor imagery movements. This research paper is divided into three main sections in order to address the above mentioned problem: (1) Firstly, it is proven that a suitable scaling of the class conditional covariance matrices can be used to link the Common Spatial Pattern (CSP) solution with a predefined number of spatial filters for each class and its representation as a divergence optimization problem by making their different filter selection policies compatible; (2) A closed form formula for the gradient of the Alpha-Beta Log-Det divergences is derived that allows to perform optimization as well as easily use it in many practical applications; (3) Finally, in similarity with the work of Samek et al. 2014, which proposed the robust spatial filtering of the motor imagery movements based on the beta-divergence, the optimization of the Alpha-Beta Log-Det divergences is applied to this problem. The resulting subspace algorithm provides a unified framework for testing the performance and robustness of the several divergences in different scenarios.Entropy2017-02-25193Article10.3390/e19030089891099-43002017-02-25doi: 10.3390/e19030089Deepa ThiyamSergio CrucesJavier OliasAndrzej Cichocki<![CDATA[Entropy, Vol. 19, Pages 88: Systematic Analysis of the Non-Extensive Statistical Approach in High Energy Particle Collisions—Experiment vs. Theory]]>
http://www.mdpi.com/1099-4300/19/3/88
The analysis of high-energy particle collisions is an excellent testbed for the non-extensive statistical approach. In these reactions we are far from the thermodynamical limit. In small colliding systems, such as electron-positron or nuclear collisions, the number of particles is several orders of magnitude smaller than the Avogadro number; therefore, finite-size and fluctuation effects strongly influence the final-state one-particle energy distributions. Due to the simple characterization, the description of the identified hadron spectra with the Boltzmann–Gibbs thermodynamical approach is insufficient. These spectra can be described very well with Tsallis–Pareto distributions instead, derived from non-extensive thermodynamics. Using the q-entropy formula, we interpret the microscopic physics in terms of the Tsallis q and T parameters. In this paper we give a view on these parameters, analyzing identified hadron spectra from recent years in a wide center-of-mass energy range. We demonstrate that the fitted Tsallis-parameters show dependency on the center-of-mass energy and particle species (mass). Our findings are described well by a QCD (Quantum Chromodynamics) inspired parton evolution ansatz. Based on this comprehensive study, apart from the evolution, both mesonic and baryonic components found to be non-extensive ( q &gt; 1 ), besides the mass ordered hierarchy observed in the parameter T. We also study and compare in details the theory-obtained parameters for the case of PYTHIA8 Monte Carlo Generator, perturbative QCD and quark coalescence models.Entropy2017-02-24193Article10.3390/e19030088881099-43002017-02-24doi: 10.3390/e19030088Gábor BíróGergely BarnaföldiTamás BiróKároly ÜrmössyÁdám Takács<![CDATA[Entropy, Vol. 19, Pages 86: Motion Sequence Decomposition-Based Hybrid Entropy Feature and Its Application to Fault Diagnosis of a High-Speed Automatic Mechanism]]>
http://www.mdpi.com/1099-4300/19/3/86
High-speed automatic weapons play an important role in the field of national defense. However, current research on reliability analysis of automaton principally relies on simulations due to the fact that experimental data are difficult to collect in real life. Different from rotating machinery, a high-speed automaton needs to accomplish complex motion consisting of a series of impacts. In addition to strong noise, the impacts generated by different components of the automaton will interfere with each other. There is no effective approach to cope with this in the fault diagnosis of automatic mechanisms. This paper proposes a motion sequence decomposition approach combining modern signal processing techniques to develop an effective approach to fault detection in high-speed automatons. We first investigate the entire working procedure of the automatic mechanism and calculate the corresponding action times of travel involved. The vibration signal collected from the shooting experiment is then divided into a number of impacts corresponding to action orders. Only the segment generated by a faulty component is isolated from the original impacts according to the action time of the component. Wavelet packet decomposition (WPD) is first applied on the resulting signals for investigation of energy distribution, and the components with higher energy are selected for feature extraction. Three information entropy features are utilized to distinguish various states of the automaton using empirical mode decomposition (EMD). A gray-wolf optimization (GWO) algorithm is introduced as an alternative to improve the performance of the support vector machine (SVM) classifier. We carry out shooting experiments to collect vibration data for demonstration of the proposed work. Experimental results show that the proposed work in this paper is effective for fault diagnosis of a high-speed automaton and can be applied in real applications. Moreover, the GWO is able to provide a competitive diagnosis result compared with the genetic algorithm (GA) and the particle swarm optimization (PSO) algorithm.Entropy2017-02-24193Article10.3390/e19030086861099-43002017-02-24doi: 10.3390/e19030086Baoxiang WangHongxia PanHeng Du<![CDATA[Entropy, Vol. 19, Pages 87: Entropy, Topological Theories and Emergent Quantum Mechanics]]>
http://www.mdpi.com/1099-4300/19/3/87
The classical thermostatics of equilibrium processes is shown to possess a quantum mechanical dual theory with a ﬁnite dimensional Hilbert space of quantum states. Speciﬁcally, the kernel of a certain Hamiltonian operator becomes the Hilbert space of quasistatic quantum mechanics. The relation of thermostatics to topological ﬁeld theory is also discussed in the context of the approach of the emergence of quantum theory, where the concept of entropy plays a key role.Entropy2017-02-23193Article10.3390/e19030087871099-43002017-02-23doi: 10.3390/e19030087D. CabreraP. de CórdobaJ. IsidroJ. Molina<![CDATA[Entropy, Vol. 19, Pages 79: Using k-Mix-Neighborhood Subdigraphs to Compute Canonical Labelings of Digraphs]]>
http://www.mdpi.com/1099-4300/19/2/79
This paper presents a novel theory and method to calculate the canonical labelings of digraphs whose definition is entirely different from the traditional definition of Nauty. It indicates the mutual relationships that exist between the canonical labeling of a digraph and the canonical labeling of its complement graph. It systematically examines the link between computing the canonical labeling of a digraph and the k-neighborhood and k-mix-neighborhood subdigraphs. To facilitate the presentation, it introduces several concepts including mix diffusion outdegree sequence and entire mix diffusion outdegree sequences. For each node in a digraph G, it assigns an attribute m_NearestNode to enhance the accuracy of calculating canonical labeling. The four theorems proved here demonstrate how to determine the first nodes added into M a x Q ( G ) . Further, the other two theorems stated below deal with identifying the second nodes added into M a x Q ( G ) . When computing C m a x ( G ) , if M a x Q ( G ) already contains the first i vertices u 1 , u 2 , ⋯ , u i , Diffusion Theorem provides a guideline on how to choose the subsequent node of M a x Q ( G ) . Besides, the Mix Diffusion Theorem shows that the selection of the ( i + 1 ) th vertex of M a x Q ( G ) for computing C m a x ( G ) is from the open mix-neighborhood subdigraph N + + ( Q ) of the nodes set Q = { u 1 , u 2 , ⋯ , u i } . It also offers two theorems to calculate the C m a x ( G ) of the disconnected digraphs. The four algorithms implemented in it illustrate how to calculate M a x Q ( G ) of a digraph. Through software testing, the correctness of our algorithms is preliminarily verified. Our method can be utilized to mine the frequent subdigraph. We also guess that if there exists a vertex v ∈ S + ( G ) satisfying conditions C m a x ( G − v ) ⩽ C m a x ( G − w ) for each w ∈ S + ( G ) ∧ w ≠ v , then u 1 = v for M a x Q ( G ) .Entropy2017-02-22192Article10.3390/e19020079791099-43002017-02-22doi: 10.3390/e19020079Jianqiang HaoYunzhan GongYawen WangLi TanJianzhi Sun<![CDATA[Entropy, Vol. 19, Pages 85: Quantifying Synergistic Information Using Intermediate Stochastic Variables]]>
http://www.mdpi.com/1099-4300/19/2/85
Quantifying synergy among stochastic variables is an important open problem in information theory. Information synergy occurs when multiple sources together predict an outcome variable better than the sum of single-source predictions. It is an essential phenomenon in biology such as in neuronal networks and cellular regulatory processes, where different information flows integrate to produce a single response, but also in social cooperation processes as well as in statistical inference tasks in machine learning. Here we propose a metric of synergistic entropy and synergistic information from first principles. The proposed measure relies on so-called synergistic random variables (SRVs) which are constructed to have zero mutual information about individual source variables but non-zero mutual information about the complete set of source variables. We prove several basic and desired properties of our measure, including bounds and additivity properties. In addition, we prove several important consequences of our measure, including the fact that different types of synergistic information may co-exist between the same sets of variables. A numerical implementation is provided, which we use to demonstrate that synergy is associated with resilience to noise. Our measure may be a marked step forward in the study of multivariate information theory and its numerous applications.Entropy2017-02-22192Article10.3390/e19020085851099-43002017-02-22doi: 10.3390/e19020085Rick QuaxOmri Har-ShemeshPeter Sloot<![CDATA[Entropy, Vol. 19, Pages 82: The More You Know, the More You Can Grow: An Information Theoretic Approach to Growth in the Information Age]]>
http://www.mdpi.com/1099-4300/19/2/82
In our information age, information alone has become a driver of social growth. Information is the fuel of “big data” companies, and the decision-making compass of policy makers. Can we quantify how much information leads to how much social growth potential? Information theory is used to show that information (in bits) is effectively a quantifiable ingredient of growth. The article presents a single equation that allows both to describe hands-off natural selection of evolving populations and to optimize population fitness in uncertain environments through intervention. The setup analyzes the communication channel between the growing population and its uncertain environment. The role of information in population growth can be thought of as the optimization of information flow over this (more or less) noisy channel. Optimized growth implies that the population absorbs all communicated environmental structure during evolutionary updating (measured by their mutual information). This is achieved by endogenously adjusting the population structure to the exogenous environmental pattern (through bet-hedging/portfolio management). The setup can be applied to decompose the growth of any discrete population in stationary, stochastic environments (economic, cultural, or biological). Two empirical examples from the information economy reveal inherent trade-offs among the involved information quantities during growth optimization.Entropy2017-02-22192Article10.3390/e19020082821099-43002017-02-22doi: 10.3390/e19020082Martin Hilbert<![CDATA[Entropy, Vol. 19, Pages 83: Breakdown Point of Robust Support Vector Machines]]>
http://www.mdpi.com/1099-4300/19/2/83
Support vector machine (SVM) is one of the most successful learning methods for solving classiﬁcation problems. Despite its popularity, SVM has the serious drawback that it is sensitive to outliers in training samples. The penalty on misclassiﬁcation is deﬁned by a convex loss called the hinge loss, and the unboundedness of the convex loss causes the sensitivity to outliers. To deal with outliers, robust SVMs have been proposed by replacing the convex loss with a non-convex bounded loss called the ramp loss. In this paper, we study the breakdown point of robust SVMs. The breakdown point is a robustness measure that is the largest amount of contamination such that the estimated classiﬁer still gives information about the non-contaminated data. The main contribution of this paper is to show an exact evaluation of the breakdown point of robust SVMs. For learning parameters such as the regularization parameter, we derive a simple formula that guarantees the robustness of the classiﬁer. When the learning parameters are determined with a grid search using cross-validation, our formula works to reduce the number of candidate search points. Furthermore, the theoretical ﬁndings are conﬁrmed in numerical experiments. We show that the statistical properties of robust SVMs are well explained by a theoretical analysis of the breakdown point.Entropy2017-02-21192Article10.3390/e19020083831099-43002017-02-21doi: 10.3390/e19020083Takafumi KanamoriShuhei FujiwaraAkiko Takeda<![CDATA[Entropy, Vol. 19, Pages 84: Sequential Batch Design for Gaussian Processes Employing Marginalization †]]>
http://www.mdpi.com/1099-4300/19/2/84
Within the Bayesian framework, we utilize Gaussian processes for parametric studies of long running computer codes. Since the simulations are expensive, it is necessary to exploit the computational budget in the best possible manner. Employing the sum over variances —being indicators for the quality of the fit—as the utility function, we establish an optimized and automated sequential parameter selection procedure. However, it is also often desirable to utilize the parallel running capabilities of present computer technology and abandon the sequential parameter selection for a faster overall turn-around time (wall-clock time). This paper proposes to achieve this by marginalizing over the expected outcomes at optimized test points in order to set up a pool of starting values for batch execution. For a one-dimensional test case, the numerical results are validated with the analytical solution. Eventually, a systematic convergence study demonstrates the advantage of the optimized approach over randomly chosen parameter settings.Entropy2017-02-21192Article10.3390/e19020084841099-43002017-02-21doi: 10.3390/e19020084Roland PreussUdo von Toussaint<![CDATA[Entropy, Vol. 19, Pages 70: User-Centric Key Entropy: Study of Biometric Key Derivation Subject to Spoofing Attacks]]>
http://www.mdpi.com/1099-4300/19/2/70
Biometric data can be used as input for PKI key pair generation. The concept of not saving the private key is very appealing, but the implementation of such a system shouldn’t be rushed because it might prove less secure then current PKI infrastructure. One biometric characteristic can be easily spoofed, so it was believed that multi-modal biometrics would offer more security, because spoofing two or more biometrics would be very hard. This notion, of increased security of multi-modal biometric systems, was disproved for authentication and matching, studies showing that not only multi-modal biometric systems are not more secure, but they introduce additional vulnerabilities. This paper is a study on the implications of spoofing biometric data for retrieving the derived key. We demonstrate that spoofed biometrics can yield the same key, which in turn will lead an attacker to obtain the private key. A practical implementation is proposed using fingerprint and iris as biometrics and the fuzzy extractor for biometric key extraction. Our experiments show what happens when the biometric data is spoofed for both uni-modal systems and multi-modal. In case of multi-modal system tests were performed when spoofing one biometric or both. We provide detailed analysis of every scenario in regard to successful tests and overall key entropy. Our paper defines a biometric PKI scenario and an in depth security analysis for it. The analysis can be viewed as a blueprint for implementations of future similar systems, because it highlights the main security vulnerabilities for bioPKI. The analysis is not constrained to the biometric part of the system, but covers CA security, sensor security, communication interception, RSA encryption vulnerabilities regarding key entropy, and much more.Entropy2017-02-21192Article10.3390/e19020070701099-43002017-02-21doi: 10.3390/e19020070Lavinia DincaGerhard Hancke<![CDATA[Entropy, Vol. 19, Pages 80: A Risk-Free Protection Index Model for Portfolio Selection with Entropy Constraint under an Uncertainty Framework]]>
http://www.mdpi.com/1099-4300/19/2/80
This paper aims to develop a risk-free protection index model for portfolio selection based on the uncertain theory. First, the returns of risk assets are assumed as uncertain variables and subject to reputable experts’ evaluations. Second, under this assumption, combining with the risk-free interest rate we define a risk-free protection index (RFPI), which can measure the protection degree when the loss of risk assets happens. Third, note that the proportion entropy serves as a complementary means to reduce the risk by the preset diversification requirement. We put forward a risk-free protection index model with an entropy constraint under an uncertainty framework by applying the RFPI, Huang’s risk index model (RIM), and mean-variance-entropy model (MVEM). Furthermore, to solve our portfolio model, an algorithm is given to estimate the uncertain expected return and standard deviation of different risk assets by applying the Delphi method. Finally, an example is provided to show that the risk-free protection index model performs better than the traditional MVEM and RIM.Entropy2017-02-21192Article10.3390/e19020080801099-43002017-02-21doi: 10.3390/e19020080Jianwei GaoHuicheng Liu