Next Issue
Previous Issue

E-Mail Alert

Add your e-mail address to receive forthcoming issues of this journal:

Journal Browser

Journal Browser

Table of Contents

Entropy, Volume 18, Issue 4 (April 2016)

  • Issues are regarded as officially published after their release is announced to the table of contents alert mailing list.
  • You may sign up for e-mail alerts to receive table of contents of newly released issues.
  • PDF is the official format for papers published in both, html and pdf forms. To view the papers in pdf format, click on the "PDF Full-text" link, and use the free Adobe Readerexternal link to open them.
View options order results:
result details:
Displaying articles 1-53
Export citation of selected articles as:

Research

Jump to: Review, Other

Open AccessArticle Bayesian Genetic Association Test when Secondary Phenotypes Are Available Only in the Case Group
Entropy 2016, 18(4), 91; doi:10.3390/e18040091
Received: 14 September 2015 / Revised: 3 December 2015 / Accepted: 7 December 2015 / Published: 6 April 2016
PDF Full-text (292 KB) | HTML Full-text | XML Full-text
Abstract
In many case-control genetic association studies, a secondary phenotype that may have common genetic factors with disease status can be identified. When information on the secondary phenotype is available only for the case group due to cost and different data sources, a fitting
[...] Read more.
In many case-control genetic association studies, a secondary phenotype that may have common genetic factors with disease status can be identified. When information on the secondary phenotype is available only for the case group due to cost and different data sources, a fitting linear regression model ignoring supplementary phenotype data may provide limited knowledge regarding genetic association. We set up a joint model and use a Bayesian framework to estimate and test the effect of genetic covariates on disease status considering the secondary phenotype as an instrumental variable. The application of our proposed procedure is demonstrated through the rheumatoid arthritis data provided by the 16th Genetic Analysis Workshop. Full article
(This article belongs to the Section Information Theory)
Open AccessArticle Chaos on the Vallis Model for El Niño with Fractional Operators
Entropy 2016, 18(4), 100; doi:10.3390/e18040100
Received: 13 January 2016 / Revised: 9 March 2016 / Accepted: 10 March 2016 / Published: 23 March 2016
Cited by 8 | PDF Full-text (5283 KB) | HTML Full-text | XML Full-text
Abstract
The Vallis model for El Niño is an important model describing a very interesting physical problem. The aim of this paper is to investigate and compare the models using both integer and non-integer order derivatives. We first studied the model with the local
[...] Read more.
The Vallis model for El Niño is an important model describing a very interesting physical problem. The aim of this paper is to investigate and compare the models using both integer and non-integer order derivatives. We first studied the model with the local derivative by presenting for the first time the exact solution for equilibrium points, and then we presented the exact solutions with the numerical simulations. We further examined the model within the scope of fractional order derivatives. The fractional derivatives used here are the Caputo derivative and Caputo–Fabrizio type. Within the scope of fractional derivatives, we presented the existence and unique solutions of the model. We derive special solutions of both models with Caputo and Caputo–Fabrizio derivatives. Some numerical simulations are presented to compare the models. We obtained more chaotic behavior from the model with Caputo–Fabrizio derivative than other one with local and Caputo derivative. When compare the three models, we realized that, the Caputo derivative plays a role of low band filter when the Caputo–Fabrizio presents more information that were not revealed in the model with local derivative. Full article
(This article belongs to the Special Issue Complex and Fractional Dynamics)
Open AccessArticle On the Path to Optimizing the Al-Co-Cr-Cu-Fe-Ni-Ti High Entropy Alloy Family for High Temperature Applications
Entropy 2016, 18(4), 104; doi:10.3390/e18040104
Received: 19 February 2016 / Revised: 14 March 2016 / Accepted: 15 March 2016 / Published: 23 March 2016
Cited by 8 | PDF Full-text (3134 KB) | HTML Full-text | XML Full-text
Abstract
The most commonly investigated high entropy alloy, AlCoCrCuFeNi, has been chosen for optimization of its microstructural and mechanical properties by means of compositional changes and heat treatments. Among the different available optimization paths, the decrease of segregating element Cu, the increase of oxidation
[...] Read more.
The most commonly investigated high entropy alloy, AlCoCrCuFeNi, has been chosen for optimization of its microstructural and mechanical properties by means of compositional changes and heat treatments. Among the different available optimization paths, the decrease of segregating element Cu, the increase of oxidation protective elements Al and Cr and the approach towards a γ-γ′ microstructure like in Ni-based superalloys have been probed and compared. Microscopical observations have been made for every optimization step. Vickers microhardness measurements and/or tensile/compression test have been carried out when the alloy was appropriate. Five derived alloys AlCoCrFeNi, Al23Co15Cr23Cu8Fe15Ni16, Al8Co17Cr17Cu8Fe17Ni33, Al8Co17Cr14Cu8Fe17Ni34.8Mo0.1Ti1W0.1 and Al10Co25Cr8Fe15Ni36Ti6 (all at.%) have been compared to the original AlCoCrCuFeNi and the most promising one has been selected for further investigation. Full article
(This article belongs to the Special Issue High-Entropy Alloys and High-Entropy-Related Materials)
Open AccessArticle Generalized Analysis of a Distribution Separation Method
Entropy 2016, 18(4), 105; doi:10.3390/e18040105
Received: 25 November 2015 / Revised: 11 March 2016 / Accepted: 15 March 2016 / Published: 13 April 2016
PDF Full-text (461 KB) | HTML Full-text | XML Full-text
Abstract
Separating two probability distributions from a mixture model that is made up of the combinations of the two is essential to a wide range of applications. For example, in information retrieval (IR), there often exists a mixture distribution consisting of a relevance distribution
[...] Read more.
Separating two probability distributions from a mixture model that is made up of the combinations of the two is essential to a wide range of applications. For example, in information retrieval (IR), there often exists a mixture distribution consisting of a relevance distribution that we need to estimate and an irrelevance distribution that we hope to get rid of. Recently, a distribution separation method (DSM) was proposed to approximate the relevance distribution, by separating a seed irrelevance distribution from the mixture distribution. It was successfully applied to an IR task, namely pseudo-relevance feedback (PRF), where the query expansion model is often a mixture term distribution. Although initially developed in the context of IR, DSM is indeed a general mathematical formulation for probability distribution separation. Thus, it is important to further generalize its basic analysis and to explore its connections to other related methods. In this article, we first extend DSM’s theoretical analysis, which was originally based on the Pearson correlation coefficient, to entropy-related measures, including the KL-divergence (Kullback–Leibler divergence), the symmetrized KL-divergence and the JS-divergence (Jensen–Shannon divergence). Second, we investigate the distribution separation idea in a well-known method, namely the mixture model feedback (MMF) approach. We prove that MMF also complies with the linear combination assumption, and then, DSM’s linear separation algorithm can largely simplify the EM algorithm in MMF. These theoretical analyses, as well as further empirical evaluation results demonstrate the advantages of our DSM approach. Full article
(This article belongs to the Section Information Theory)
Open AccessArticle Complexity Analysis of Surface EMG for Overcoming ECG Interference toward Proportional Myoelectric Control
Entropy 2016, 18(4), 106; doi:10.3390/e18040106
Received: 7 December 2015 / Revised: 3 February 2016 / Accepted: 14 March 2016 / Published: 30 March 2016
Cited by 4 | PDF Full-text (1073 KB) | HTML Full-text | XML Full-text
Abstract
Electromyographic (EMG) signals from muscles in the body torso are often contaminated by electrocardiography (ECG) interferences, which consequently compromise EMG intensity estimation. The ECG interference has become a barrier to proportional control of myoelectric prosthesis using a neural machine interface called targeted muscle
[...] Read more.
Electromyographic (EMG) signals from muscles in the body torso are often contaminated by electrocardiography (ECG) interferences, which consequently compromise EMG intensity estimation. The ECG interference has become a barrier to proportional control of myoelectric prosthesis using a neural machine interface called targeted muscle reinnervation (TMR), which involves transferring the residual amputated nerves to nonfunctional muscles (typically pectoralis muscles for high level amputations). This study investigates a novel approach toward implementation of proportional myoelectric control by applying sample entropy (SampEn) analysis of surface EMG signals for robust intensity estimation in the presence of significant ECG interference. Surface EMG data from able-bodied and TMR amputee subjects with different degrees of ECG interference were used for performance evaluation. The results showed that the SampEn analysis had high correlation with surface EMG amplitude measurement but low sensitivity to different degrees of ECG interference. Taking this advantage, SampEn analysis of surface EMG signal can be used to facilitate implementation of proportional myoelectric control against ECG interference. This is particularly important for TMR prosthesis users. Full article
Open AccessArticle Thermodynamic Analysis of the Irreversibilities in Solar Absorption Refrigerators
Entropy 2016, 18(4), 107; doi:10.3390/e18040107
Received: 29 October 2015 / Revised: 21 March 2016 / Accepted: 22 March 2016 / Published: 24 March 2016
PDF Full-text (1146 KB) | HTML Full-text | XML Full-text
Abstract
A thermodynamic analysis of the irreversibility on solar absorption refrigerators is presented. Under the hierarchical decomposition and the hypothesis of an endoreversible model, many functional and practical domains are defined. The effect of external heat source temperature on the entropy rate and on
[...] Read more.
A thermodynamic analysis of the irreversibility on solar absorption refrigerators is presented. Under the hierarchical decomposition and the hypothesis of an endoreversible model, many functional and practical domains are defined. The effect of external heat source temperature on the entropy rate and on the inverse specific cooling load (ISCL) multiplied by the total area of the refrigerator A/Qe are studied. This may help a constructor to well dimension the solar machine under an optimal technico-economical criterion A/Qe and with reasonable irreversibility on the refrigerator. The solar concentrator temperature effect on the total exchanged area, on the technico-economical ratio A/Qe, and on the internal entropy rate are illustrated and discussed. The originality of these results is that they allow a conceptual study of a solar absorption refrigeration cycle. Full article
(This article belongs to the Special Issue Entropy Generation in Thermal Systems and Processes 2015)
Open AccessArticle An Estimator of Mutual Information and its Application to Independence Testing
Entropy 2016, 18(4), 109; doi:10.3390/e18040109
Received: 22 February 2016 / Revised: 14 March 2016 / Accepted: 23 March 2016 / Published: 29 March 2016
PDF Full-text (910 KB) | HTML Full-text | XML Full-text
Abstract
This paper proposes a novel estimator of mutual information for discrete and continuous variables. The main feature of this estimator is that it is zero for a large sample size n if and only if the two variables are independent. The estimator can
[...] Read more.
This paper proposes a novel estimator of mutual information for discrete and continuous variables. The main feature of this estimator is that it is zero for a large sample size n if and only if the two variables are independent. The estimator can be used to construct several histograms, compute estimations of mutual information, and choose the maximum value. We prove that the number of histograms constructed has an upper bound of O(log n) and apply this fact to the search. We compare the performance of the proposed estimator with an estimator of the Hilbert-Schmidt independence criterion (HSIC), though the proposed method is based on the minimum description length (MDL) principle and the HSIC provides a statistical test. The proposed method completes the estimation in O(n log n) time, whereas the HSIC kernel computation requires O(n3) time. We also present examples in which the HSIC fails to detect independence but the proposed method successfully detects it. Full article
(This article belongs to the Section Information Theory)
Open AccessArticle Syntactic Parameters and a Coding Theory Perspective on Entropy and Complexity of Language Families
Entropy 2016, 18(4), 110; doi:10.3390/e18040110
Received: 14 January 2016 / Revised: 13 March 2016 / Accepted: 18 March 2016 / Published: 7 April 2016
Cited by 3 | PDF Full-text (291 KB) | HTML Full-text | XML Full-text
Abstract
We present a simple computational approach to assigning a measure of complexity and information/entropy to families of natural languages, based on syntactic parameters and the theory of error correcting codes. We associate to each language a binary string of syntactic parameters and to
[...] Read more.
We present a simple computational approach to assigning a measure of complexity and information/entropy to families of natural languages, based on syntactic parameters and the theory of error correcting codes. We associate to each language a binary string of syntactic parameters and to a language family a binary code, with code words the binary string associated to each language. We then evaluate the code parameters (rate and relative minimum distance) and the position of the parameters with respect to the asymptotic bound of error correcting codes and the Gilbert–Varshamov bound. These bounds are, respectively, related to the Kolmogorov complexity and the Shannon entropy of the code and this gives us a computationally simple way to obtain estimates on the complexity and information, not of individual languages but of language families. This notion of complexity is related, from the linguistic point of view to the degree of variability of syntactic parameter across languages belonging to the same (historical) family. Full article
(This article belongs to the Special Issue Differential Geometrical Theory of Statistics) Printed Edition available
Open AccessArticle Identifying the Probability Distribution of Fatigue Life Using the Maximum Entropy Principle
Entropy 2016, 18(4), 111; doi:10.3390/e18040111
Received: 17 December 2015 / Revised: 7 March 2016 / Accepted: 23 March 2016 / Published: 30 March 2016
Cited by 1 | PDF Full-text (1224 KB) | HTML Full-text | XML Full-text
Abstract
It is well-known that the fatigue lives of materials and structures have a considerable amount of scatter and they are commonly suggested to be considered in engineering design. In order to reduce the introduction of subjective uncertainties and obtain rational probability distributions, a
[...] Read more.
It is well-known that the fatigue lives of materials and structures have a considerable amount of scatter and they are commonly suggested to be considered in engineering design. In order to reduce the introduction of subjective uncertainties and obtain rational probability distributions, a computational method based on the maximum entropy principle is proposed for identifying the probability distribution of fatigue life in this paper. The first four statistical moments of fatigue life are involved to formulate constraints in the maximum entropy principle optimization problem. An accurate algorithm is also presented to find the Lagrange multipliers in the maximum entropy distribution, which can avoid the numerical singularity when solving a system of equations. Two fit indexes are used to measure the goodness-of-fit of the proposed method. The rationality and effectiveness of the proposed method are demonstrated by two groups of fatigue data sets available in the literature. Comparisons among the proposed method, the lognormal distribution and the three-parameter Weibull distribution are also carried out for the investigated groups of fatigue data sets. Full article
(This article belongs to the Section Information Theory)
Open AccessArticle A Hybrid EEMD-Based SampEn and SVD for Acoustic Signal Processing and Fault Diagnosis
Entropy 2016, 18(4), 112; doi:10.3390/e18040112
Received: 14 December 2015 / Revised: 3 March 2016 / Accepted: 23 March 2016 / Published: 1 April 2016
Cited by 12 | PDF Full-text (1821 KB) | HTML Full-text | XML Full-text
Abstract
Acoustic signals are an ideal source of diagnosis data thanks to their intrinsic non-directional coverage, sensitivity to incipient defects, and insensitivity to structural resonance characteristics. However this makes prevailing signal de-nosing and feature extraction methods suffer from high computational cost, low signal to
[...] Read more.
Acoustic signals are an ideal source of diagnosis data thanks to their intrinsic non-directional coverage, sensitivity to incipient defects, and insensitivity to structural resonance characteristics. However this makes prevailing signal de-nosing and feature extraction methods suffer from high computational cost, low signal to noise ratio (S/N), and difficulty to extract the compound acoustic emissions for various failure types. To address these challenges, we propose a hybrid signal processing technique to depict the embedded signal using generally effective features. The ensemble empirical mode decomposition (EEMD) is adopted as the fundamental pre-processor, which is integrated with the sample entropy (SampEn), singular value decomposition (SVD), and statistic feature processing (SFP) methods. The SampEn and SVD are identified as the condition indicators for periodical and irregular signals, respectively. Moreover, such a hybrid module is self-adaptive and robust to different signals, which ensures the generality of its performance. The hybrid signal processor is further integrated with a probabilistic classifier, pairwise-coupled relevance vector machine (PCRVM), to construct a new fault diagnosis system. Experimental verifications for industrial equipment show that the proposed diagnostic system is superior to prior methods in computational efficiency and the capability of simultaneously processing non-stationary and nonlinear condition monitoring signals. Full article
(This article belongs to the Special Issue Information Theoretic Learning)
Open AccessArticle Second Law Analysis of Adiabatic and Non-Adiabatic Pipeline Flows of Unstable and Surfactant-Stabilized Emulsions
Entropy 2016, 18(4), 113; doi:10.3390/e18040113
Received: 17 December 2015 / Revised: 5 March 2016 / Accepted: 25 March 2016 / Published: 30 March 2016
Cited by 2 | PDF Full-text (11267 KB) | HTML Full-text | XML Full-text
Abstract
Entropy generation, and hence exergy destruction, in adiabatic flow of unstable and surfactant-stabilized emulsions was investigated experimentally in different diameter pipes. Four types of emulsion systems are investigated covering a broad range of the dispersed-phase concentration: (a) unstable oil-in-water (O/W) emulsions without surfactant;
[...] Read more.
Entropy generation, and hence exergy destruction, in adiabatic flow of unstable and surfactant-stabilized emulsions was investigated experimentally in different diameter pipes. Four types of emulsion systems are investigated covering a broad range of the dispersed-phase concentration: (a) unstable oil-in-water (O/W) emulsions without surfactant; (b) surfactant-stabilized O/W emulsions; (c) unstable water-in-oil (W/O) emulsions without surfactant; and (d) surfactant-stabilized W/O emulsions. The entropy generation rate per unit pipe length is affected by the type of the emulsion as well as its stability. Unstable emulsions without any surfactant present at the interface generate less entropy in the turbulent regime as compared with the surfactant-stabilized emulsions of the same viscosity and density. The effect of surfactant is particularly severe in the case of W/O emulsions. In the turbulent regime, the rate of entropy generation in unstable W/O emulsions is much lower in comparison with that observed in the stable W/O emulsions. A significant delay in the transition from laminar to turbulent regime is also observed in the case of unstable W/O emulsion. Finally, the analysis and simulation results are presented on non-adiabatic pipeline flow of emulsions. Full article
(This article belongs to the Special Issue Exploring the Second Law of Thermodynamics)
Open AccessArticle Statistical Evidence Measured on a Properly Calibrated Scale for Multinomial Hypothesis Comparisons
Entropy 2016, 18(4), 114; doi:10.3390/e18040114
Received: 13 January 2016 / Revised: 22 March 2016 / Accepted: 23 March 2016 / Published: 30 March 2016
Cited by 1 | PDF Full-text (3675 KB) | HTML Full-text | XML Full-text
Abstract
Measurement of the strength of statistical evidence is a primary objective of statistical analysis throughout the biological and social sciences. Various quantities have been proposed as definitions of statistical evidence, notably the likelihood ratio, the Bayes factor and the relative belief ratio. Each
[...] Read more.
Measurement of the strength of statistical evidence is a primary objective of statistical analysis throughout the biological and social sciences. Various quantities have been proposed as definitions of statistical evidence, notably the likelihood ratio, the Bayes factor and the relative belief ratio. Each of these can be motivated by direct appeal to intuition. However, for an evidence measure to be reliably used for scientific purposes, it must be properly calibrated, so that one “degree” on the measurement scale always refers to the same amount of underlying evidence, and the calibration problem has not been resolved for these familiar evidential statistics. We have developed a methodology for addressing the calibration issue itself, and previously applied this methodology to derive a calibrated evidence measure E in application to a broad class of hypothesis contrasts in the setting of binomial (single-parameter) likelihoods. Here we substantially generalize previous results to include the m-dimensional multinomial (multiple-parameter) likelihood. In the process we further articulate our methodology for addressing the measurement calibration issue, and we show explicitly how the more familiar definitions of statistical evidence are patently not well behaved with respect to the underlying evidence. We also continue to see striking connections between the calculating equations for E and equations from thermodynamics as we move to more complicated forms of the likelihood. Full article
(This article belongs to the Special Issue Statistical Significance and the Logic of Hypothesis Testing)
Figures

Open AccessArticle A Comparison of Classification Methods for Telediagnosis of Parkinson’s Disease
Entropy 2016, 18(4), 115; doi:10.3390/e18040115
Received: 14 February 2016 / Revised: 13 March 2016 / Accepted: 24 March 2016 / Published: 30 March 2016
Cited by 5 | PDF Full-text (3850 KB) | HTML Full-text | XML Full-text
Abstract
Parkinson’s disease (PD) is a progressive and chronic nervous system disease that impairs the ability of speech, gait, and complex muscle-and-nerve actions. Early diagnosis of PD is quite important for alleviating the symptoms. Cost effective and convenient telemedicine technology helps to distinguish the
[...] Read more.
Parkinson’s disease (PD) is a progressive and chronic nervous system disease that impairs the ability of speech, gait, and complex muscle-and-nerve actions. Early diagnosis of PD is quite important for alleviating the symptoms. Cost effective and convenient telemedicine technology helps to distinguish the patients with PD from healthy people using variations of dysphonia, gait or motor skills. In this study, a novel telemedicine technology was developed to detect PD remotely using dysphonia features. Feature transformation and several machine learning (ML) methods with 2-, 5- and 10-fold cross-validations were implemented on the vocal features. It was observed that the combination of principal component analysis (PCA) as a feature transformation (FT) and k-nearest neighbor (k-NN) as a classifier with 10-fold cross-validation has the best accuracy as 99.1%. All ML processes were applied to the prerecorded PD dataset using a newly created program named ParkDet 2.0. Additionally, the blind test interface was created on the ParkDet so that users could detect new patients with PD in future. Clinicians or medical technicians, without any knowledge of ML, will be able to use the blind test interface to detect PD at a clinic or remote location utilizing internet as a telemedicine application. Full article
(This article belongs to the Special Issue Computational Complexity)
Open AccessArticle The Effect of Spin Squeezing on the Entanglement Entropy of Kicked Tops
Entropy 2016, 18(4), 116; doi:10.3390/e18040116
Received: 20 November 2015 / Revised: 14 March 2016 / Accepted: 22 March 2016 / Published: 2 April 2016
PDF Full-text (8634 KB) | HTML Full-text | XML Full-text
Abstract
In this paper, we investigate the effects of spin squeezing on two-coupled quantum kicked tops, which have been previously shown to exhibit a quantum signature of chaos in terms of entanglement dynamics. Our results show that initial spin squeezing can lead to an
[...] Read more.
In this paper, we investigate the effects of spin squeezing on two-coupled quantum kicked tops, which have been previously shown to exhibit a quantum signature of chaos in terms of entanglement dynamics. Our results show that initial spin squeezing can lead to an enhancement in both the entanglement rate and the asymptotic entanglement for kicked tops when the initial state resides in the regular islands within a mixed classical phase space. On the other hand, we found a reduction in these two quantities if we were to choose the initial state deep inside the chaotic sea. More importantly, we have uncovered that an application of periodic spin squeezing can yield the maximum attainable entanglement entropy, albeit this is achieved at a reduced entanglement rate. Full article
(This article belongs to the Special Issue Entanglement Entropy)
Open AccessArticle Entropy Generation on MHD Blood Flow of Nanofluid Due to Peristaltic Waves
Entropy 2016, 18(4), 117; doi:10.3390/e18040117
Received: 19 January 2016 / Revised: 24 March 2016 / Accepted: 24 March 2016 / Published: 1 April 2016
Cited by 13 | PDF Full-text (5104 KB) | HTML Full-text | XML Full-text
Abstract
This present study describes the entropy generation on magnetohydrodynamic (MHD) blood flow of a nanofluid induced by peristaltic waves. The governing equation of continuity, equation of motion, nano-particle and entropy equations are solved by neglecting the inertial forces and taking long wavelength approximation.
[...] Read more.
This present study describes the entropy generation on magnetohydrodynamic (MHD) blood flow of a nanofluid induced by peristaltic waves. The governing equation of continuity, equation of motion, nano-particle and entropy equations are solved by neglecting the inertial forces and taking long wavelength approximation. The resulting highly non-linear coupled partial differential equation has been solved analytically with the help of perturbation method. Mathematical and graphical results of all the physical parameters for velocity, concentration, temperature, and entropy are also presented. Numerical computation has been used to evaluate the expression for the pressure rise and friction forces. Currently, magnetohydrodynamics is applicable in pumping the fluids for pulsating and non-pulsating continuous flows in different microchannel designs and it also very helpful to control the flow. Full article
(This article belongs to the Special Issue Entropy in Nanofluids)
Open AccessArticle Generalized Einstein’s Equations from Wald Entropy
Entropy 2016, 18(4), 119; doi:10.3390/e18040119
Received: 26 February 2016 / Revised: 14 March 2016 / Accepted: 17 March 2016 / Published: 31 March 2016
Cited by 2 | PDF Full-text (225 KB) | HTML Full-text | XML Full-text
Abstract
We derive the gravitational equations of motion of general theories of gravity from thermodynamics applied to a local Rindler horizon through any point in spacetime. Specifically, for a given theory of gravity, we substitute the corresponding Wald entropy into the Clausius relation. Our
[...] Read more.
We derive the gravitational equations of motion of general theories of gravity from thermodynamics applied to a local Rindler horizon through any point in spacetime. Specifically, for a given theory of gravity, we substitute the corresponding Wald entropy into the Clausius relation. Our approach works for all diffeomorphism-invariant theories of gravity in which the Lagrangian is a polynomial in the Riemann tensor. Full article
(This article belongs to the Special Issue Black Hole Thermodynamics II)
Open AccessFeature PaperArticle An Exact Efficiency Formula for Holographic Heat Engines
Entropy 2016, 18(4), 120; doi:10.3390/e18040120
Received: 10 February 2016 / Revised: 22 March 2016 / Accepted: 28 March 2016 / Published: 31 March 2016
Cited by 10 | PDF Full-text (820 KB) | HTML Full-text | XML Full-text
Abstract
Further consideration is given to the efficiency of a class of black hole heat engines that perform mechanical work via the pdV terms present in the First Law of extended gravitational thermodynamics. It is noted that, when the engine cycle is a rectangle
[...] Read more.
Further consideration is given to the efficiency of a class of black hole heat engines that perform mechanical work via the pdV terms present in the First Law of extended gravitational thermodynamics. It is noted that, when the engine cycle is a rectangle with sides parallel to the (p,V) axes, the efficiency can be written simply in terms of the mass of the black hole evaluated at the corners. Since an arbitrary cycle can be approximated to any desired accuracy by a tiling of rectangles, a general geometrical algorithm for computing the efficiency of such a cycle follows. A simple generalization of the algorithm renders it applicable to broader classes of heat engine, even beyond the black hole context. Full article
(This article belongs to the Special Issue Black Hole Thermodynamics II)
Open AccessArticle A Kinetic Perspective on k‒ε Turbulence Model and Corresponding Entropy Production
Entropy 2016, 18(4), 121; doi:10.3390/e18040121
Received: 11 February 2016 / Revised: 24 March 2016 / Accepted: 28 March 2016 / Published: 31 March 2016
Cited by 1 | PDF Full-text (746 KB) | HTML Full-text | XML Full-text
Abstract
In this paper, we present an alternative derivation of the entropy production in turbulent flows, based on a formal analogy with the kinetic theory of rarefied gas. This analogy allows for proving that the celebrated \(k - \epsilon\) model for turbulent flows is
[...] Read more.
In this paper, we present an alternative derivation of the entropy production in turbulent flows, based on a formal analogy with the kinetic theory of rarefied gas. This analogy allows for proving that the celebrated \(k - \epsilon\) model for turbulent flows is nothing more than a set of coupled BGK (Bhatnagar–Gross–Krook)-like equations with a proper forcing. This opens a novel perspective on this model, which may help in sorting out the heuristic assumptions essential for its derivation, such as the balance between turbulent kinetic energy production and dissipation. The entropy production is an essential condition for the design and optimization of devices where turbulent flows are involved. Full article
Open AccessArticle Many-Body-Localization Transition in the Strong Disorder Limit: Entanglement Entropy from the Statistics of Rare Extensive Resonances
Entropy 2016, 18(4), 122; doi:10.3390/e18040122
Received: 25 January 2016 / Revised: 22 March 2016 / Accepted: 29 March 2016 / Published: 1 April 2016
Cited by 15 | PDF Full-text (337 KB) | HTML Full-text | XML Full-text
Abstract
The space of one-dimensional disordered interacting quantum models displaying a many-body localization (MBL) transition seems sufficiently rich to produce critical points with level statistics interpolating continuously between the Poisson statistics of the localized phase and the Wigner–Dyson statistics of the delocalized phase. In
[...] Read more.
The space of one-dimensional disordered interacting quantum models displaying a many-body localization (MBL) transition seems sufficiently rich to produce critical points with level statistics interpolating continuously between the Poisson statistics of the localized phase and the Wigner–Dyson statistics of the delocalized phase. In this paper, we consider the strong disorder limit of the MBL transition, where the level statistics at the MBL critical point is close to the Poisson statistics. We analyze a one-dimensional quantum spin model, in order to determine the statistical properties of the rare extensive resonances that are needed to destabilize the MBL phase. At criticality, we find that the entanglement entropy can grow with an exponent 0 < α < 1 anywhere between the area law α = 0 and the volume law α = 1 , as a function of the resonances properties, while the entanglement spectrum follows the strong multifractality statistics. In the MBL phase near criticality, we obtain the simple value ν = 1 for the correlation length exponent. Independently of the strong disorder limit, we explain why, for the many-body localization transition concerning individual eigenstates, the correlation length exponent ν is not constrained by the usual Harris inequality ν 2 / d , so that there is no theoretical inconsistency with the best numerical measure ν = 0 . 8 ( 3 ) obtained by Luitz et al. (2015). Full article
(This article belongs to the Special Issue Quantum Information 2016)
Open AccessArticle Entropy Generation on MHD Casson Nanofluid Flow over a Porous Stretching/Shrinking Surface
Entropy 2016, 18(4), 123; doi:10.3390/e18040123
Received: 24 February 2016 / Revised: 28 March 2016 / Accepted: 30 March 2016 / Published: 6 April 2016
Cited by 34 | PDF Full-text (2899 KB) | HTML Full-text | XML Full-text
Abstract
In this article, entropy generation on MHD Casson nanofluid over a porous Stretching/Shrinking surface has been investigated. The influences of nonlinear thermal radiation and chemical reaction have also taken into account. The governing Casson nanofluid flow problem consists of momentum equation, energy equation
[...] Read more.
In this article, entropy generation on MHD Casson nanofluid over a porous Stretching/Shrinking surface has been investigated. The influences of nonlinear thermal radiation and chemical reaction have also taken into account. The governing Casson nanofluid flow problem consists of momentum equation, energy equation and nanoparticle concentration. Similarity transformation variables have been used to transform the governing coupled partial differential equations into ordinary differential equations. The resulting highly nonlinear coupled ordinary differential equations have been solved numerically with the help of Successive linearization method (SLM) and Chebyshev spectral collocation method. The impacts of various pertinent parameters of interest are discussed for velocity profile, temperature profile, concentration profile and entropy profile. The expression for local Nusselt number and local Sherwood number are also analyzed and discussed with the help of tables. Furthermore, comparison with the existing is also made as a special case of our study. Full article
(This article belongs to the Special Issue Entropy in Nanofluids)
Open AccessArticle Quantum Heat Machines Equivalence, Work Extraction beyond Markovianity, and Strong Coupling via Heat Exchangers
Entropy 2016, 18(4), 124; doi:10.3390/e18040124
Received: 3 March 2016 / Revised: 20 March 2016 / Accepted: 31 March 2016 / Published: 6 April 2016
Cited by 11 | PDF Full-text (783 KB) | HTML Full-text | XML Full-text
Abstract
Various engine types are thermodynamically equivalent in the quantum limit of small “engine action”. Our previous derivation of the equivalence is restricted to Markovian heat baths and to implicit classical work repository (e.g., laser light in the semi-classical approximation). In this paper, all
[...] Read more.
Various engine types are thermodynamically equivalent in the quantum limit of small “engine action”. Our previous derivation of the equivalence is restricted to Markovian heat baths and to implicit classical work repository (e.g., laser light in the semi-classical approximation). In this paper, all the components, baths, batteries, and engines, are explicitly taken into account. To neatly treat non-Markovian dynamics, we use mediating particles that function as a heat exchanger. We find that, on top of the previously observed equivalence, there is a higher degree of equivalence that cannot be achieved in the Markovian regime. Next, we focus on the quality of the battery charging process. A condition for positive energy increase and zero entropy increase (work) is given. Moreover, it is shown that, in the strong coupling regime, it is possible to super-charge a battery. With super-charging, the energy of the battery is increased while its entropy is being reduced at the same time. Full article
(This article belongs to the Special Issue Quantum Thermodynamics)
Figures

Open AccessArticle Exergy Analysis of Complex Ship Energy Systems
Entropy 2016, 18(4), 127; doi:10.3390/e18040127
Received: 12 October 2015 / Revised: 1 February 2016 / Accepted: 21 March 2016 / Published: 8 April 2016
Cited by 1 | PDF Full-text (1756 KB) | HTML Full-text | XML Full-text
Abstract
With multiple primary and secondary energy converters (diesel engines, steam turbines, waste heat recovery (WHR) and oil-fired boilers, etc.) and extensive energy networks (steam, cooling water, exhaust gases, etc.), ships may be considered as complex energy systems. Understanding and optimizing such
[...] Read more.
With multiple primary and secondary energy converters (diesel engines, steam turbines, waste heat recovery (WHR) and oil-fired boilers, etc.) and extensive energy networks (steam, cooling water, exhaust gases, etc.), ships may be considered as complex energy systems. Understanding and optimizing such systems requires advanced holistic energy modeling. This modeling can be done in two ways: The simpler approach focuses on energy flows, and has already been tested, approved and presented; a new, more complicated approach, focusing on energy quality, i.e., exergy, is presented in this paper. Exergy analysis has rarely been applied to ships, and, as a general rule, the shipping industry is not familiar with this tool. This paper tries to fill this gap. We start by giving a short reminder of what exergy is and describe the principles of exergy modeling to explain what kind of results should be expected from such an analysis. We then apply these principles to the analysis of a large two-stroke diesel engine with its cooling and exhaust systems. Simulation results are then presented along with the exergy analysis. Finally, we propose solutions for energy and exergy saving which could be applied to marine engines and ships in general. Full article
(This article belongs to the Special Issue Entropy Generation in Thermal Systems and Processes 2015)
Open AccessArticle The Effect of Threshold Values and Weighting Factors on the Association between Entropy Measures and Mortality after Myocardial Infarction in the Cardiac Arrhythmia Suppression Trial (CAST)
Entropy 2016, 18(4), 129; doi:10.3390/e18040129
Received: 28 January 2016 / Revised: 23 March 2016 / Accepted: 31 March 2016 / Published: 8 April 2016
Cited by 7 | PDF Full-text (683 KB) | HTML Full-text | XML Full-text | Supplementary Files
Abstract
Heart rate variability (HRV) is a non-invasive measurement based on the intervals between normal heart beats that characterize cardiac autonomic function. Decreased HRV is associated with increased risk of cardiovascular events. Characterizing HRV using only moment statistics fails to capture abnormalities in regulatory
[...] Read more.
Heart rate variability (HRV) is a non-invasive measurement based on the intervals between normal heart beats that characterize cardiac autonomic function. Decreased HRV is associated with increased risk of cardiovascular events. Characterizing HRV using only moment statistics fails to capture abnormalities in regulatory function that are important aspects of disease risk. Thus, entropy measures are a promising approach to quantify HRV for risk stratification. The purpose of this study was to investigate this potential for approximate, corrected approximate, sample, fuzzy, and fuzzy measure entropy and its dependency on the parameter selection. Recently, published parameter sets and further parameter combinations were investigated. Heart rate data were obtained from the "Cardiac Arrhythmia Suppression Trial (CAST) RR Interval Sub-Study Database" (Physionet). Corresponding outcomes and clinical data were provided by one of the investigators. The use of previously-reported parameter sets on the pre-treatment data did not significantly add to the identification of patients at risk for cardiovascular death on follow-up. After arrhythmia suppression treatment, several parameter sets predicted outcomes for all patients and patients without coronary artery bypass grafting (CABG). The strongest results were seen using the threshold parameter as a multiple of the data’s standard deviation ( r = 0 . 2 · σ ). Approximate and sample entropy provided significant hazard ratios for patients without CABG and without diabetes for an entropy maximizing threshold approximation. Additional parameter combinations did not improve the results for pre-treatment data. The results of this study illustrate the influence of parameter selection on entropy measures’ potential for cardiovascular risk stratification and support the potential use of entropy measures in future studies. Full article
Open AccessArticle An Informed Framework for Training Classifiers from Social Media
Entropy 2016, 18(4), 130; doi:10.3390/e18040130
Received: 18 January 2016 / Revised: 22 March 2016 / Accepted: 28 March 2016 / Published: 9 April 2016
PDF Full-text (6825 KB) | HTML Full-text | XML Full-text | Supplementary Files
Abstract
Extracting information from social media has become a major focus of companies and researchers in recent years. Aside from the study of the social aspects, it has also been found feasible to exploit the collaborative strength of crowds to help solve classical machine
[...] Read more.
Extracting information from social media has become a major focus of companies and researchers in recent years. Aside from the study of the social aspects, it has also been found feasible to exploit the collaborative strength of crowds to help solve classical machine learning problems like object recognition. In this work, we focus on the generally underappreciated problem of building effective datasets for training classifiers by automatically assembling data from social media. We detail some of the challenges of this approach and outline a framework that uses expanded search queries to retrieve more qualified data. In particular, we concentrate on collaboratively tagged media on the social platform Flickr, and on the problem of image classification to evaluate our approach. Finally, we describe a novel entropy-based method to incorporate an information-theoretic principle to guide our framework. Experimental validation against well-known public datasets shows the viability of this approach and marks an improvement over the state of the art in terms of simplicity and performance. Full article
Open AccessArticle Anti-Icing Superhydrophobic Surfaces: Controlling Entropic Molecular Interactions to Design Novel Icephobic Concrete
Entropy 2016, 18(4), 132; doi:10.3390/e18040132
Received: 22 January 2016 / Revised: 2 March 2016 / Accepted: 6 April 2016 / Published: 12 April 2016
Cited by 9 | PDF Full-text (4482 KB) | HTML Full-text | XML Full-text | Supplementary Files
Abstract
Tribology involves the study of friction, wear, lubrication, and adhesion, including biomimetic superhydrophobic and icephobic surfaces. The three aspects of icephobicity are the low ice adhesion, repulsion of incoming water droplets prior to freezing, and delayed frost formation. Although superhydrophobic surfaces are not
[...] Read more.
Tribology involves the study of friction, wear, lubrication, and adhesion, including biomimetic superhydrophobic and icephobic surfaces. The three aspects of icephobicity are the low ice adhesion, repulsion of incoming water droplets prior to freezing, and delayed frost formation. Although superhydrophobic surfaces are not always icephobic, the theoretical mechanisms behind icephobicity are similar to the entropically driven hydrophobic interactions. The growth of ice crystals in saturated vapor is partially governed by entropically driven diffusion of water molecules to definite locations similarly to hydrophobic interactions. The ice crystal formation can be compared to protein folding controlled by hydrophobic forces. Surface topography and surface energy can affect both the icephobicity and hydrophobicity. By controlling these properties, micro/nanostructured icephobic concrete was developed. The concrete showed ice adhesion strength one order of magnitude lower than regular concrete and could repel incoming water droplets at −5 °C. The icephobic performance of the concrete can be optimized by controlling the sand and polyvinyl alcohol fiber content. Full article
(This article belongs to the Special Issue Entropy Application in Tribology)
Open AccessArticle Heat Transfer Enhancement and Entropy Generation of Nanofluids Laminar Convection in Microchannels with Flow Control Devices
Entropy 2016, 18(4), 134; doi:10.3390/e18040134
Received: 15 February 2016 / Revised: 31 March 2016 / Accepted: 7 April 2016 / Published: 21 April 2016
Cited by 8 | PDF Full-text (4193 KB) | HTML Full-text | XML Full-text
Abstract
The heat transfer enhancement and entropy generation of Al2O3-water nanofluids laminar convective flow in the microchannels with flow control devices (cylinder, rectangle, protrusion, and v-groove) were investigated in this research. The effects of the geometrical structure of the microchannel,
[...] Read more.
The heat transfer enhancement and entropy generation of Al2O3-water nanofluids laminar convective flow in the microchannels with flow control devices (cylinder, rectangle, protrusion, and v-groove) were investigated in this research. The effects of the geometrical structure of the microchannel, nanofluids concentration φ(0%–3%), and Reynolds number Re (50–300) were comparatively studied by means of performance parameters, as well as the limiting streamlines and temperature contours on the modified heated surfaces. The results reveal that the relative Fanning frictional factor f/f0 of the microchannel with rectangle and protrusion devices are much larger and smaller than others, respectively. As the nanofluids concentration increases, f/f0 increases accordingly. For the microchannel with rectangle ribs, there is a transition Re for obtaining the largest heat transfer. The relative Nusselt number Nu/Nu0 of the cases with larger nanofluids concentration are greater. The microchannels with cylinder and v-groove profiles have better heat transfer performance, especially at larger Re cases, while, the microchannel with the protrusion devices is better from an entropy generation minimization perspective. Furthermore, the variation of the relative entropy generation S′/S′0 are influenced by not only the change of Nu/Nu0 and f/f0, but also the physical parameters of working substances. Full article
(This article belongs to the Special Issue Entropy in Nanofluids)
Open AccessArticle On the Stability of Classical Orbits of the Hydrogen Ground State in Stochastic Electrodynamics
Entropy 2016, 18(4), 135; doi:10.3390/e18040135
Received: 19 February 2016 / Revised: 30 March 2016 / Accepted: 31 March 2016 / Published: 13 April 2016
PDF Full-text (291 KB) | HTML Full-text | XML Full-text
Abstract
De la Peña 1980 and Puthoff 1987 show that circular orbits in the hydrogen problem of Stochastic Electrodynamics connect to a stable situation, where the electron neither collapses onto the nucleus nor gets expelled from the atom. Although the Cole-Zou 2003 simulations support
[...] Read more.
De la Peña 1980 and Puthoff 1987 show that circular orbits in the hydrogen problem of Stochastic Electrodynamics connect to a stable situation, where the electron neither collapses onto the nucleus nor gets expelled from the atom. Although the Cole-Zou 2003 simulations support the stability, our recent numerics always lead to self-ionisation. Here the de la Peña-Puthoff argument is extended to elliptic orbits. For very eccentric orbits with energy close to zero and angular momentum below some not-small value, there is on the average a net gain in energy for each revolution, which explains the self-ionisation. Next, an 1 / r 2 potential is added, which could stem from a dipolar deformation of the nuclear charge by the electron at its moving position. This shape retains the analytical solvability. When it is enough repulsive, the ground state of this modified hydrogen problem is predicted to be stable. The same conclusions hold for positronium. Full article
Open AccessArticle Operational Complexity of Supplier-Customer Systems Measured by Entropy—Case Studies
Entropy 2016, 18(4), 137; doi:10.3390/e18040137
Received: 3 December 2015 / Revised: 14 March 2016 / Accepted: 28 March 2016 / Published: 14 April 2016
Cited by 1 | PDF Full-text (5074 KB) | HTML Full-text | XML Full-text
Abstract
This paper discusses a unified entropy-based approach for the quantitative measurement of operational complexity of company supplier-customer relations. Classical Shannon entropy is utilized. Beside this quantification tool, we also explore the relations between Shannon entropy and (c,d)-entropy in more
[...] Read more.
This paper discusses a unified entropy-based approach for the quantitative measurement of operational complexity of company supplier-customer relations. Classical Shannon entropy is utilized. Beside this quantification tool, we also explore the relations between Shannon entropy and (c,d)-entropy in more details. An analytic description of so called iso-quant curves is given, too. We present five case studies, albeit in an anonymous setting, describing various details of general procedures for measuring the operational complexity of supplier-customer systems. In general, we assume a problem-oriented database exists, which contains detailed records of all product forecasts, orders and deliveries both in quantity and time, scheduled and realized, too. Data processing detects important flow variations both in volumes and times, e.g., order—forecast, delivery—order, and actual production—scheduled one. The unifying quantity used for entropy computation is the time gap between actual delivery time and order issue time, which is nothing else but a lead time in inventory control models. After data consistency checks, histograms and empirical distribution functions are constructed. Finally, the entropy, information-theoretic measure of supplier-customer operational complexity, is calculated. Basic steps of the algorithm are mentioned briefly, too. Results of supplier-customer system analysis from selected Czech small and medium-sized enterprises (SMEs) are presented in various computational and managerial decision making details. An enterprise is ranked as SME one, if it has at most 250 employees and its turnover does not exceed 50 million USD per year, or its balance sheet total does not exceed 43 million USD per year, alternatively. Full article
(This article belongs to the Special Issue Computational Complexity)
Open AccessArticle The Free Energy Requirements of Biological Organisms; Implications for Evolution
Entropy 2016, 18(4), 138; doi:10.3390/e18040138
Received: 8 February 2016 / Revised: 24 March 2016 / Accepted: 8 April 2016 / Published: 13 April 2016
Cited by 5 | PDF Full-text (331 KB) | HTML Full-text | XML Full-text | Correction
Abstract
Recent advances in nonequilibrium statistical physics have provided unprecedented insight into the thermodynamics of dynamic processes. The author recently used these advances to extend Landauer’s semi-formal reasoning concerning the thermodynamics of bit erasure, to derive the minimal free energy required to implement an
[...] Read more.
Recent advances in nonequilibrium statistical physics have provided unprecedented insight into the thermodynamics of dynamic processes. The author recently used these advances to extend Landauer’s semi-formal reasoning concerning the thermodynamics of bit erasure, to derive the minimal free energy required to implement an arbitrary computation. Here, I extend this analysis, deriving the minimal free energy required by an organism to run a given (stochastic) map π from its sensor inputs to its actuator outputs. I use this result to calculate the input-output map π of an organism that optimally trades off the free energy needed to run π with the phenotypic fitness that results from implementing π. I end with a general discussion of the limits imposed on the rate of the terrestrial biosphere’s information processing by the flux of sunlight on the Earth. Full article
(This article belongs to the Special Issue Information and Entropy in Biological Systems)
Open AccessArticle Open Markov Processes: A Compositional Perspective on Non-Equilibrium Steady States in Biology
Entropy 2016, 18(4), 140; doi:10.3390/e18040140
Received: 5 January 2016 / Revised: 16 February 2016 / Accepted: 6 April 2016 / Published: 15 April 2016
Cited by 2 | PDF Full-text (289 KB) | HTML Full-text | XML Full-text
Abstract
In recent work, Baez, Fong and the author introduced a framework for describing Markov processes equipped with a detailed balanced equilibrium as open systems of a certain type. These “open Markov processes” serve as the building blocks for more complicated processes. In this
[...] Read more.
In recent work, Baez, Fong and the author introduced a framework for describing Markov processes equipped with a detailed balanced equilibrium as open systems of a certain type. These “open Markov processes” serve as the building blocks for more complicated processes. In this paper, we describe the potential application of this framework in the modeling of biological systems as open systems maintained away from equilibrium. We show that non-equilibrium steady states emerge in open systems of this type, even when the rates of the underlying process are such that a detailed balanced equilibrium is permitted. It is shown that these non-equilibrium steady states minimize a quadratic form which we call “dissipation”. In some circumstances, the dissipation is approximately equal to the rate of change of relative entropy plus a correction term. On the other hand, Prigogine’s principle of minimum entropy production generally fails for non-equilibrium steady states. We use a simple model of membrane transport to illustrate these concepts. Full article
(This article belongs to the Special Issue Information and Entropy in Biological Systems)
Open AccessArticle Testing a Quantum Heat Pump with a Two-Level Spin
Entropy 2016, 18(4), 141; doi:10.3390/e18040141
Received: 9 February 2016 / Revised: 24 March 2016 / Accepted: 8 April 2016 / Published: 15 April 2016
Cited by 2 | PDF Full-text (411 KB) | HTML Full-text | XML Full-text
Abstract
Once in its non-equilibrium steady state, a nanoscale system coupled to several heat baths may be thought of as a “quantum heat pump”. Depending on the direction of its stationary heat flows, it may function as, e.g., a refrigerator or a heat transformer.
[...] Read more.
Once in its non-equilibrium steady state, a nanoscale system coupled to several heat baths may be thought of as a “quantum heat pump”. Depending on the direction of its stationary heat flows, it may function as, e.g., a refrigerator or a heat transformer. These continuous heat devices can be arbitrarily complex multipartite systems, and yet, their working principle is always the same: they are made up of several elementary three-level stages operating in parallel. As a result, it is possible to devise external “black-box” testing strategies to learn about their functionality and performance regardless of any internal details. In particular, one such heat pump can be tested by coupling a two-level spin to one of its “contact transitions”. The steady state of this external probe contains information about the presence of heat leaks and internal dissipation in the device and, also, about the direction of its steady-state heat currents. Provided that the irreversibility of the heat pump is low, one can further estimate its coefficient of performance. These techniques may find applications in the emerging field of quantum thermal engineering, as they facilitate the diagnosis and design optimization of complex thermodynamic cycles. Full article
(This article belongs to the Special Issue Quantum Thermodynamics)
Open AccessArticle Reproducibility Probability Estimation and RP-Testing for Some Nonparametric Tests
Entropy 2016, 18(4), 142; doi:10.3390/e18040142
Received: 13 January 2016 / Revised: 10 March 2016 / Accepted: 6 April 2016 / Published: 16 April 2016
Cited by 1 | PDF Full-text (834 KB) | HTML Full-text | XML Full-text | Supplementary Files
Abstract
Several reproducibility probability (RP)-estimators for the binomial, sign, Wilcoxon signed rank and Kendall tests are studied. Their behavior in terms of MSE is investigated, as well as their performances for RP-testing. Two classes of estimators are considered: the semi-parametric one, where RP-estimators are
[...] Read more.
Several reproducibility probability (RP)-estimators for the binomial, sign, Wilcoxon signed rank and Kendall tests are studied. Their behavior in terms of MSE is investigated, as well as their performances for RP-testing. Two classes of estimators are considered: the semi-parametric one, where RP-estimators are derived from the expression of the exact or approximated power function, and the non-parametric one, whose RP-estimators are obtained on the basis of the nonparametric plug-in principle. In order to evaluate the precision of RP-estimators for each test, the MSE is computed, and the best overall estimator turns out to belong to the semi-parametric class. Then, in order to evaluate the RP-testing performances provided by RP estimators for each test, the disagreement between the RP-testing decision rule, i.e., “accept H0 if the RP-estimate is lower than, or equal to, 1/2, and reject H0 otherwise”, and the classical one (based on the critical value or on the p-value) is obtained. It is shown that the RP-based testing decision for some semi-parametric RP estimators exactly replicates the classical one. In many situations, the RP-estimator replicating the classical decision rule also provides the best MSE. Full article
(This article belongs to the Special Issue Statistical Significance and the Logic of Hypothesis Testing)
Open AccessFeature PaperArticle Mixed Diffusive-Convective Relaxation of a Warm Beam of Energetic Particles in Cold Plasma
Entropy 2016, 18(4), 143; doi:10.3390/e18040143
Received: 9 December 2015 / Revised: 29 February 2016 / Accepted: 11 April 2016 / Published: 16 April 2016
Cited by 2 | PDF Full-text (4120 KB) | HTML Full-text | XML Full-text
Abstract
This work addresses the features of fast particle transport in the bump-on-tail problem for varying the width of the fluctuation spectrum, in the view of possible applications to studies of energetic particle transport in fusion plasmas. Our analysis is built around the idea
[...] Read more.
This work addresses the features of fast particle transport in the bump-on-tail problem for varying the width of the fluctuation spectrum, in the view of possible applications to studies of energetic particle transport in fusion plasmas. Our analysis is built around the idea that strongly-shaped beams do not relax through diffusion only and that there exists an intermediate time scale where the relaxations are convective (ballistic-like). We cast this idea in the form of a self-consistent nonlinear dynamical model, which extends the classic equations of the quasi-linear theory to “broad” beams with internal structure. We also present numerical simulation results of the relaxation of a broad beam of energetic particles in cold plasma. These generally demonstrate the mixed diffusive-convective features of supra-thermal particle transport essentially depending on nonlinear wave-particle interactions and phase-space structures. Taking into account the modes of the stable linear spectrum is crucial for the self-consistent evolution of the distribution function and the fluctuation intensity spectrum. Full article
Open AccessArticle Exploration of Quantum Interference in Document Relevance Judgement Discrepancy
Entropy 2016, 18(4), 144; doi:10.3390/e18040144
Received: 30 January 2016 / Revised: 28 March 2016 / Accepted: 8 April 2016 / Published: 18 April 2016
Cited by 2 | PDF Full-text (863 KB) | HTML Full-text | XML Full-text
Abstract
Quantum theory has been applied in a number of fields outside physics, e.g., cognitive science and information retrieval (IR). Recently, it has been shown that quantum theory can subsume various key IR models into a single mathematical formalism of Hilbert vector spaces. While
[...] Read more.
Quantum theory has been applied in a number of fields outside physics, e.g., cognitive science and information retrieval (IR). Recently, it has been shown that quantum theory can subsume various key IR models into a single mathematical formalism of Hilbert vector spaces. While a series of quantum-inspired IR models has been proposed, limited effort has been devoted to verify the existence of the quantum-like phenomenon in real users’ information retrieval processes, from a real user study perspective. In this paper, we aim to explore and model the quantum interference in users’ relevance judgement about documents, caused by the presentation order of documents. A user study in the context of IR tasks have been carried out. The existence of the quantum interference is tested by the violation of the law of total probability and the validity of the order effect. Our main findings are: (1) there is an apparent judging discrepancy across different users and document presentation orders, and empirical data have violated the law of total probability; (2) most search trials recorded in the user study show the existence of the order effect, and the incompatible decision perspectives in the quantum question (QQ) model are valid in some trials. We further explain the judgement discrepancy in more depth, in terms of four effects (comparison, unfamiliarity, attraction and repulsion) and also analyse the dynamics of document relevance judgement in terms of the evolution of the information need subspace. Full article
Open AccessArticle Training Concept, Evolution Time, and the Maximum Entropy Production Principle
Entropy 2016, 18(4), 145; doi:10.3390/e18040145
Received: 15 December 2015 / Revised: 17 March 2016 / Accepted: 7 April 2016 / Published: 18 April 2016
Cited by 1 | PDF Full-text (1893 KB) | HTML Full-text | XML Full-text | Supplementary Files
Abstract
The maximum entropy production principle (MEPP) is a type of entropy optimization which demands that complex non-equilibrium systems should organize such that the rate of the entropy production is maximized. Our take on this principle is that to prove or disprove the validity
[...] Read more.
The maximum entropy production principle (MEPP) is a type of entropy optimization which demands that complex non-equilibrium systems should organize such that the rate of the entropy production is maximized. Our take on this principle is that to prove or disprove the validity of the MEPP and to test the scope of its applicability, it is necessary to conduct experiments in which the entropy produced per unit time is measured with a high precision. Thus we study electric-field-induced self-assembly in suspensions of carbon nanotubes and realize precise measurements of the entropy production rate (EPR). As a strong voltage is applied the suspended nanotubes merge together into a conducting cloud which produces Joule heat and, correspondingly, produces entropy. We introduce two types of EPR, which have qualitatively different significance: global EPR (g-EPR) and the entropy production rate of the dissipative cloud itself (DC-EPR). The following results are obtained: (1) As the system reaches the maximum of the DC-EPR, it becomes stable because the applied voltage acts as a stabilizing thermodynamic potential; (2) We discover metastable states characterized by high, near-maximum values of the DC-EPR. Under certain conditions, such efficient entropy-producing regimes can only be achieved if the system is allowed to initially evolve under mildly non-equilibrium conditions, namely at a reduced voltage; (3) Without such a “training” period the system typically is not able to reach the allowed maximum of the DC-EPR if the bias is high; (4) We observe that the DC-EPR maximum is achieved within a time, Te, the evolution time, which scales as a power-law function of the applied voltage; (5) Finally, we present a clear example in which the g-EPR theoretical maximum can never be achieved. Yet, under a wide range of conditions, the system can self-organize and achieve a dissipative regime in which the DC-EPR equals its theoretical maximum. Full article
Open AccessArticle A Quantum Query Expansion Approach for Session Search
Entropy 2016, 18(4), 146; doi:10.3390/e18040146
Received: 30 January 2016 / Revised: 9 April 2016 / Accepted: 11 April 2016 / Published: 18 April 2016
Cited by 2 | PDF Full-text (1097 KB) | HTML Full-text | XML Full-text
Abstract
Recently, Quantum Theory (QT) has been employed to advance the theory of Information Retrieval (IR). Various analogies between QT and IR have been established. Among them, a typical one is applying the idea of photon polarization in IR tasks, e.g., for document ranking
[...] Read more.
Recently, Quantum Theory (QT) has been employed to advance the theory of Information Retrieval (IR). Various analogies between QT and IR have been established. Among them, a typical one is applying the idea of photon polarization in IR tasks, e.g., for document ranking and query expansion. In this paper, we aim to further extend this work by constructing a new superposed state of each document in the information need space, based on which we can incorporate the quantum interference idea in query expansion. We then apply the new quantum query expansion model to session search, which is a typical Web search task. Empirical evaluation on the large-scale Clueweb12 dataset has shown that the proposed model is effective in the session search tasks, demonstrating the potential of developing novel and effective IR models based on intuitions and formalisms of QT. Full article
Open AccessArticle Numerical Simulation of Williamson Combined Natural and Forced Convective Fluid Flow between Parallel Vertical Walls with Slip Effects and Radiative Heat Transfer in a Porous Medium
Entropy 2016, 18(4), 147; doi:10.3390/e18040147
Received: 29 February 2016 / Revised: 5 April 2016 / Accepted: 8 April 2016 / Published: 18 April 2016
Cited by 5 | PDF Full-text (2831 KB) | HTML Full-text | XML Full-text | Correction
Abstract
Numerical study of the slip effects and radiative heat transfer on a steady state fully developed Williamson flow of an incompressible Newtonian fluid; between parallel vertical walls of a microchannel with isothermal walls in a porous medium is performed. The slip effects are
[...] Read more.
Numerical study of the slip effects and radiative heat transfer on a steady state fully developed Williamson flow of an incompressible Newtonian fluid; between parallel vertical walls of a microchannel with isothermal walls in a porous medium is performed. The slip effects are considered at both boundary conditions. Radiative highly absorbing medium is modeled by the Rosseland approximation. The non-dimensional governing Navier–Stokes and energy coupled partial differential equations formed a boundary problem are solved numerically using the fourth order Runge–Kutta algorithm by means of a shooting method. Numerical outcomes for the skin friction coefficient, the rate of heat transfer represented by the local Nusselt number were presented even as the velocity and temperature profiles illustrated graphically and analyzed. The effects of the temperature number, Grashof number, thermal radiation parameter, Reynolds number, velocity slip length, Darcy number, and temperature jump, on the flow field and temperature field and their effects on the boundaries are presented and discussed. Full article
(This article belongs to the Section Thermodynamics)
Figures

Figure 1

Open AccessArticle Entropy Generation and Heat Transfer Performances of Al2O3-Water Nanofluid Transitional Flow in Rectangular Channels with Dimples and Protrusions
Entropy 2016, 18(4), 148; doi:10.3390/e18040148
Received: 25 February 2016 / Revised: 8 April 2016 / Accepted: 13 April 2016 / Published: 19 April 2016
Cited by 3 | PDF Full-text (4032 KB) | HTML Full-text | XML Full-text
Abstract
Nanofluid has great potentials in heat transfer enhancement and entropy generation decrease as an effective cooling medium. Effects of Al2O3-water nanofluid flow on entropy generation and heat transfer performance in a rectangular conventional channel are numerically investigated in this
[...] Read more.
Nanofluid has great potentials in heat transfer enhancement and entropy generation decrease as an effective cooling medium. Effects of Al2O3-water nanofluid flow on entropy generation and heat transfer performance in a rectangular conventional channel are numerically investigated in this study. Four different volume fractions are considered and the boundary condition with a constant heat flux is adopted. The flow Reynolds number covers laminar flow, transitional flow and turbulent flow. The influences of the flow regime and nanofluid volume fraction are examined. Furthermore, dimples and protrusions are employed, and the impacts on heat transfer characteristic and entropy generation are acquired. It is found that the average heat transfer entropy generation rate descends and the average friction entropy generation rate rises with an increasing nanofluid volume fraction. The effect of nanofluid on average heat transfer entropy generation rate declines when Reynolds number ascends, which is inverse for average friction entropy generation rate. The average wall temperature and temperature uniformity both drop accompanied with increasing pumping power with the growth in nanofluid volume fraction. The employment of dimples and protrusions significantly decreases the average entropy generation rate and improve the heat transfer performance. The effect of dimple-case shows great difference with that of protrusion-case. Full article
(This article belongs to the Special Issue Entropy in Nanofluids)
Figures

Open AccessArticle Interference Energy Spectrum of the Infinite Square Well
Entropy 2016, 18(4), 149; doi:10.3390/e18040149
Received: 26 February 2016 / Revised: 7 April 2016 / Accepted: 13 April 2016 / Published: 19 April 2016
PDF Full-text (819 KB) | HTML Full-text | XML Full-text
Abstract
Certain superposition states of the 1-D infinite square well have transient zeros at locations other than the nodes of the eigenstates that comprise them. It is shown that if an infinite potential barrier is suddenly raised at some or all of these zeros,
[...] Read more.
Certain superposition states of the 1-D infinite square well have transient zeros at locations other than the nodes of the eigenstates that comprise them. It is shown that if an infinite potential barrier is suddenly raised at some or all of these zeros, the well can be split into multiple adjacent infinite square wells without affecting the wavefunction. This effects a change of the energy eigenbasis of the state to a basis that does not commute with the original, and a subsequent measurement of the energy now reveals a completely different spectrum, which we call the interference energy spectrum of the state. This name is appropriate because the same splitting procedure applied at the stationary nodes of any eigenstate does not change the measurable energy of the state. Of particular interest, this procedure can result in measurable energies that are greater than the energy of the highest mode in the original superposition, raising questions about the conservation of energy akin to those that have been raised in the study of superoscillations. An analytic derivation is given for the interference spectrum of a given wavefunction Ψ ( x , t ) with N known zeros located at points s i = ( x i , t i ) . Numerical simulations were used to verify that a barrier can be rapidly raised at a zero of the wavefunction without significantly affecting it. The interpretation of this result with respect to the conservation of energy and the energy-time uncertainty relation is discussed, and the idea of alternate energy eigenbases is fleshed out. The question of whether or not a preferred discrete energy spectrum is an inherent feature of a particle’s quantum state is examined. Full article
Open AccessArticle On the Approximate Solutions of Local Fractional Differential Equations with Local Fractional Operators
Entropy 2016, 18(4), 150; doi:10.3390/e18040150
Received: 5 March 2016 / Revised: 5 April 2016 / Accepted: 13 April 2016 / Published: 19 April 2016
Cited by 5 | PDF Full-text (225 KB) | HTML Full-text | XML Full-text
Abstract
In this paper, we consider the local fractional decomposition method, variational iteration method, and differential transform method for analytic treatment of linear and nonlinear local fractional differential equations, homogeneous or nonhomogeneous. The operators are taken in the local fractional sense. Some examples are
[...] Read more.
In this paper, we consider the local fractional decomposition method, variational iteration method, and differential transform method for analytic treatment of linear and nonlinear local fractional differential equations, homogeneous or nonhomogeneous. The operators are taken in the local fractional sense. Some examples are given to demonstrate the simplicity and the efficiency of the presented methods. Full article
(This article belongs to the Section Complexity)
Open AccessArticle Computational Principle and Performance Evaluation of Coherent Ising Machine Based on Degenerate Optical Parametric Oscillator Network
Entropy 2016, 18(4), 151; doi:10.3390/e18040151
Received: 20 February 2016 / Revised: 8 April 2016 / Accepted: 12 April 2016 / Published: 19 April 2016
Cited by 7 | PDF Full-text (2378 KB) | HTML Full-text | XML Full-text
Abstract
We present the operational principle of a coherent Ising machine (CIM) based on a degenerate optical parametric oscillator (DOPO) network. A quantum theory of CIM is formulated, and the computational ability of CIM is evaluated by numerical simulation based on c-number stochastic differential
[...] Read more.
We present the operational principle of a coherent Ising machine (CIM) based on a degenerate optical parametric oscillator (DOPO) network. A quantum theory of CIM is formulated, and the computational ability of CIM is evaluated by numerical simulation based on c-number stochastic differential equations. We also discuss the advanced CIM with quantum measurement-feedback control and various problems which can be solved by CIM. Full article
Open AccessArticle An Evolutionary Game Theoretic Approach to Multi-Sector Coordination and Self-Organization
Entropy 2016, 18(4), 152; doi:10.3390/e18040152
Received: 20 November 2015 / Revised: 15 March 2016 / Accepted: 12 April 2016 / Published: 20 April 2016
Cited by 3 | PDF Full-text (1372 KB) | HTML Full-text | XML Full-text
Abstract
Coordination games provide ubiquitous interaction paradigms to frame human behavioral features, such as information transmission, conventions and languages as well as socio-economic processes and institutions. By using a dynamical approach, such as Evolutionary Game Theory (EGT), one is able to follow, in detail,
[...] Read more.
Coordination games provide ubiquitous interaction paradigms to frame human behavioral features, such as information transmission, conventions and languages as well as socio-economic processes and institutions. By using a dynamical approach, such as Evolutionary Game Theory (EGT), one is able to follow, in detail, the self-organization process by which a population of individuals coordinates into a given behavior. Real socio-economic scenarios, however, often involve the interaction between multiple co-evolving sectors, with specific options of their own, that call for generalized and more sophisticated mathematical frameworks. In this paper, we explore a general EGT approach to deal with coordination dynamics in which individuals from multiple sectors interact. Starting from a two-sector, consumer/producer scenario, we investigate the effects of including a third co-evolving sector that we call public. We explore the changes in the self-organization process of all sectors, given the feedback that this new sector imparts on the other two. Full article
(This article belongs to the Special Issue Information and Self-Organization)
Open AccessArticle Measuring Electromechanical Coupling in Patients with Coronary Artery Disease and Healthy Subjects
Entropy 2016, 18(4), 153; doi:10.3390/e18040153
Received: 21 January 2016 / Revised: 7 April 2016 / Accepted: 15 April 2016 / Published: 21 April 2016
Cited by 2 | PDF Full-text (2236 KB) | HTML Full-text | XML Full-text | Supplementary Files
Abstract
Coronary artery disease (CAD) is the most common cause of death globally. To detect CAD noninvasively at an early stage before clinical symptoms occur is still nowadays challenging. Analysis of the variation of heartbeat interval (RRI) opens a new avenue for evaluating the
[...] Read more.
Coronary artery disease (CAD) is the most common cause of death globally. To detect CAD noninvasively at an early stage before clinical symptoms occur is still nowadays challenging. Analysis of the variation of heartbeat interval (RRI) opens a new avenue for evaluating the functional change of cardiovascular system which is accepted to occur at the subclinical stage of CAD. In addition, systolic time interval (STI) and diastolic time interval (DTI) also show potential. There may be coupling in these electromechanical time series due to their physiological connection. However, to the best of our knowledge no publication has systematically investigated how can the coupling be measured and how it changes in CAD patients. In this study, we enrolled 39 CAD patients and 36 healthy subjects and for each subject the electrocardiogram (ECG) and photoplethysmography (PPG) signals were recorded simultaneously for 5 min. The RRI series, STI series, and DTI series were constructed, respectively. We used linear cross correlation (CC), coherence function (CF), as well as nonlinear mutual information (MI), cross conditional entropy (XCE), cross sample entropy (XSampEn), and cross fuzzy entropy (XFuzzyEn) to analyse the bivariate RRI-DTI coupling, RRI-STI coupling, and STI-DTI coupling, respectively. Our results suggest that the linear CC and CF generally have no significant difference between the two groups for all three types of bivariate coupling. The MI only shows weak change in RRI-DTI coupling. By comparison, the three entropy-based coupling measurements show significantly decreased coupling in CAD patients except XSampEn for RRI-DTI coupling (less significant) and XCE for STI-DTI and RRI-STI coupling (not significant). Additionally, the XFuzzyEn performs best as it was still significant if we further applied the Bonferroni correction in our statistical analysis. Our study indicates that the intrinsic electromechanical coupling is most probably nonlinear and can better be measured by nonlinear entropy-based measurements especially the XFuzzyEn. Besides, CAD patients are accompanied by a loss of electromechanical coupling. Our results suggest that cardiac electromechanical coupling may potentially serve as a noninvasive diagnostic tool for CAD. Full article
Open AccessArticle Energetic and Exergetic Analysis of a Heat Exchanger Integrated in a Solid Biomass-Fuelled Micro-CHP System with an Ericsson Engine
Entropy 2016, 18(4), 154; doi:10.3390/e18040154
Received: 22 October 2015 / Revised: 2 March 2016 / Accepted: 12 April 2016 / Published: 20 April 2016
PDF Full-text (2929 KB) | HTML Full-text | XML Full-text
Abstract
A specific heat exchanger has been developed to transfer heat from flue gas to the working fluid (hot air) of the Ericsson engine of a solid biomass-fuelled micro combined heat and power (CHP). In this paper, the theoretical and experimental energetic analyses of
[...] Read more.
A specific heat exchanger has been developed to transfer heat from flue gas to the working fluid (hot air) of the Ericsson engine of a solid biomass-fuelled micro combined heat and power (CHP). In this paper, the theoretical and experimental energetic analyses of this heat exchanger are compared. The experimental performances are described considering energetic and exergetic parameters, in particular the effectiveness on both hot and cold sides. A new exergetic parameter called the exergetic effectiveness is introduced, which allows a comparison between the real and the ideal heat exchanger considering the Second Law of Thermodynamics. A global analysis of exergetic fluxes in the whole micro-CHP system is presented, showing the repartition of the exergy destruction among the components. Full article
(This article belongs to the Special Issue Entropy Generation in Thermal Systems and Processes 2015)
Open AccessArticle Analyses of the Instabilities in the Discretized Diffusion Equations via Information Theory
Entropy 2016, 18(4), 155; doi:10.3390/e18040155
Received: 26 October 2015 / Revised: 15 March 2016 / Accepted: 12 April 2016 / Published: 21 April 2016
PDF Full-text (4372 KB) | HTML Full-text | XML Full-text
Abstract
In a previous investigation (Bigerelle and Iost, 2004), the authors have proposed a physical interpretation of the instability λ = Δtx2 > 1/2 of the parabolic partial differential equations when solved by finite differences. However, our results were obtained
[...] Read more.
In a previous investigation (Bigerelle and Iost, 2004), the authors have proposed a physical interpretation of the instability λ = Δtx2 > 1/2 of the parabolic partial differential equations when solved by finite differences. However, our results were obtained using integration techniques based on erf functions meaning that no statistical fluctuation was introduced in the mathematical background. In this paper, we showed that the diffusive system can be divided into sub-systems onto which a Brownian motion is applied. Monte Carlo simulations are carried out to reproduce the macroscopic diffusive system. It is shown that the amount of information characterized by the compression ratio of information of the system is pertinent to quantify the entropy of the system according to some concepts introduced by the authors (Bigerelle and Iost, 2007). Thanks to this mesoscopic discretization, it is proved that information on each sub-cell of the diffusion map decreases with time before the unstable equality λ = 1/2 and increases after this threshold involving an increase in negentropy, i.e., a decrease in entropy contrarily to the second principle of thermodynamics. Full article
(This article belongs to the Special Issue Entropy Generation in Thermal Systems and Processes 2015)
Figures

Open AccessArticle Logical Entropy of Fuzzy Dynamical Systems
Entropy 2016, 18(4), 157; doi:10.3390/e18040157
Received: 23 February 2016 / Revised: 23 March 2016 / Accepted: 12 April 2016 / Published: 23 April 2016
Cited by 4 | PDF Full-text (249 KB) | HTML Full-text | XML Full-text
Abstract
Recently the logical entropy was suggested by D. Ellerman (2013) as a new information measure. The present paper deals with studying logical entropy and logical mutual information and their properties in a fuzzy probability space. In particular, chain rules for logical entropy and
[...] Read more.
Recently the logical entropy was suggested by D. Ellerman (2013) as a new information measure. The present paper deals with studying logical entropy and logical mutual information and their properties in a fuzzy probability space. In particular, chain rules for logical entropy and for logical mutual information of fuzzy partitions are established. Using the concept of logical entropy of fuzzy partition we define the logical entropy of fuzzy dynamical systems. Finally, it is proved that the logical entropy of fuzzy dynamical systems is invariant under isomorphism of fuzzy dynamical systems. Full article
(This article belongs to the Section Complexity)

Review

Jump to: Research, Other

Open AccessReview Introduction to Supersymmetric Theory of Stochastics
Entropy 2016, 18(4), 108; doi:10.3390/e18040108
Received: 31 October 2015 / Revised: 8 March 2016 / Accepted: 21 March 2016 / Published: 28 March 2016
Cited by 5 | PDF Full-text (1755 KB) | HTML Full-text | XML Full-text
Abstract
Many natural and engineered dynamical systems, including all living objects, exhibit signatures of what can be called spontaneous dynamical long-range order (DLRO). This order’s omnipresence has long been recognized by the scientific community, as evidenced by a myriad of related concepts, theoretical and
[...] Read more.
Many natural and engineered dynamical systems, including all living objects, exhibit signatures of what can be called spontaneous dynamical long-range order (DLRO). This order’s omnipresence has long been recognized by the scientific community, as evidenced by a myriad of related concepts, theoretical and phenomenological frameworks, and experimental phenomena such as turbulence, 1/f noise, dynamical complexity, chaos and the butterfly effect, the Richter scale for earthquakes and the scale-free statistics of other sudden processes, self-organization and pattern formation, self-organized criticality, etc. Although several successful approaches to various realizations of DLRO have been established, the universal theoretical understanding of this phenomenon remained elusive. The possibility of constructing a unified theory of DLRO has emerged recently within the approximation-free supersymmetric theory of stochastics (STS). There, DLRO is the spontaneous breakdown of the topological or de Rahm supersymmetry that all stochastic differential equations (SDEs) possess. This theory may be interesting to researchers with very different backgrounds because the ubiquitous DLRO is a truly interdisciplinary entity. The STS is also an interdisciplinary construction. This theory is based on dynamical systems theory, cohomological field theories, the theory of pseudo-Hermitian operators, and the conventional theory of SDEs. Reviewing the literature on all these mathematical disciplines can be time consuming. As such, a concise and self-contained introduction to the STS, the goal of this paper, may be useful. Full article
(This article belongs to the Special Issue Quantum Nonequilibrium Dynamics)
Open AccessReview Nonlinear Phenomena of Ultracold Atomic Gases in Optical Lattices: Emergence of Novel Features in Extended States
Entropy 2016, 18(4), 118; doi:10.3390/e18040118
Received: 16 December 2015 / Revised: 5 March 2016 / Accepted: 17 March 2016 / Published: 31 March 2016
Cited by 6 | PDF Full-text (1886 KB) | HTML Full-text | XML Full-text
Abstract
The system of a cold atomic gas in an optical lattice is governed by two factors: nonlinearity originating from the interparticle interaction, and the periodicity of the system set by the lattice. The high level of controllability associated with such an arrangement allows
[...] Read more.
The system of a cold atomic gas in an optical lattice is governed by two factors: nonlinearity originating from the interparticle interaction, and the periodicity of the system set by the lattice. The high level of controllability associated with such an arrangement allows for the study of the competition and interplay between these two, and gives rise to a whole range of interesting and rich nonlinear effects. This review covers the basic idea and overview of such nonlinear phenomena, especially those corresponding to extended states. This includes “swallowtail” loop structures of the energy band, Bloch states with multiple periodicity, and those in “nonlinear lattices”, i.e., systems with the nonlinear interaction term itself being a periodic function in space. Full article
(This article belongs to the Special Issue Non-Linear Lattice) Printed Edition available
Figures

Open AccessReview Progress in Finite Time Thermodynamic Studies for Internal Combustion Engine Cycles
Entropy 2016, 18(4), 139; doi:10.3390/e18040139
Received: 31 January 2016 / Revised: 15 March 2016 / Accepted: 7 April 2016 / Published: 15 April 2016
Cited by 35 | PDF Full-text (8848 KB) | HTML Full-text | XML Full-text
Abstract
On the basis of introducing the origin and development of finite time thermodynamics (FTT), this paper reviews the progress in FTT optimization for internal combustion engine (ICE) cycles from the following four aspects: the studies on the optimum performances of air standard endoreversible
[...] Read more.
On the basis of introducing the origin and development of finite time thermodynamics (FTT), this paper reviews the progress in FTT optimization for internal combustion engine (ICE) cycles from the following four aspects: the studies on the optimum performances of air standard endoreversible (with only the irreversibility of heat resistance) and irreversible ICE cycles, including Otto, Diesel, Atkinson, Brayton, Dual, Miller, Porous Medium and Universal cycles with constant specific heats, variable specific heats, and variable specific ratio of the conventional and quantum working fluids (WFs); the studies on the optimum piston motion (OPM) trajectories of ICE cycles, including Otto and Diesel cycles with Newtonian and other heat transfer laws; the studies on the performance limits of ICE cycles with non-uniform WF with Newtonian and other heat transfer laws; as well as the studies on the performance simulation of ICE cycles. In the studies, the optimization objectives include work, power, power density, efficiency, entropy generation rate, ecological function, and so on. The further direction for the studies is explored. Full article
(This article belongs to the Section Thermodynamics)

Other

Jump to: Research, Review

Open AccessComment Comments on Piero Quarati et al. Negentropy in Many-Body Quantum Systems. Entropy 2016, 18, 63
Entropy 2016, 18(4), 125; doi:10.3390/e18040125
Received: 30 March 2016 / Accepted: 30 March 2016 / Published: 7 April 2016
PDF Full-text (179 KB) | HTML Full-text | XML Full-text
Abstract
The purpose of this note is to express my concerns about the published paper by Quarati et al. (Entropy 2016, 18, 63). It is hoped that these comments will stimulate a constructive discussion of the issues involved. Full article
(This article belongs to the Section Quantum Information)
Open AccessReply Reply to Jay Lawrence. Comments on Piero Quarati et al. Negentropy in Many-Body Quantum Systems. Entropy 2016, 18, 63
Entropy 2016, 18(4), 126; doi:10.3390/e18040126
Received: 30 March 2016 / Accepted: 30 March 2016 / Published: 7 April 2016
PDF Full-text (179 KB) | HTML Full-text | XML Full-text
Abstract
The Comments are explicitly related to contents of two published papers: actual [1] and [2].[...] Full article
(This article belongs to the Section Quantum Information)
Open AccessCorrection Correction on Liu, X.; Jiang, A.; Xu, N.; Xue, J. Increment Entropy as a Measure of Complexity for Time Series. Entropy 2016, 18, 22
Entropy 2016, 18(4), 133; doi:10.3390/e18040133
Received: 10 March 2016 / Accepted: 7 April 2016 / Published: 13 April 2016
PDF Full-text (145 KB) | HTML Full-text | XML Full-text
Abstract
The authors wish to make the following correction to their paper [1].[...] Full article
Open AccessCorrection Correction: Kay, B.S. Entropy and Quantum Gravity. Entropy 2015, 17, 8174–8186
Entropy 2016, 18(4), 136; doi:10.3390/e18040136
Received: 24 March 2016 / Accepted: 7 April 2016 / Published: 13 April 2016
PDF Full-text (169 KB) | HTML Full-text | XML Full-text
Abstract
The following corrections should be made to the published paper [1]: First, the paragraph beginning with “One might argue that . . . ” and ending with “. . . increase monotonically with time.”[...] Full article
Back to Top