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 2 (February 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 1-27
Export citation of selected articles as:

Research

Jump to: Review

Open AccessArticle New Derivatives on the Fractal Subset of Real-Line
Entropy 2016, 18(2), 1; doi:10.3390/e18020001
Received: 6 October 2015 / Revised: 4 December 2015 / Accepted: 15 December 2015 / Published: 29 January 2016
Cited by 8 | PDF Full-text (258 KB) | HTML Full-text | XML Full-text
Abstract
In this manuscript we introduced the generalized fractional Riemann-Liouville and Caputo like derivative for functions defined on fractal sets. The Gamma, Mittag-Leffler and Beta functions were defined on the fractal sets. The non-local Laplace transformation is given and applied for solving linear and
[...] Read more.
In this manuscript we introduced the generalized fractional Riemann-Liouville and Caputo like derivative for functions defined on fractal sets. The Gamma, Mittag-Leffler and Beta functions were defined on the fractal sets. The non-local Laplace transformation is given and applied for solving linear and non-linear fractal equations. The advantage of using these new nonlocal derivatives on the fractals subset of real-line lies in the fact that they are better at modeling processes with memory effect. Full article
(This article belongs to the Special Issue Complex and Fractional Dynamics)
Open AccessArticle Understanding Interdependency Through Complex Information Sharing
Entropy 2016, 18(2), 38; doi:10.3390/e18020038
Received: 14 September 2015 / Revised: 18 December 2015 / Accepted: 22 December 2015 / Published: 26 January 2016
Cited by 5 | PDF Full-text (1122 KB) | HTML Full-text | XML Full-text
Abstract
The interactions between three or more random variables are often nontrivial, poorly understood and, yet, are paramount for future advances in fields such as network information theory, neuroscience and genetics. In this work, we analyze these interactions as different modes of information sharing.
[...] Read more.
The interactions between three or more random variables are often nontrivial, poorly understood and, yet, are paramount for future advances in fields such as network information theory, neuroscience and genetics. In this work, we analyze these interactions as different modes of information sharing. Towards this end, and in contrast to most of the literature that focuses on analyzing the mutual information, we introduce an axiomatic framework for decomposing the joint entropy that characterizes the various ways in which random variables can share information. Our framework distinguishes between interdependencies where the information is shared redundantly and synergistic interdependencies where the sharing structure exists in the whole, but not between the parts. The key contribution of our approach is to focus on symmetric properties of this sharing, which do not depend on a specific point of view for differentiating roles between its components. We show that our axioms determine unique formulas for all of the terms of the proposed decomposition for systems of three variables in several cases of interest. Moreover, we show how these results can be applied to several network information theory problems, providing a more intuitive understanding of their fundamental limits. Full article
(This article belongs to the Section Information Theory)
Open AccessArticle Structure of Optimal State Discrimination in Generalized Probabilistic Theories
Entropy 2016, 18(2), 39; doi:10.3390/e18020039
Received: 30 November 2015 / Revised: 12 January 2016 / Accepted: 20 January 2016 / Published: 26 January 2016
PDF Full-text (494 KB) | HTML Full-text | XML Full-text
Abstract
We consider optimal state discrimination in a general convex operational framework, so-called generalized probabilistic theories (GPTs), and present a general method of optimal discrimination by applying the complementarity problem from convex optimization. The method exploits the convex geometry of states but not other
[...] Read more.
We consider optimal state discrimination in a general convex operational framework, so-called generalized probabilistic theories (GPTs), and present a general method of optimal discrimination by applying the complementarity problem from convex optimization. The method exploits the convex geometry of states but not other detailed conditions or relations of states and effects. We also show that properties in optimal quantum state discrimination are shared in GPTs in general: (i) no measurement sometimes gives optimal discrimination, and (ii) optimal measurement is not unique. Full article
(This article belongs to the Section Quantum Information)
Figures

Open AccessArticle Modelling the Spread of River Blindness Disease via the Caputo Fractional Derivative and the Beta-derivative
Entropy 2016, 18(2), 40; doi:10.3390/e18020040
Received: 17 September 2015 / Revised: 3 November 2015 / Accepted: 5 November 2015 / Published: 26 January 2016
Cited by 4 | PDF Full-text (1572 KB) | HTML Full-text | XML Full-text
Abstract
Information theory is used in many branches of science and technology. For instance, to inform a set of human beings living in a particular region about the fatality of a disease, one makes use of existing information and then converts it into a
[...] Read more.
Information theory is used in many branches of science and technology. For instance, to inform a set of human beings living in a particular region about the fatality of a disease, one makes use of existing information and then converts it into a mathematical equation for prediction. In this work, a model of the well-known river blindness disease is created via the Caputo and beta derivatives. A partial study of stability analysis was presented. The extended system describing the spread of this disease was solved via two analytical techniques: the Laplace perturbation and the homotopy decomposition methods. Summaries of the iteration methods used were provided to derive special solutions to the extended systems. Employing some theoretical parameters, we present some numerical simulations. Full article
(This article belongs to the Special Issue Wavelets, Fractals and Information Theory)
Open AccessArticle Local Band Spectral Entropy Based on Wavelet Packet Applied to Surface EMG Signals Analysis
Entropy 2016, 18(2), 41; doi:10.3390/e18020041
Received: 18 September 2015 / Revised: 31 December 2015 / Accepted: 18 January 2016 / Published: 26 January 2016
PDF Full-text (1192 KB) | HTML Full-text | XML Full-text
Abstract
An efficient analytical method for electromyogram (EMG) signals is of great significance to research the inherent mechanism of a motor-control system. In this paper, we proposed an improved approach named wavelet-packet-based local band spectral entropy (WP-LBSE) by introducing the concept of frequency band
[...] Read more.
An efficient analytical method for electromyogram (EMG) signals is of great significance to research the inherent mechanism of a motor-control system. In this paper, we proposed an improved approach named wavelet-packet-based local band spectral entropy (WP-LBSE) by introducing the concept of frequency band local-energy (ELF) into the wavelet packet entropy, in order to characterize the time-varying complexity of the EMG signals in the local frequency band. The EMG data were recorded from the biceps brachii (BB) muscle and triceps brachii (TB) muscle at 40°, 100° and 180° of elbow flexion by 10 healthy participants. Significant differences existed among any pair of the three patterns (p < 0.05). The WP-LBSE values of the EMG signals in BB muscle and TB muscle demonstrated a decreased tendency from 40° to 180° of elbow flexion, while the distributions of spectral energy were decreased to a stable state as time periods progressed under the same pattern. The result of this present work is helpful to describe the time-varying complexity characteristics of the EMG signals under different joint angles, and is meaningful to research the dynamic variation of the activated motor units and muscle fibers in the motor-control system. Full article
Open AccessArticle Non-Extensive Entropic Distance Based on Diffusion: Restrictions on Parameters in Entropy Formulae
Entropy 2016, 18(2), 42; doi:10.3390/e18020042
Received: 25 November 2015 / Revised: 15 January 2016 / Accepted: 22 January 2016 / Published: 27 January 2016
Cited by 2 | PDF Full-text (219 KB) | HTML Full-text | XML Full-text
Abstract
Based on a diffusion-like master equation we propose a formula using the Bregman divergence for measuring entropic distance in terms of different non-extensive entropy expressions. We obtain the non-extensivity parameter range for a universal approach to the stationary distribution by simple diffusive dynamics
[...] Read more.
Based on a diffusion-like master equation we propose a formula using the Bregman divergence for measuring entropic distance in terms of different non-extensive entropy expressions. We obtain the non-extensivity parameter range for a universal approach to the stationary distribution by simple diffusive dynamics for the Tsallis and the Kaniadakis entropies, for the Hanel–Thurner generalization, and finally for a recently suggested log-log type entropy formula which belongs to diverging variance in the inverse temperature superstatistics. Full article
Open AccessArticle Natural Convection and Entropy Generation in Nanofluid Filled Entrapped Trapezoidal Cavities under the Influence of Magnetic Field
Entropy 2016, 18(2), 43; doi:10.3390/e18020043
Received: 19 November 2015 / Revised: 13 January 2016 / Accepted: 22 January 2016 / Published: 28 January 2016
Cited by 13 | PDF Full-text (3518 KB) | HTML Full-text | XML Full-text
Abstract
In this article, entropy generation due to natural convection in entrapped trapezoidal cavities filled with nanofluid under the influence of magnetic field was numerically investigated. The upper (lower) enclosure is filled with CuO-water (Al2O3-water) nanofluid. The top and bottom
[...] Read more.
In this article, entropy generation due to natural convection in entrapped trapezoidal cavities filled with nanofluid under the influence of magnetic field was numerically investigated. The upper (lower) enclosure is filled with CuO-water (Al2O3-water) nanofluid. The top and bottom horizontal walls of the trapezoidal enclosures are maintained at constant hot temperature while other inclined walls of the enclosures are at constant cold temperature. Different combinations of Hartmann numbers are imposed on the upper and lower trapezoidal cavities. Numerical simulations are conducted for different values of Rayleigh numbers, Hartmann number and solid volume fraction of the nanofluid by using the finite element method. In the upper and lower trapezoidal cavities magnetic fields with different combinations of Hartmann numbers are imposed. It is observed that the averaged heat transfer reduction with magnetic field is more pronounced at the highest value of the Rayleigh number. When there is no magnetic field in the lower cavity, the averaged Nusselt number enhances as the value of the Hartmann number of the upper cavity increases. The heat transfer enhancement rates with nanofluids which are in the range of 10% and 12% are not affected by the presence of the magnetic field. Second law analysis of the system for various values of Hartmann number and nanoparticle volume fractions of upper and lower trapezoidal domains is performed. Full article
(This article belongs to the Special Issue Entropy in Nanofluids)
Open AccessArticle Feature Selection of Power Quality Disturbance Signals with an Entropy-Importance-Based Random Forest
Entropy 2016, 18(2), 44; doi:10.3390/e18020044
Received: 4 November 2015 / Revised: 3 January 2016 / Accepted: 18 January 2016 / Published: 28 January 2016
Cited by 2 | PDF Full-text (2212 KB) | HTML Full-text | XML Full-text
Abstract
Power quality signal feature selection is an effective method to improve the accuracy and efficiency of power quality (PQ) disturbance classification. In this paper, an entropy-importance (EnI)-based random forest (RF) model for PQ feature selection and disturbance classification is proposed. Firstly, 35 kinds
[...] Read more.
Power quality signal feature selection is an effective method to improve the accuracy and efficiency of power quality (PQ) disturbance classification. In this paper, an entropy-importance (EnI)-based random forest (RF) model for PQ feature selection and disturbance classification is proposed. Firstly, 35 kinds of signal features extracted from S-transform (ST) with random noise are used as the original input feature vector of RF classifier to recognize 15 kinds of PQ signals with six kinds of complex disturbance. During the RF training process, the classification ability of different features is quantified by EnI. Secondly, without considering the features with zero EnI, the optimal perturbation feature subset is obtained by applying the sequential forward search (SFS) method which considers the classification accuracy and feature dimension. Then, the reconstructed RF classifier is applied to identify disturbances. According to the simulation results, the classification accuracy is higher than that of other classifiers, and the feature selection effect of the new approach is better than SFS and sequential backward search (SBS) without EnI. With the same feature subset, the new method can maintain a classification accuracy above 99.7% under the condition of 30 dB or above, and the accuracy under 20 dB is 96.8%. Full article
Open AccessArticle Entropy-Weighted Instance Matching Between Different Sourcing Points of Interest
Entropy 2016, 18(2), 45; doi:10.3390/e18020045
Received: 13 September 2015 / Revised: 24 November 2015 / Accepted: 21 January 2016 / Published: 28 January 2016
Cited by 2 | PDF Full-text (5404 KB) | HTML Full-text | XML Full-text
Abstract
The crucial problem for integrating geospatial data is finding the corresponding objects (the counterpart) from different sources. Most current studies focus on object matching with individual attributes such as spatial, name, or other attributes, which avoids the difficulty of integrating those attributes, but
[...] Read more.
The crucial problem for integrating geospatial data is finding the corresponding objects (the counterpart) from different sources. Most current studies focus on object matching with individual attributes such as spatial, name, or other attributes, which avoids the difficulty of integrating those attributes, but at the cost of an ineffective matching. In this study, we propose an approach for matching instances by integrating heterogeneous attributes with the allocation of suitable attribute weights via information entropy. First, a normalized similarity formula is developed, which can simplify the calculation of spatial attribute similarity. Second, sound-based and word segmentation-based methods are adopted to eliminate the semantic ambiguity when there is a lack of a normative coding standard in geospatial data to express the name attribute. Third, category mapping is established to address the heterogeneity among different classifications. Finally, to address the non-linear characteristic of attribute similarity, the weights of the attributes are calculated by the entropy of the attributes. Experiments demonstrate that the Entropy-Weighted Approach (EWA) has good performance both in terms of precision and recall for instance matching from different data sets. Full article
(This article belongs to the Special Issue Applications of Information Theory in the Geosciences)
Figures

Open AccessArticle Entropy Generation through Deterministic Spiral Structures in Corner Flows with Sidewall Surface Mass Injection
Entropy 2016, 18(2), 47; doi:10.3390/e18020047
Received: 3 November 2015 / Revised: 20 January 2016 / Accepted: 22 January 2016 / Published: 2 February 2016
Cited by 2 | PDF Full-text (2780 KB) | HTML Full-text | XML Full-text
Abstract
Results are presented for an innovative computational procedure that predicts time-dependent instabilities and deterministic ordered structures in three-dimensional steady-state laminar boundary-layer flows. The flow configuration considered is a corner flow with sidewall surface mass injection into a horizontal boundary-layer flow. The equations for
[...] Read more.
Results are presented for an innovative computational procedure that predicts time-dependent instabilities and deterministic ordered structures in three-dimensional steady-state laminar boundary-layer flows. The flow configuration considered is a corner flow with sidewall surface mass injection into a horizontal boundary-layer flow. The equations for the velocity fluctuations are cast into a spectral Lorenz-type format and incorporated into the overall computational procedure for the three-dimensional flow. The non-linear time-dependent solutions of the spectral equations predict deterministic spectral ordered structures within spiral structures. Spectral analysis of these fluctuating solutions yields the resulting entropy generation rates resulting from the dissipation of the ordered structures. The results for the entropy generation rates indicate the prediction of a strong burst of ordered structures within the range of injection velocities studied. This new computational method is applicable to only selected thermal design processes. Full article
(This article belongs to the Special Issue Exploring the Second Law of Thermodynamics)
Open AccessArticle Thermodynamics of Quantum Feedback Cooling
Entropy 2016, 18(2), 48; doi:10.3390/e18020048
Received: 24 November 2015 / Revised: 27 January 2016 / Accepted: 28 January 2016 / Published: 4 February 2016
Cited by 5 | PDF Full-text (1130 KB) | HTML Full-text | XML Full-text
Abstract
The ability to initialize quantum registers in pure states lies at the core of many applications of quantum technologies, from sensing to quantum information processing and computation. In this paper, we tackle the problem of increasing the polarization bias of an ensemble of
[...] Read more.
The ability to initialize quantum registers in pure states lies at the core of many applications of quantum technologies, from sensing to quantum information processing and computation. In this paper, we tackle the problem of increasing the polarization bias of an ensemble of two-level register spins by means of joint coherent manipulations, involving a second ensemble of ancillary spins and energy dissipation into an external heat bath. We formulate this spin refrigeration protocol, akin to algorithmic cooling, in the general language of quantum feedback control, and identify the relevant thermodynamic variables involved. Our analysis is two-fold: on the one hand, we assess the optimality of the protocol by means of suitable figures of merit, accounting for both its work cost and effectiveness; on the other hand, we characterise the nature of correlations built up between the register and the ancilla. In particular, we observe that neither the amount of classical correlations nor the quantum entanglement seem to be key ingredients fuelling our spin refrigeration protocol. We report instead that a more general indicator of quantumness beyond entanglement, the so-called quantum discord, is closely related to the cooling performance. Full article
(This article belongs to the Special Issue Quantum Thermodynamics)
Open AccessArticle Particular Solutions of the Confluent Hypergeometric Differential Equation by Using the Nabla Fractional Calculus Operator
Entropy 2016, 18(2), 49; doi:10.3390/e18020049
Received: 13 November 2015 / Revised: 25 January 2016 / Accepted: 27 January 2016 / Published: 5 February 2016
Cited by 4 | PDF Full-text (204 KB) | HTML Full-text | XML Full-text
Abstract
In this work; we present a method for solving the second-order linear ordinary differential equation of hypergeometric type. The solutions of this equation are given by the confluent hypergeometric functions (CHFs). Unlike previous studies, we obtain some different new solutions of the equation
[...] Read more.
In this work; we present a method for solving the second-order linear ordinary differential equation of hypergeometric type. The solutions of this equation are given by the confluent hypergeometric functions (CHFs). Unlike previous studies, we obtain some different new solutions of the equation without using the CHFs. Therefore, we obtain new discrete fractional solutions of the homogeneous and non-homogeneous confluent hypergeometric differential equation (CHE) by using a discrete fractional Nabla calculus operator. Thus, we obtain four different new discrete complex fractional solutions for these equations. Full article
(This article belongs to the Special Issue Complex and Fractional Dynamics)
Open AccessArticle Entropy Generation and Natural Convection of CuO-Water Nanofluid in C-Shaped Cavity under Magnetic Field
Entropy 2016, 18(2), 50; doi:10.3390/e18020050
Received: 28 November 2015 / Revised: 10 January 2016 / Accepted: 27 January 2016 / Published: 5 February 2016
Cited by 12 | PDF Full-text (3608 KB) | HTML Full-text | XML Full-text
Abstract
This paper investigates the entropy generation and natural convection inside a C-shaped cavity filled with CuO-water nanofluid and subjected to a uniform magnetic field. The Brownian motion effect is considered in predicting the nanofluid properties. The governing equations are solved using the finite
[...] Read more.
This paper investigates the entropy generation and natural convection inside a C-shaped cavity filled with CuO-water nanofluid and subjected to a uniform magnetic field. The Brownian motion effect is considered in predicting the nanofluid properties. The governing equations are solved using the finite volume method with the SIMPLE (Semi-Implicit Method for Pressure Linked Equations) algorithm. The studied parameters are the Rayleigh number (1000 ≤ Ra ≤ 15,000), Hartman number (0 ≤ Ha ≤ 45), nanofluid volume fraction (0 ≤ φ ≤ 0.06), and the cavity aspect ratio (0.1 ≤ AR ≤ 0.7). The results have shown that the nanoparticles volume fraction enhances the natural convection but undesirably increases the entropy generation rate. It is also found that the applied magnetic field can suppress both the natural convection and the entropy generation rate, where for Ra = 1000 and φ = 0.04, the percentage reductions in total entropy generation decreases from 96.27% to 48.17% for Ha = 45 compared to zero magnetic field when the aspect ratio is increased from 0.1 to 0.7. The results of performance criterion have shown that the nanoparticles addition can be useful if a compromised magnetic field value represented by a Hartman number of 30 is applied. Full article
(This article belongs to the Special Issue Entropy in Nanofluids)
Open AccessArticle Classification Active Learning Based on Mutual Information
Entropy 2016, 18(2), 51; doi:10.3390/e18020051
Received: 15 December 2015 / Revised: 28 January 2016 / Accepted: 1 February 2016 / Published: 5 February 2016
Cited by 3 | PDF Full-text (625 KB) | HTML Full-text | XML Full-text
Abstract
Selecting a subset of samples to label from a large pool of unlabeled data points, such that a sufficiently accurate classifier is obtained using a reasonably small training set is a challenging, yet critical problem. Challenging, since solving this problem includes cumbersome combinatorial
[...] Read more.
Selecting a subset of samples to label from a large pool of unlabeled data points, such that a sufficiently accurate classifier is obtained using a reasonably small training set is a challenging, yet critical problem. Challenging, since solving this problem includes cumbersome combinatorial computations, and critical, due to the fact that labeling is an expensive and time-consuming task, hence we always aim to minimize the number of required labels. While information theoretical objectives, such as mutual information (MI) between the labels, have been successfully used in sequential querying, it is not straightforward to generalize these objectives to batch mode. This is because evaluation and optimization of functions which are trivial in individual querying settings become intractable for many objectives when we are to select multiple queries. In this paper, we develop a framework, where we propose efficient ways of evaluating and maximizing the MI between labels as an objective for batch mode active learning. Our proposed framework efficiently reduces the computational complexity from an order proportional to the batch size, when no approximation is applied, to the linear cost. The performance of this framework is evaluated using data sets from several fields showing that the proposed framework leads to efficient active learning for most of the data sets. Full article
(This article belongs to the Special Issue Information Theoretic Learning)
Open AccessArticle Sensitivity Analysis of Entropy Generation in Nanofluid Flow inside a Channel by Response Surface Methodology
Entropy 2016, 18(2), 52; doi:10.3390/e18020052
Received: 20 December 2015 / Revised: 18 January 2016 / Accepted: 27 January 2016 / Published: 5 February 2016
Cited by 7 | PDF Full-text (2504 KB) | HTML Full-text | XML Full-text
Abstract
Nanofluids can afford excellent thermal performance and have a major role in energy conservation aspect. In this paper, a sensitivity analysis has been performed by using response surface methodology to calculate the effects of nanoparticles on the entropy generation. For this purpose, the
[...] Read more.
Nanofluids can afford excellent thermal performance and have a major role in energy conservation aspect. In this paper, a sensitivity analysis has been performed by using response surface methodology to calculate the effects of nanoparticles on the entropy generation. For this purpose, the laminar forced convection of Al2O3-water nanofluid flow inside a channel is considered. The total entropy generation rates consist of the entropy generation rates due to heat transfer and friction loss are calculated by using velocity and temperature gradients. The continuity, momentum and energy equations have been solved numerically using a finite volume method. The sensitivity of the entropy generation rate to different parameters such as the solid volume fraction, the particle diameter, and the Reynolds number is studied in detail. Series of simulations were performed for a range of solid volume fraction 0 ≤ ϕ ≤ 0.05 , particle diameter 30  nm ≤ d p ≤ 90 ​ nm , and the Reynolds number 200 ≤ Re ≤ 800. The results showed that the total entropy generation is more sensitive to the Reynolds number rather than the nanoparticles diameter or solid volume fraction. Also, the magnitude of total entropy generation, which increases with increase in the Reynolds number, is much higher for the pure fluid rather than the nanofluid. Full article
(This article belongs to the Special Issue Entropy in Nanofluids)
Open AccessArticle Bounding Extremal Degrees of Edge-Independent Random Graphs Using Relative Entropy
Entropy 2016, 18(2), 53; doi:10.3390/e18020053
Received: 2 December 2015 / Revised: 1 February 2016 / Accepted: 1 February 2016 / Published: 5 February 2016
Cited by 2 | PDF Full-text (256 KB) | HTML Full-text | XML Full-text
Abstract
Edge-independent random graphs are a model of random graphs in which each potential edge appears independently with an individual probability. Based on the relative entropy method, we determine the upper and lower bounds for the extremal vertex degrees using the edge probability matrix
[...] Read more.
Edge-independent random graphs are a model of random graphs in which each potential edge appears independently with an individual probability. Based on the relative entropy method, we determine the upper and lower bounds for the extremal vertex degrees using the edge probability matrix and its largest eigenvalue. Moreover, an application to random graphs with given expected degree sequences is presented. Full article
(This article belongs to the Section Complexity)
Open AccessArticle Definition and Counting of Configurational Microstates in Steady-State Two-Phase Flows in Pore Networks
Entropy 2016, 18(2), 54; doi:10.3390/e18020054
Received: 12 October 2015 / Accepted: 22 January 2016 / Published: 6 February 2016
Cited by 1 | PDF Full-text (4861 KB) | HTML Full-text | XML Full-text
Abstract
Steady-state two-phase flow in porous media is a process whereby a wetting phase displaces a non-wetting phase within a pore network. It is an off-equilibrium stationary process—in the sense that it is maintained in dynamic equilibrium at the expense of energy supplied to
[...] Read more.
Steady-state two-phase flow in porous media is a process whereby a wetting phase displaces a non-wetting phase within a pore network. It is an off-equilibrium stationary process—in the sense that it is maintained in dynamic equilibrium at the expense of energy supplied to the system. The efficiency of the process depends on its spontaneity, measurable by the rate of global entropy production. The latter has been proposed to comprise two components: the rate of mechanical energy dissipation at constant temperature (a thermal entropy component, Q/T, in the continuum mechanics scale) and the configurational entropy (a Boltzmann–Gibbs entropy component, klnW), due to the existence of a canonical ensemble of flow configurations, physically admissible to the externally imposed macrostate conditions. Here, we propose an analytical model to account the number of microstates, lnW, in two-phase flows in pore networks. Combinatorial analysis is implemented to evaluate the number of identified microstates per physically admissible internal flow arrangement, compatible with the imposed steady-state flow conditions. Then, Stirling’s approximation is applied to downscale the large factorial numbers. Finally, the number of microstates is estimated by contriving an appropriate mixing scheme over the canonical ensemble of the physically admissible flow configurations. Indicative computations are furnished. Full article
(This article belongs to the Section Statistical Mechanics)
Open AccessArticle Stability Analysis and Synchronization for a Class of Fractional-Order Neural Networks
Entropy 2016, 18(2), 55; doi:10.3390/e18020055
Received: 26 November 2015 / Accepted: 2 February 2016 / Published: 6 February 2016
Cited by 6 | PDF Full-text (719 KB) | HTML Full-text | XML Full-text
Abstract
Stability of a class of fractional-order neural networks (FONNs) is analyzed in this paper. First, two sufficient conditions for convergence of the solution for such systems are obtained by utilizing Gronwall–Bellman lemma and Laplace transform technique. Then, according to the fractional-order Lyapunov second
[...] Read more.
Stability of a class of fractional-order neural networks (FONNs) is analyzed in this paper. First, two sufficient conditions for convergence of the solution for such systems are obtained by utilizing Gronwall–Bellman lemma and Laplace transform technique. Then, according to the fractional-order Lyapunov second method and linear feedback control, the synchronization problem between two fractional-order chaotic neural networks is investigated. Finally, several numerical examples are presented to justify the feasibility of the proposed methods. Full article
(This article belongs to the Special Issue Complex and Fractional Dynamics)
Open AccessArticle Fractal Representation of Exergy
Entropy 2016, 18(2), 56; doi:10.3390/e18020056
Received: 2 November 2015 / Accepted: 29 January 2016 / Published: 6 February 2016
PDF Full-text (357 KB) | HTML Full-text | XML Full-text
Abstract
We developed a geometrical model to represent the thermodynamic concepts of exergy and anergy. The model leads to multi-scale energy lines (correlons) that we characterised by fractal dimension and entropy analyses. A specific attention will be paid to overlapping points, rising interesting remarks
[...] Read more.
We developed a geometrical model to represent the thermodynamic concepts of exergy and anergy. The model leads to multi-scale energy lines (correlons) that we characterised by fractal dimension and entropy analyses. A specific attention will be paid to overlapping points, rising interesting remarks about trans-scale dynamics of heat flows. Full article
(This article belongs to the Special Issue Entropy Generation in Thermal Systems and Processes 2015)
Open AccessArticle Markov Chain Monte Carlo Used in Parameter Inference of Magnetic Resonance Spectra
Entropy 2016, 18(2), 57; doi:10.3390/e18020057
Received: 31 October 2015 / Accepted: 25 January 2016 / Published: 6 February 2016
PDF Full-text (2865 KB) | HTML Full-text | XML Full-text
Abstract
In this paper, we use Boltzmann statistics and the maximum likelihood distribution derived from Bayes’ Theorem to infer parameter values for a Pake Doublet Spectrum, a lineshape of historical significance and contemporary relevance for determining distances between interacting magnetic dipoles. A Metropolis Hastings
[...] Read more.
In this paper, we use Boltzmann statistics and the maximum likelihood distribution derived from Bayes’ Theorem to infer parameter values for a Pake Doublet Spectrum, a lineshape of historical significance and contemporary relevance for determining distances between interacting magnetic dipoles. A Metropolis Hastings Markov Chain Monte Carlo algorithm is implemented and designed to find the optimum parameter set and to estimate parameter uncertainties. The posterior distribution allows us to define a metric on parameter space that induces a geometry with negative curvature that affects the parameter uncertainty estimates, particularly for spectra with low signal to noise. Full article
Figures

Open AccessArticle A Memristor-Based Hyperchaotic Complex Lü System and Its Adaptive Complex Generalized Synchronization
Entropy 2016, 18(2), 58; doi:10.3390/e18020058
Received: 7 December 2015 / Revised: 3 February 2016 / Accepted: 4 February 2016 / Published: 22 February 2016
Cited by 7 | PDF Full-text (3068 KB) | HTML Full-text | XML Full-text
Abstract
This paper introduces a new memristor-based hyperchaotic complex Lü system (MHCLS) and investigates its adaptive complex generalized synchronization (ACGS). Firstly, the complex system is constructed based on a memristor-based hyperchaotic real Lü system, and its properties are analyzed theoretically. Secondly, its dynamical behaviors,
[...] Read more.
This paper introduces a new memristor-based hyperchaotic complex Lü system (MHCLS) and investigates its adaptive complex generalized synchronization (ACGS). Firstly, the complex system is constructed based on a memristor-based hyperchaotic real Lü system, and its properties are analyzed theoretically. Secondly, its dynamical behaviors, including hyperchaos, chaos, transient phenomena, as well as periodic behaviors, are explored numerically by means of bifurcation diagrams, Lyapunov exponents, phase portraits, and time history diagrams. Thirdly, an adaptive controller and a parameter estimator are proposed to realize complex generalized synchronization and parameter identification of two identical MHCLSs with unknown parameters based on Lyapunov stability theory. Finally, the numerical simulation results of ACGS and its applications to secure communication are presented to verify the feasibility and effectiveness of the proposed method. Full article
(This article belongs to the Section Complexity)
Open AccessArticle An Optimization Approach of Deriving Bounds between Entropy and Error from Joint Distribution: Case Study for Binary Classifications
Entropy 2016, 18(2), 59; doi:10.3390/e18020059
Received: 3 December 2015 / Revised: 3 February 2016 / Accepted: 4 February 2016 / Published: 19 February 2016
PDF Full-text (1541 KB) | HTML Full-text | XML Full-text
Abstract
In this work, we propose a new approach of deriving the bounds between entropy and error from a joint distribution through an optimization means. The specific case study is given on binary classifications. Two basic types of classification errors are investigated, namely, the
[...] Read more.
In this work, we propose a new approach of deriving the bounds between entropy and error from a joint distribution through an optimization means. The specific case study is given on binary classifications. Two basic types of classification errors are investigated, namely, the Bayesian and non-Bayesian errors. The consideration of non-Bayesian errors is due to the facts that most classifiers result in non-Bayesian solutions. For both types of errors, we derive the closed-form relations between each bound and error components. When Fano’s lower bound in a diagram of “Error Probability vs. Conditional Entropy” is realized based on the approach, its interpretations are enlarged by including non-Bayesian errors and the two situations along with independent properties of the variables. A new upper bound for the Bayesian error is derived with respect to the minimum prior probability, which is generally tighter than Kovalevskij’s upper bound. Full article
(This article belongs to the Special Issue Information Theoretic Learning)
Open AccessArticle Varying Constants Entropic-ΛCDM Cosmology
Entropy 2016, 18(2), 60; doi:10.3390/e18020060
Received: 22 December 2015 / Revised: 26 January 2016 / Accepted: 27 January 2016 / Published: 22 February 2016
Cited by 4 | PDF Full-text (4271 KB) | HTML Full-text | XML Full-text
Abstract
We formulate the basic framework of thermodynamical entropic force cosmology which allows variation of the gravitational constant G and the speed of light c. Three different approaches to the formulation of the field equations are presented. Some cosmological solutions for each framework
[...] Read more.
We formulate the basic framework of thermodynamical entropic force cosmology which allows variation of the gravitational constant G and the speed of light c. Three different approaches to the formulation of the field equations are presented. Some cosmological solutions for each framework are given and one of them is tested against combined observational data (supernovae, BAO, and CMB). From the fit of the data, it is found that the Hawking temperature numerical coefficient γ is two to four orders of magnitude less than usually assumed on the geometrical ground theoretical value of O(1) and that it is also compatible with zero. In addition, in the entropic scenario, we observationally test that the fit of the data is allowed for the speed of light c growing and the gravitational constant G diminishing during the evolution of the universe. We also obtain a bound on the variation of c to be Δc / c ∝ 10-5 > 0 , which is at least one order of magnitude weaker than the quasar spectra observational bound. Full article
(This article belongs to the Special Issue Entropy in Quantum Gravity and Quantum Cosmology)
Open AccessArticle Nonparametric Problem-Space Clustering: Learning Efficient Codes for Cognitive Control Tasks
Entropy 2016, 18(2), 61; doi:10.3390/e18020061
Received: 16 July 2015 / Revised: 29 January 2016 / Accepted: 14 February 2016 / Published: 19 February 2016
Cited by 6 | PDF Full-text (2143 KB) | HTML Full-text | XML Full-text
Abstract
We present an information-theoretic method permitting one to find structure in a problem space (here, in a spatial navigation domain) and cluster it in ways that are convenient to solve different classes of control problems, which include planning a path to a goal
[...] Read more.
We present an information-theoretic method permitting one to find structure in a problem space (here, in a spatial navigation domain) and cluster it in ways that are convenient to solve different classes of control problems, which include planning a path to a goal from a known or an unknown location, achieving multiple goals and exploring a novel environment. Our generative nonparametric approach, called the generative embedded Chinese restaurant process (geCRP), extends the family of Chinese restaurant process (CRP) models by introducing a parameterizable notion of distance (or kernel) between the states to be clustered together. By using different kernels, such as the the conditional probability or joint probability of two states, the same geCRP method clusters the environment in ways that are more sensitive to different control-related information, such as goal, sub-goal and path information. We perform a series of simulations in three scenarios—an open space, a grid world with four rooms and a maze having the same structure as the Hanoi Tower—in order to illustrate the characteristics of the different clusters (obtained using different kernels) and their relative benefits for solving planning and control problems. Full article
(This article belongs to the Special Issue Information Theoretic Incentives for Cognitive Systems)
Open AccessArticle High Temperature Oxidation and Corrosion Properties of High Entropy Superalloys
Entropy 2016, 18(2), 62; doi:10.3390/e18020062
Received: 11 January 2016 / Revised: 1 February 2016 / Accepted: 15 February 2016 / Published: 22 February 2016
Cited by 9 | PDF Full-text (10038 KB) | HTML Full-text | XML Full-text
Abstract
The present work investigates the high temperature oxidation and corrosion behaviour of high entropy superalloys (HESA). A high content of various solutes in HESA leads to formation of complex oxides, however the Cr and Al activities of HESA are sufficient to promote protective
[...] Read more.
The present work investigates the high temperature oxidation and corrosion behaviour of high entropy superalloys (HESA). A high content of various solutes in HESA leads to formation of complex oxides, however the Cr and Al activities of HESA are sufficient to promote protective chromia or alumina formation on the surface. By comparing the oxidation and corrosion resistances of a Ni-based superalloy—CM247LC, Al2O3-forming HESA can possess comparable oxidation resistance at 1100 °C, and Cr2O3-forming HESA can exhibit superior resistance against hot corrosion at 900 °C. This work has demonstrated the potential of HESA to maintain surface stability in oxidizing and corrosive environments. Full article
(This article belongs to the Special Issue High-Entropy Alloys and High-Entropy-Related Materials)
Figures

Open AccessArticle Negentropy in Many-Body Quantum Systems
Entropy 2016, 18(2), 63; doi:10.3390/e18020063
Received: 25 June 2015 / Revised: 26 January 2016 / Accepted: 17 February 2016 / Published: 22 February 2016
Cited by 2 | PDF Full-text (279 KB) | HTML Full-text | XML Full-text
Abstract
Negentropy (negative entropy) is the negative contribution to the total entropy of correlated many-body environments. Negentropy can play a role in transferring its related stored mobilizable energy to colliding nuclei that participate in spontaneous or induced nuclear fusions in solid or liquid metals
[...] Read more.
Negentropy (negative entropy) is the negative contribution to the total entropy of correlated many-body environments. Negentropy can play a role in transferring its related stored mobilizable energy to colliding nuclei that participate in spontaneous or induced nuclear fusions in solid or liquid metals or in stellar plasmas. This energy transfer mechanism can explain the observed increase of nuclear fusion rates relative to the standard Salpeter screening. The importance of negentropy in these specific many-body quantum systems and its relation to many-body correlation entropy are discussed. Full article

Review

Jump to: Research

Open AccessReview Relative Entropy in Biological Systems
Entropy 2016, 18(2), 46; doi:10.3390/e18020046
Received: 9 December 2015 / Revised: 18 January 2016 / Accepted: 21 January 2016 / Published: 2 February 2016
Cited by 5 | PDF Full-text (291 KB) | HTML Full-text | XML Full-text
Abstract
In this paper we review various information-theoretic characterizations of the approach to equilibrium in biological systems. The replicator equation, evolutionary game theory, Markov processes and chemical reaction networks all describe the dynamics of a population or probability distribution. Under suitable assumptions, the distribution
[...] Read more.
In this paper we review various information-theoretic characterizations of the approach to equilibrium in biological systems. The replicator equation, evolutionary game theory, Markov processes and chemical reaction networks all describe the dynamics of a population or probability distribution. Under suitable assumptions, the distribution will approach an equilibrium with the passage of time. Relative entropy—that is, the Kullback–Leibler divergence, or various generalizations of this—provides a quantitative measure of how far from equilibrium the system is. We explain various theorems that give conditions under which relative entropy is nonincreasing. In biochemical applications these results can be seen as versions of the Second Law of Thermodynamics, stating that free energy can never increase with the passage of time. In ecological applications, they make precise the notion that a population gains information from its environment as it approaches equilibrium. Full article
(This article belongs to the Special Issue Information and Entropy in Biological Systems)
Back to Top