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Entropy, Volume 18, Issue 4 (April 2016)

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Open AccessArticle Logical Entropy of Fuzzy Dynamical Systems
Entropy 2016, 18(4), 157; https://doi.org/10.3390/e18040157
Received: 23 February 2016 / Revised: 23 March 2016 / Accepted: 12 April 2016 / Published: 23 April 2016
Cited by 11 | 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
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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)
Open AccessArticle Analyses of the Instabilities in the Discretized Diffusion Equations via Information Theory
Entropy 2016, 18(4), 155; https://doi.org/10.3390/e18040155
Received: 26 October 2015 / Revised: 15 March 2016 / Accepted: 12 April 2016 / Published: 21 April 2016
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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
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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)
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Open AccessArticle Measuring Electromechanical Coupling in Patients with Coronary Artery Disease and Healthy Subjects
Entropy 2016, 18(4), 153; https://doi.org/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
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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
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Open AccessArticle Heat Transfer Enhancement and Entropy Generation of Nanofluids Laminar Convection in Microchannels with Flow Control Devices
Entropy 2016, 18(4), 134; https://doi.org/10.3390/e18040134
Received: 15 February 2016 / Revised: 31 March 2016 / Accepted: 7 April 2016 / Published: 21 April 2016
Cited by 13 | 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,
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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)
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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; https://doi.org/10.3390/e18040154
Received: 22 October 2015 / Revised: 2 March 2016 / Accepted: 12 April 2016 / Published: 20 April 2016
Cited by 1 | 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
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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)
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Open AccessArticle An Evolutionary Game Theoretic Approach to Multi-Sector Coordination and Self-Organization
Entropy 2016, 18(4), 152; https://doi.org/10.3390/e18040152
Received: 20 November 2015 / Revised: 15 March 2016 / Accepted: 12 April 2016 / Published: 20 April 2016
Cited by 5 | 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,
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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)
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Open AccessArticle Computational Principle and Performance Evaluation of Coherent Ising Machine Based on Degenerate Optical Parametric Oscillator Network
Entropy 2016, 18(4), 151; https://doi.org/10.3390/e18040151
Received: 20 February 2016 / Revised: 8 April 2016 / Accepted: 12 April 2016 / Published: 19 April 2016
Cited by 8 | 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
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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
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Open AccessArticle On the Approximate Solutions of Local Fractional Differential Equations with Local Fractional Operators
Entropy 2016, 18(4), 150; https://doi.org/10.3390/e18040150
Received: 5 March 2016 / Revised: 5 April 2016 / Accepted: 13 April 2016 / Published: 19 April 2016
Cited by 10 | 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
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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 Interference Energy Spectrum of the Infinite Square Well
Entropy 2016, 18(4), 149; https://doi.org/10.3390/e18040149
Received: 26 February 2016 / Revised: 7 April 2016 / Accepted: 13 April 2016 / Published: 19 April 2016
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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,
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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
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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; https://doi.org/10.3390/e18040148
Received: 25 February 2016 / Revised: 8 April 2016 / Accepted: 13 April 2016 / Published: 19 April 2016
Cited by 5 | 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
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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)
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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; https://doi.org/10.3390/e18040147
Received: 29 February 2016 / Revised: 5 April 2016 / Accepted: 8 April 2016 / Published: 18 April 2016
Cited by 7 | 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
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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)
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Open AccessArticle A Quantum Query Expansion Approach for Session Search
Entropy 2016, 18(4), 146; https://doi.org/10.3390/e18040146
Received: 30 January 2016 / Revised: 9 April 2016 / Accepted: 11 April 2016 / Published: 18 April 2016
Cited by 5 | 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
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Open AccessArticle Training Concept, Evolution Time, and the Maximum Entropy Production Principle
Entropy 2016, 18(4), 145; https://doi.org/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
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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
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Open AccessArticle Exploration of Quantum Interference in Document Relevance Judgement Discrepancy
Entropy 2016, 18(4), 144; https://doi.org/10.3390/e18040144
Received: 30 January 2016 / Revised: 28 March 2016 / Accepted: 8 April 2016 / Published: 18 April 2016
Cited by 6 | 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
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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
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Open AccessFeature PaperArticle Mixed Diffusive-Convective Relaxation of a Warm Beam of Energetic Particles in Cold Plasma
Entropy 2016, 18(4), 143; https://doi.org/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
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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
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Open AccessArticle Reproducibility Probability Estimation and RP-Testing for Some Nonparametric Tests
Entropy 2016, 18(4), 142; https://doi.org/10.3390/e18040142
Received: 13 January 2016 / Revised: 10 March 2016 / Accepted: 6 April 2016 / Published: 16 April 2016
Cited by 2 | 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
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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)
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Open AccessArticle Testing a Quantum Heat Pump with a Two-Level Spin
Entropy 2016, 18(4), 141; https://doi.org/10.3390/e18040141
Received: 9 February 2016 / Revised: 24 March 2016 / Accepted: 8 April 2016 / Published: 15 April 2016
Cited by 3 | 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.
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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)
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Open AccessArticle Open Markov Processes: A Compositional Perspective on Non-Equilibrium Steady States in Biology
Entropy 2016, 18(4), 140; https://doi.org/10.3390/e18040140
Received: 5 January 2016 / Revised: 16 February 2016 / Accepted: 6 April 2016 / Published: 15 April 2016
Cited by 6 | 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
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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)
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Open AccessReview Progress in Finite Time Thermodynamic Studies for Internal Combustion Engine Cycles
Entropy 2016, 18(4), 139; https://doi.org/10.3390/e18040139
Received: 31 January 2016 / Revised: 15 March 2016 / Accepted: 7 April 2016 / Published: 15 April 2016
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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
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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)
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Open AccessArticle Operational Complexity of Supplier-Customer Systems Measured by Entropy—Case Studies
Entropy 2016, 18(4), 137; https://doi.org/10.3390/e18040137
Received: 3 December 2015 / Revised: 14 March 2016 / Accepted: 28 March 2016 / Published: 14 April 2016
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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
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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)
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Open AccessArticle The Free Energy Requirements of Biological Organisms; Implications for Evolution
Entropy 2016, 18(4), 138; https://doi.org/10.3390/e18040138
Received: 8 February 2016 / Revised: 24 March 2016 / Accepted: 8 April 2016 / Published: 13 April 2016
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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
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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 AccessCorrection Correction: Kay, B.S. Entropy and Quantum Gravity. Entropy 2015, 17, 8174–8186
Entropy 2016, 18(4), 136; https://doi.org/10.3390/e18040136
Received: 24 March 2016 / Accepted: 7 April 2016 / Published: 13 April 2016
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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
Open AccessArticle On the Stability of Classical Orbits of the Hydrogen Ground State in Stochastic Electrodynamics
Entropy 2016, 18(4), 135; https://doi.org/10.3390/e18040135
Received: 19 February 2016 / Revised: 30 March 2016 / Accepted: 31 March 2016 / Published: 13 April 2016
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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
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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
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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; https://doi.org/10.3390/e18040133
Received: 10 March 2016 / Accepted: 7 April 2016 / Published: 13 April 2016
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Abstract
The authors wish to make the following correction to their paper [1].[...] Full article
Open AccessArticle Generalized Analysis of a Distribution Separation Method
Entropy 2016, 18(4), 105; https://doi.org/10.3390/e18040105
Received: 25 November 2015 / Revised: 11 March 2016 / Accepted: 15 March 2016 / Published: 13 April 2016
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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
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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)
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Open AccessArticle Anti-Icing Superhydrophobic Surfaces: Controlling Entropic Molecular Interactions to Design Novel Icephobic Concrete
Entropy 2016, 18(4), 132; https://doi.org/10.3390/e18040132
Received: 22 January 2016 / Revised: 2 March 2016 / Accepted: 6 April 2016 / Published: 12 April 2016
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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
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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)
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Open AccessArticle An Informed Framework for Training Classifiers from Social Media
Entropy 2016, 18(4), 130; https://doi.org/10.3390/e18040130
Received: 18 January 2016 / Revised: 22 March 2016 / Accepted: 28 March 2016 / Published: 9 April 2016
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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
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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
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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; https://doi.org/10.3390/e18040129
Received: 28 January 2016 / Revised: 23 March 2016 / Accepted: 31 March 2016 / Published: 8 April 2016
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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
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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
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Open AccessArticle Exergy Analysis of Complex Ship Energy Systems
Entropy 2016, 18(4), 127; https://doi.org/10.3390/e18040127
Received: 12 October 2015 / Revised: 1 February 2016 / Accepted: 21 March 2016 / Published: 8 April 2016
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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
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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)
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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; https://doi.org/10.3390/e18040126
Received: 30 March 2016 / Accepted: 30 March 2016 / Published: 7 April 2016
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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)
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