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Entropy, Volume 15, Issue 12 (December 2013), Pages 5084-5596

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Open AccessArticle Co-Evolutionary Mechanisms of Emotional Bursts in Online Social Dynamics and Networks
Entropy 2013, 15(12), 5084-5120; doi:10.3390/e15125084
Received: 4 October 2013 / Revised: 6 November 2013 / Accepted: 12 November 2013 / Published: 26 November 2013
Cited by 11 | PDF Full-text (4021 KB) | HTML Full-text | XML Full-text
Abstract
Collective emotional behavior of users is frequently observed on various Web portals; however, its complexity and the role of emotions in the acting mechanisms are still not thoroughly understood. In this work, using the empirical data and agent-based modeling, a parallel analysis [...] Read more.
Collective emotional behavior of users is frequently observed on various Web portals; however, its complexity and the role of emotions in the acting mechanisms are still not thoroughly understood. In this work, using the empirical data and agent-based modeling, a parallel analysis is performed of two archetypal systems—Blogs and Internet-Relayed-Chats—both of which maintain self-organized dynamics but not the same communication rules and time scales. The emphasis is on quantifying the collective emotions by means of fractal analysis of the underlying processes as well as topology of social networks, which arise and co-evolve in these stochastic processes. The results reveal that two distinct mechanisms, which are based on different use of emotions (an emotion is characterized by two components, arousal and valence), are intrinsically associated with two classes of emergent social graphs. Their hallmarks are the evolution of communities in accordance with the excess of the negative emotions on popular Blogs, on one side, and smooth spreading of the Bot’s emotional impact over the entire hierarchical network of chats, on the other. Another emphasis of this work is on the understanding of nonextensivity of the emotion dynamics; it was found that, in its own way, each mechanism leads to a reduced phase space of the emotion components when the collective dynamics takes place. That a non-additive entropy describes emotion dynamics, is further confirmed by computing the q-generalized Kolmogorov-Sinai entropy rate in the empirical data of chats as well as in the simulations of interacting emotional agents and Bots. Full article
(This article belongs to the Special Issue Complex Systems)
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Open AccessArticle Energy Transfer Using Unitary Transformations
Entropy 2013, 15(12), 5121-5143; doi:10.3390/e15125121
Received: 16 July 2013 / Revised: 22 October 2013 / Accepted: 18 November 2013 / Published: 26 November 2013
Cited by 1 | PDF Full-text (268 KB) | HTML Full-text | XML Full-text
Abstract
We study the unitary time evolution of a simple quantum Hamiltonian describing two harmonic oscillators coupled via a three-level system. The latter acts as an engine transferring energy from one oscillator to the other and is driven in a cyclic manner by [...] Read more.
We study the unitary time evolution of a simple quantum Hamiltonian describing two harmonic oscillators coupled via a three-level system. The latter acts as an engine transferring energy from one oscillator to the other and is driven in a cyclic manner by time-dependent external fields. The S-matrix (scattering matrix) of the cycle is obtained in analytic form. The total number of quanta contained in the system is a conserved quantity. As a consequence, the spectrum of the S-matrix is purely discrete, and the evolution of the system is quasi-periodic. The explicit knowledge of the S-matrix makes it possible to do accurate numerical evaluations of the time-dependent wave function. They confirm the quasi-periodic behavior. In particular, the energy flows back and forth between the two oscillators in a quasi-periodic manner. Full article
Open AccessArticle The κ-Generalizations of Stirling Approximation and Multinominal Coefficients
Entropy 2013, 15(12), 5144-5153; doi:10.3390/e15125144
Received: 20 August 2013 / Revised: 20 November 2013 / Accepted: 21 November 2013 / Published: 26 November 2013
Cited by 1 | PDF Full-text (131 KB) | HTML Full-text | XML Full-text
Abstract Stirling approximation of the factorials and multinominal coefficients are generalized based on the κ-generalized functions introduced by Kaniadakis. We have related the κ-generalized multinominal coefficients to the κ-entropy by introducing a new κ-product operation, which exists only when κ ≠ 0. Full article
(This article belongs to the collection Advances in Applied Statistical Mechanics)
Open AccessArticle Non–Parametric Estimation of Mutual Information through the Entropy of the Linkage
Entropy 2013, 15(12), 5154-5177; doi:10.3390/e15125154
Received: 25 September 2013 / Revised: 30 October 2013 / Accepted: 11 November 2013 / Published: 26 November 2013
Cited by 1 | PDF Full-text (376 KB) | HTML Full-text | XML Full-text | Supplementary Files
Abstract
A new, non–parametric and binless estimator for the mutual information of a d–dimensional random vector is proposed. First of all, an equation that links the mutual information to the entropy of a suitable random vector with uniformly distributed components is deduced. When [...] Read more.
A new, non–parametric and binless estimator for the mutual information of a d–dimensional random vector is proposed. First of all, an equation that links the mutual information to the entropy of a suitable random vector with uniformly distributed components is deduced. When d = 2 this equation reduces to the well known connection between mutual information and entropy of the copula function associated to the original random variables. Hence, the problem of estimating the mutual information of the original random vector is reduced to the estimation of the entropy of a random vector obtained through a multidimensional transformation. The estimator we propose is a two–step method: first estimate the transformation and obtain the transformed sample, then estimate its entropy. The properties of the new estimator are discussed through simulation examples and its performances are compared to those of the best estimators in the literature. The precision of the estimator converges to values of the same order of magnitude of the best estimator tested. However, the new estimator is unbiased even for larger dimensions and smaller sample sizes, while the other tested estimators show a bias in these cases. Full article
(This article belongs to the Special Issue Estimating Information-Theoretic Quantities from Data)
Open AccessArticle Performance Optimization of Generalized Irreversible Refrigerator Based on a New Ecological Criterion
Entropy 2013, 15(12), 5277-5291; doi:10.3390/e15125277
Received: 10 October 2013 / Revised: 10 November 2013 / Accepted: 18 November 2013 / Published: 29 November 2013
Cited by 3 | PDF Full-text (434 KB) | HTML Full-text | XML Full-text
Abstract
On the basis of the exergy analysis, a performance optimization is carried out for a generalized irreversible refrigerator model, which takes into account the heat resistance, heat leakage and internal irreversibility losses. A new ecological criterion, named coefficient of performance of exergy [...] Read more.
On the basis of the exergy analysis, a performance optimization is carried out for a generalized irreversible refrigerator model, which takes into account the heat resistance, heat leakage and internal irreversibility losses. A new ecological criterion, named coefficient of performance of exergy (COPE), defined as the dimensionless ratio of the exergy output rate to the exergy loss rate, is proposed as an objective function in this paper. The optimal performance factors which maximize the ecological objective function have been discussed. Numerical examples are given to explain the influences of heat leakage and internal irreversibility on the generalized and optimal performances. This new ecological criterion may be beneficial for determining the reasonable design of refrigerators. Full article
Open AccessArticle Competition of Dynamic Self-Confidence and Inhomogeneous Individual Influence in Voter Models
Entropy 2013, 15(12), 5292-5304; doi:10.3390/e15125292
Received: 9 September 2013 / Revised: 11 November 2013 / Accepted: 27 November 2013 / Published: 2 December 2013
Cited by 8 | PDF Full-text (604 KB) | HTML Full-text | XML Full-text
Abstract
In social systems, agents often have different ability to persuade neighbors to adopt their opinions. In this paper, we aim to investigate how the location and heterogeneity of influencers in social networks can improve convergence. We propose a voter model with dynamic [...] Read more.
In social systems, agents often have different ability to persuade neighbors to adopt their opinions. In this paper, we aim to investigate how the location and heterogeneity of influencers in social networks can improve convergence. We propose a voter model with dynamic self-conviction and heterogeneous individual influence which is related to the underlying network topology. An agent may keep its current opinion according to personal conviction, or otherwise, it may preferentially choose the opinion of the neighbor that has a great influence. Individual conviction evolves during the dynamic process, and can be strengthened by social recognition. Simulations indicate our model has three nontrivial results. First, the conservation of average magnetization in the voter model is broken under the effect of individual conviction and influence, and the system evolves to an ordered state in which one opinion is dominant, but total consensus is prevented by extremists. Furthermore, individual influence has a subtle action on opinion evolution. The heterogeneity of individual influence accelerates the relaxation process, but, with the action of dynamic conviction, more heterogeneous influence does not mean the average magnetization will be more ordered. In addition, when competing with agents’ conviction, more heterogeneous individual influence plays a more significant role in agents’ decisions. These results are helpful for understanding some aspects of collective phenomena that occur on online social media. Full article
Open AccessArticle New Results on Fractional Power Series: Theories and Applications
Entropy 2013, 15(12), 5305-5323; doi:10.3390/e15125305
Received: 12 September 2013 / Revised: 9 October 2013 / Accepted: 9 October 2013 / Published: 2 December 2013
Cited by 12 | PDF Full-text (1156 KB) | HTML Full-text | XML Full-text
Abstract
In this paper, some theorems of the classical power series are generalized for the fractional power series. Some of these theorems are constructed by using Caputo fractional derivatives. Under some constraints, we proved that the Caputo fractional derivative can be expressed in [...] Read more.
In this paper, some theorems of the classical power series are generalized for the fractional power series. Some of these theorems are constructed by using Caputo fractional derivatives. Under some constraints, we proved that the Caputo fractional derivative can be expressed in terms of the ordinary derivative. A new construction of the generalized Taylor’s power series is obtained. Some applications including approximation of fractional derivatives and integrals of functions and solutions of linear and nonlinear fractional differential equations are also given. In the nonlinear case, the new and simple technique is used to find out the recurrence relation that determines the coefficients of the fractional power series. Full article
(This article belongs to the Special Issue Dynamical Systems) Print Edition available
Open AccessArticle Generalized (c,d)-Entropy and Aging Random Walks
Entropy 2013, 15(12), 5324-5337; doi:10.3390/e15125324
Received: 26 September 2013 / Revised: 12 November 2013 / Accepted: 25 November 2013 / Published: 3 December 2013
Cited by 12 | PDF Full-text (474 KB) | HTML Full-text | XML Full-text
Abstract
Complex systems are often inherently non-ergodic and non-Markovian and Shannon entropy loses its applicability. Accelerating, path-dependent and aging random walks offer an intuitive picture for non-ergodic and non-Markovian systems. It was shown that the entropy of non-ergodic systems can still be derived [...] Read more.
Complex systems are often inherently non-ergodic and non-Markovian and Shannon entropy loses its applicability. Accelerating, path-dependent and aging random walks offer an intuitive picture for non-ergodic and non-Markovian systems. It was shown that the entropy of non-ergodic systems can still be derived from three of the Shannon–Khinchin axioms and by violating the fourth, the so-called composition axiom. The corresponding entropy is of the form Sc,d ~ ∑iΓ(1 + d, 1 − cln pi) and depends on two system-specific scaling exponents, c and d. This entropy contains many recently proposed entropy functionals as special cases, including Shannon and Tsallis entropy. It was shown that this entropy is relevant for a special class of non-Markovian random walks. In this work, we generalize these walks to a much wider class of stochastic systems that can be characterized as “aging” walks. These are systems whose transition rates between states are path- and time-dependent. We show that for particular aging walks, Sc,d is again the correct extensive entropy. Before the central part of the paper, we review the concept of (c,d)-entropy in a self-contained way. Full article
(This article belongs to the Special Issue Complex Systems)
Open AccessCommunication Non-Equilibrium Statistical Mechanics Inspired by Modern Information Theory
Entropy 2013, 15(12), 5346-5361; doi:10.3390/e15125346
Received: 17 August 2013 / Revised: 22 October 2013 / Accepted: 14 November 2013 / Published: 3 December 2013
Cited by 4 | PDF Full-text (1518 KB) | HTML Full-text | XML Full-text
Abstract
A collection of recent papers revisit how to quantify the relationship between information and work in the light of modern information theory, so-called single-shot information theory. This is an introduction to those papers, from the perspective of the author. Many of the [...] Read more.
A collection of recent papers revisit how to quantify the relationship between information and work in the light of modern information theory, so-called single-shot information theory. This is an introduction to those papers, from the perspective of the author. Many of the results may be viewed as a quantification of how much work a generalized Maxwell’s daemon can extract as a function of its extra information. These expressions do not in general involve the Shannon/von Neumann entropy but rather quantities from single-shot information theory. In a limit of large systems composed of many identical and independent parts the Shannon/von Neumann entropy is recovered. Full article
(This article belongs to the Special Issue Maxwell’s Demon 2013)
Open AccessArticle Ribozyme Activity of RNA Nonenzymatically Polymerized from 3′,5′-Cyclic GMP
Entropy 2013, 15(12), 5362-5383; doi:10.3390/e15125362
Received: 13 September 2013 / Revised: 19 November 2013 / Accepted: 22 November 2013 / Published: 3 December 2013
Cited by 7 | PDF Full-text (1704 KB) | HTML Full-text | XML Full-text | Supplementary Files
Abstract
3′,5′-Cyclic GMP spontaneously nonenzymatically polymerizes in a base-catalyzed reaction affording G oligonucleotides. When reacted with fully or partially sequence-complementary RNA (oligo C), the abiotically generated oligo G RNA displays a typical ribozyme activity consisting of terminal ligation accompanied by cleavage of an [...] Read more.
3′,5′-Cyclic GMP spontaneously nonenzymatically polymerizes in a base-catalyzed reaction affording G oligonucleotides. When reacted with fully or partially sequence-complementary RNA (oligo C), the abiotically generated oligo G RNA displays a typical ribozyme activity consisting of terminal ligation accompanied by cleavage of an internal phosphate site of the donor oligonucleotide stem upon attack of the acceptor 3′ terminal OH. This reaction is dubbed Ligation following Intermolecular Cleavage (LIC). In a prebiotic perspective, the ability of oligo G polynucleotides to react with other sequences outlines a simple and possible evolutionary scenario based on the autocatalytic properties of RNA. Full article
(This article belongs to the Special Issue Entropy and RNA Structure, Folding and Mechanics)
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Open AccessArticle Nonparametric Information Geometry: From Divergence Function to Referential-Representational Biduality on Statistical Manifolds
Entropy 2013, 15(12), 5384-5418; doi:10.3390/e15125384
Received: 3 July 2013 / Revised: 11 October 2013 / Accepted: 22 October 2013 / Published: 4 December 2013
Cited by 9 | PDF Full-text (346 KB) | HTML Full-text | XML Full-text
Abstract
Divergence functions are the non-symmetric “distance” on the manifold, Μθ, of parametric probability density functions over a measure space, (Χ,μ). Classical information geometry prescribes, on Μθ: (i) a Riemannian metric given by the Fisher information; (ii) [...] Read more.
Divergence functions are the non-symmetric “distance” on the manifold, Μθ, of parametric probability density functions over a measure space, (Χ,μ). Classical information geometry prescribes, on Μθ: (i) a Riemannian metric given by the Fisher information; (ii) a pair of dual connections (giving rise to the family of α-connections) that preserve the metric under parallel transport by their joint actions; and (iii) a family of divergence functions ( α-divergence) defined on ΜθΜθ, which induce the metric and the dual connections. Here, we construct an extension of this differential geometric structure from Μθ (that of parametric probability density functions) to the manifold, Μ, of non-parametric functions on X, removing the positivity and normalization constraints. The generalized Fisher information and α-connections on M are induced by an α-parameterized family of divergence functions, reflecting the fundamental convex inequality associated with any smooth and strictly convex function. The infinite-dimensional manifold, M, has zero curvature for all these α-connections; hence, the generally non-zero curvature of M can be interpreted as arising from an embedding of Μθ into Μ. Furthermore, when a parametric model (after a monotonic scaling) forms an affine submanifold, its natural and expectation parameters form biorthogonal coordinates, and such a submanifold is dually flat for α = ± 1, generalizing the results of Amari’s α-embedding. The present analysis illuminates two different types of duality in information geometry, one concerning the referential status of a point (measurable function) expressed in the divergence function (“referential duality”) and the other concerning its representation under an arbitrary monotone scaling (“representational duality”). Full article
Open AccessArticle Core-Based Dynamic Community Detection in Mobile Social Networks
Entropy 2013, 15(12), 5419-5438; doi:10.3390/e15125419
Received: 12 September 2013 / Revised: 21 November 2013 / Accepted: 21 November 2013 / Published: 6 December 2013
Cited by 3 | PDF Full-text (2205 KB) | HTML Full-text | XML Full-text
Abstract
The topic of community detection in social networks has attracted a lot of attention in recent years. Existing methods always depict the relationship of two nodes using the snapshot of the network, but these snapshots cannot reveal the real relationships, especially when [...] Read more.
The topic of community detection in social networks has attracted a lot of attention in recent years. Existing methods always depict the relationship of two nodes using the snapshot of the network, but these snapshots cannot reveal the real relationships, especially when the connection history among nodes is considered. The problem of detecting the stable community in mobile social networks has been studied in this paper. Community cores are considered as stable subsets of the network in previous work. Based on these observations, this paper divides all nodes into a few of communities due to the community cores. Meanwhile, communities can be tracked through incremental computing. Experimental results based on real-world social networks demonstrate that our proposed method performs better than the well-known static community detection algorithm in mobile social networks. Full article
(This article belongs to the Special Issue Social Networks and Information Diffusion)
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Open AccessArticle Consistency and Generalization Bounds for Maximum Entropy Density Estimation
Entropy 2013, 15(12), 5439-5463; doi:10.3390/e15125439
Received: 9 July 2013 / Revised: 13 November 2013 / Accepted: 3 December 2013 / Published: 9 December 2013
Cited by 2 | PDF Full-text (318 KB) | HTML Full-text | XML Full-text
Abstract
We investigate the statistical properties of maximum entropy density estimation, both for the complete data case and the incomplete data case. We show that under certain assumptions, the generalization error can be bounded in terms of the complexity of the underlying feature [...] Read more.
We investigate the statistical properties of maximum entropy density estimation, both for the complete data case and the incomplete data case. We show that under certain assumptions, the generalization error can be bounded in terms of the complexity of the underlying feature functions. This allows us to establish the universal consistency of maximum entropy density estimation. Full article
(This article belongs to the Special Issue Maximum Entropy and Bayes Theorem)
Open AccessArticle Structural Patterns in Complex Systems Using Multidendrograms
Entropy 2013, 15(12), 5464-5474; doi:10.3390/e15125464
Received: 9 October 2013 / Revised: 22 November 2013 / Accepted: 26 November 2013 / Published: 9 December 2013
Cited by 1 | PDF Full-text (279 KB) | HTML Full-text | XML Full-text
Abstract
Complex systems are usually represented as an intricate set of relations between their components forming a complex graph or network. The understanding of their functioning and emergent properties are strongly related to their structural properties. The finding of structural patterns is of [...] Read more.
Complex systems are usually represented as an intricate set of relations between their components forming a complex graph or network. The understanding of their functioning and emergent properties are strongly related to their structural properties. The finding of structural patterns is of utmost importance to reduce the problem of understanding the structure–function relationships. Here we propose the analysis of similarity measures between nodes using hierarchical clustering methods. The discrete nature of the networks usually leads to a small set of different similarity values, making standard hierarchical clustering algorithms ambiguous. We propose the use of multidendrograms, an algorithm that computes agglomerative hierarchical clusterings implementing a variable-group technique that solves the non-uniqueness problem found in the standard pair-group algorithm. This problem arises when there are more than two clusters separated by the same maximum similarity (or minimum distance) during the agglomerative process. Forcing binary trees in this case means breaking ties in some way, thus giving rise to different output clusterings depending on the criterion used. Multidendrograms solves this problem by grouping more than two clusters at the same time when ties occur. Full article
(This article belongs to the Special Issue Complex Systems)
Open AccessArticle Entropy Diversity in Multi-Objective Particle Swarm Optimization
Entropy 2013, 15(12), 5475-5491; doi:10.3390/e15125475
Received: 30 August 2013 / Revised: 30 November 2013 / Accepted: 3 December 2013 / Published: 10 December 2013
Cited by 4 | PDF Full-text (428 KB) | HTML Full-text | XML Full-text
Abstract
Multi-objective particle swarm optimization (MOPSO) is a search algorithm based on social behavior. Most of the existing multi-objective particle swarm optimization schemes are based on Pareto optimality and aim to obtain a representative non-dominated Pareto front for a given problem. Several approaches [...] Read more.
Multi-objective particle swarm optimization (MOPSO) is a search algorithm based on social behavior. Most of the existing multi-objective particle swarm optimization schemes are based on Pareto optimality and aim to obtain a representative non-dominated Pareto front for a given problem. Several approaches have been proposed to study the convergence and performance of the algorithm, particularly by accessing the final results. In the present paper, a different approach is proposed, by using Shannon entropy to analyze the MOPSO dynamics along the algorithm execution. The results indicate that Shannon entropy can be used as an indicator of diversity and convergence for MOPSO problems. Full article
(This article belongs to the Special Issue Dynamical Systems) Print Edition available
Open AccessArticle Bayesian Reliability Estimation for Deteriorating Systems with Limited Samples Using the Maximum Entropy Approach
Entropy 2013, 15(12), 5492-5509; doi:10.3390/e15125492
Received: 17 October 2013 / Revised: 1 December 2013 / Accepted: 3 December 2013 / Published: 12 December 2013
PDF Full-text (336 KB) | HTML Full-text | XML Full-text
Abstract
In this paper the combinations of maximum entropy method and Bayesian inference for reliability assessment of deteriorating system is proposed. Due to various uncertainties, less data and incomplete information, system parameters usually cannot be determined precisely. These uncertainty parameters can be modeled [...] Read more.
In this paper the combinations of maximum entropy method and Bayesian inference for reliability assessment of deteriorating system is proposed. Due to various uncertainties, less data and incomplete information, system parameters usually cannot be determined precisely. These uncertainty parameters can be modeled by fuzzy sets theory and the Bayesian inference which have been proved to be useful for deteriorating systems under small sample sizes. The maximum entropy approach can be used to calculate the maximum entropy density function of uncertainty parameters more accurately for it does not need any additional information and assumptions. Finally, two optimization models are presented which can be used to determine the lower and upper bounds of systems probability of failure under vague environment conditions. Two numerical examples are investigated to demonstrate the proposed method. Full article
Open AccessArticle Information-Theoretic Data Discarding for Dynamic Trees on Data Streams
Entropy 2013, 15(12), 5510-5535; doi:10.3390/e15125510
Received: 9 August 2013 / Revised: 4 December 2013 / Accepted: 9 December 2013 / Published: 13 December 2013
Cited by 2 | PDF Full-text (728 KB) | HTML Full-text | XML Full-text
Abstract
Ubiquitous automated data collection at an unprecedented scale is making available streaming, real-time information flows in a wide variety of settings, transforming both science and industry. Learning algorithms deployed in such contexts often rely on single-pass inference, where the data history is [...] Read more.
Ubiquitous automated data collection at an unprecedented scale is making available streaming, real-time information flows in a wide variety of settings, transforming both science and industry. Learning algorithms deployed in such contexts often rely on single-pass inference, where the data history is never revisited. Learning may also need to be temporally adaptive to remain up-to-date against unforeseen changes in the data generating mechanism. Online Bayesian inference remains challenged by such transient, evolving data streams. Nonparametric modeling techniques can prove particularly ill-suited, as the complexity of the model is allowed to increase with the sample size. In this work, we take steps to overcome these challenges by porting information theoretic heuristics, such as exponential forgetting and active learning, into a fully Bayesian framework. We showcase our methods by augmenting a modern non-parametric modeling framework, dynamic trees, and illustrate its performance on a number of practical examples. The end product is a powerful streaming regression and classification tool, whose performance compares favorably to the state-of-the-art. Full article
(This article belongs to the Special Issue Big Data)
Open AccessArticle Atomic Structure Modeling of Multi-Principal-Element Alloys by the Principle of Maximum Entropy
Entropy 2013, 15(12), 5536-5548; doi:10.3390/e15125536
Received: 20 September 2013 / Revised: 19 November 2013 / Accepted: 25 November 2013 / Published: 13 December 2013
Cited by 6 | PDF Full-text (704 KB) | HTML Full-text | XML Full-text
Abstract
Atomic structure models of multi-principal-element alloys (or high-entropy alloys) composed of four to eight componential elements in both BCC and FCC lattice structures are built according to the principle of maximum entropy. With the concept of entropic force, the maximum-entropy configurations of [...] Read more.
Atomic structure models of multi-principal-element alloys (or high-entropy alloys) composed of four to eight componential elements in both BCC and FCC lattice structures are built according to the principle of maximum entropy. With the concept of entropic force, the maximum-entropy configurations of these phases are generated through the use of Monte Carlo computer simulation. The efficiency of the maximum-entropy principle in modeling the atomic structure of random solid-solution phases has been demonstrated. The bulk atomic configurations of four real multi-principal-element alloys with four to six element components in either BCC or FCC lattice are studied using these models. Full article
(This article belongs to the Special Issue High Entropy Alloys)
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Open AccessArticle Risk Contagion in Chinese Banking Industry: A Transfer Entropy-Based Analysis
Entropy 2013, 15(12), 5549-5564; doi:10.3390/e15125549
Received: 7 September 2013 / Revised: 19 October 2013 / Accepted: 9 December 2013 / Published: 16 December 2013
Cited by 7 | PDF Full-text (391 KB) | HTML Full-text | XML Full-text
Abstract
What is the impact of a bank failure on the whole banking industry? To resolve this issue, the paper develops a transfer entropy-based method to determine the interbank exposure matrix between banks. This method constructs the interbank market structure by calculating the [...] Read more.
What is the impact of a bank failure on the whole banking industry? To resolve this issue, the paper develops a transfer entropy-based method to determine the interbank exposure matrix between banks. This method constructs the interbank market structure by calculating the transfer entropy matrix using bank stock price sequences. This paper also evaluates the stability of Chinese banking system by simulating the risk contagion process. This paper contributes to the literature on interbank contagion mainly in two ways: it establishes a convincing connection between interbank market and transfer entropy, and exploits the market information (stock price) rather than presumptions to determine the interbank exposure matrix. Second, the empirical analysis provides an in depth understanding of the stability of the current Chinese banking system. Full article
(This article belongs to the Special Issue Transfer Entropy)
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Open AccessArticle Global Inequality in Energy Consumption from 1980 to 2010
Entropy 2013, 15(12), 5565-5579; doi:10.3390/e15125565
Received: 21 October 2013 / Revised: 12 December 2013 / Accepted: 12 December 2013 / Published: 16 December 2013
Cited by 10 | PDF Full-text (2469 KB) | HTML Full-text | XML Full-text | Supplementary Files
Abstract
We study the global probability distribution of energy consumption per capita around the world using data from the U.S. Energy Information Administration (EIA) for 1980–2010. We find that the Lorenz curves have moved up during this time period, and the Gini coefficient, [...] Read more.
We study the global probability distribution of energy consumption per capita around the world using data from the U.S. Energy Information Administration (EIA) for 1980–2010. We find that the Lorenz curves have moved up during this time period, and the Gini coefficient, G, has decreased from 0.66 in 1980 to 0.55 in 2010, indicating a decrease in inequality. The global probability distribution of energy consumption per capita in 2010 is close to the exponential distribution withG = 0:5. We attribute this result to the globalization of the world economy, which mixes the world and brings it closer to the state of maximal entropy. We argue that global energy production is a limited resource that is partitioned among the world population. The most probable partition is the one that maximizes entropy, thus resulting in the exponential distribution function. A consequence of the latter is the law of 1/3: the top 1/3 of the world population consumes 2/3 of produced energy. We also find similar results for the global probability distribution of CO2 emissions per capita. Full article
(This article belongs to the Special Issue Complex Systems)
Open AccessArticle A Characterization of Conserved Quantities in Non-Equilibrium Thermodynamics
Entropy 2013, 15(12), 5580-5596; doi:10.3390/e15125580
Received: 30 August 2013 / Revised: 15 November 2013 / Accepted: 6 December 2013 / Published: 17 December 2013
Cited by 2 | PDF Full-text (256 KB) | HTML Full-text | XML Full-text
Abstract
The well-known Noether theorem in Lagrangian and Hamiltonian mechanics associates symmetries in the evolution equations of a mechanical system with conserved quantities. In this work, we extend this classical idea to problems of non-equilibrium thermodynamics formulated within the GENERIC (General Equations for [...] Read more.
The well-known Noether theorem in Lagrangian and Hamiltonian mechanics associates symmetries in the evolution equations of a mechanical system with conserved quantities. In this work, we extend this classical idea to problems of non-equilibrium thermodynamics formulated within the GENERIC (General Equations for Non-Equilibrium Reversible-Irreversible Coupling) framework. The geometric meaning of symmetry is reviewed in this formal setting and then utilized to identify possible conserved quantities and the conditions that guarantee their strict conservation. Examples are provided that demonstrate the validity of the proposed definition in the context of finite and infinite dimensional thermoelastic problems. Full article
(This article belongs to the Special Issue Advances in Methods and Foundations of Non-Equilibrium Thermodynamics)

Review

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Open AccessReview Generalized Statistical Mechanics at the Onset of Chaos
Entropy 2013, 15(12), 5178-5222; doi:10.3390/e15125178
Received: 4 October 2013 / Revised: 9 November 2013 / Accepted: 11 November 2013 / Published: 27 November 2013
Cited by 4 | PDF Full-text (2468 KB) | HTML Full-text | XML Full-text
Abstract
Transitions to chaos in archetypal low-dimensional nonlinear maps offer real and precise model systems in which to assess proposed generalizations of statistical mechanics. The known association of chaotic dynamics with the structure of Boltzmann–Gibbs (BG) statistical mechanics has suggested the potential verification [...] Read more.
Transitions to chaos in archetypal low-dimensional nonlinear maps offer real and precise model systems in which to assess proposed generalizations of statistical mechanics. The known association of chaotic dynamics with the structure of Boltzmann–Gibbs (BG) statistical mechanics has suggested the potential verification of these generalizations at the onset of chaos, when the only Lyapunov exponent vanishes and ergodic and mixing properties cease to hold. There are three well-known routes to chaos in these deterministic dissipative systems, period-doubling, quasi-periodicity and intermittency, which provide the setting in which to explore the limit of validity of the standard BG structure. It has been shown that there is a rich and intricate behavior for both the dynamics within and towards the attractors at the onset of chaos and that these two kinds of properties are linked via generalized statistical-mechanical expressions. Amongst the topics presented are: (i) permanently growing sensitivity fluctuations and their infinite family of generalized Pesin identities; (ii) the emergence of statistical-mechanical structures in the dynamics along the routes to chaos; (iii) dynamical hierarchies with modular organization; and (iv) limit distributions of sums of deterministic variables. The occurrence of generalized entropy properties in condensed-matter physical systems is illustrated by considering critical fluctuations, localization transition and glass formation. We complete our presentation with the description of the manifestations of the dynamics at the transitions to chaos in various kinds of complex systems, such as, frequency and size rank distributions and complex network images of time series. We discuss the results. Full article
(This article belongs to the Special Issue Complex Systems)
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Open AccessReview Entropy in Urban Systems
Entropy 2013, 15(12), 5223-5236; doi:10.3390/e15125223
Received: 23 October 2013 / Revised: 16 November 2013 / Accepted: 25 November 2013 / Published: 27 November 2013
Cited by 8 | PDF Full-text (361 KB) | HTML Full-text | XML Full-text
Abstract
Entropy is a useful concept that has been used to describe the structure and behavior of different systems. We summarize its multifaceted character with regard to its implications for urban sprawl, and propose a framework to apply the concept of entropy to [...] Read more.
Entropy is a useful concept that has been used to describe the structure and behavior of different systems. We summarize its multifaceted character with regard to its implications for urban sprawl, and propose a framework to apply the concept of entropy to urban sprawl for monitoring and management. Full article
(This article belongs to the Special Issue Entropy and Urban Sprawl)
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Open AccessReview Statistical Mechanics Ideas and Techniques Applied to Selected Problems in Ecology
Entropy 2013, 15(12), 5237-5276; doi:10.3390/e15125237
Received: 22 August 2013 / Revised: 15 November 2013 / Accepted: 20 November 2013 / Published: 27 November 2013
Cited by 4 | PDF Full-text (2213 KB) | HTML Full-text | XML Full-text
Abstract
Ecosystem dynamics provides an interesting arena for the application of a plethora concepts and techniques from statistical mechanics. Here I review three examples corresponding each one to an important problem in ecology. First, I start with an analytical derivation of clumpy patterns [...] Read more.
Ecosystem dynamics provides an interesting arena for the application of a plethora concepts and techniques from statistical mechanics. Here I review three examples corresponding each one to an important problem in ecology. First, I start with an analytical derivation of clumpy patterns for species relative abundances (SRA) empirically observed in several ecological communities involving a high number n of species, a phenomenon which have puzzled ecologists for decades. An interesting point is that this derivation uses results obtained from a statistical mechanics model for ferromagnets. Second, going beyond the mean field approximation, I study the spatial version of a popular ecological model involving just one species representing vegetation. The goal is to address the phenomena of catastrophic shifts—gradual cumulative variations in some control parameter that suddenly lead to an abrupt change in the system—illustrating it by means of the process of desertification of arid lands. The focus is on the aggregation processes and the effects of diffusion that combined lead to the formation of non trivial spatial vegetation patterns. It is shown that different quantities—like the variance, the two-point correlation function and the patchiness—may serve as early warnings for the desertification of arid lands. Remarkably, in the onset of a desertification transition the distribution of vegetation patches exhibits scale invariance typical of many physical systems in the vicinity a phase transition. I comment on similarities of and differences between these catastrophic shifts and paradigmatic thermodynamic phase transitions like the liquid-vapor change of state for a fluid. Third, I analyze the case of many species interacting in space. I choose tropical forests, which are mega-diverse ecosystems that exhibit remarkable dynamics. Therefore these ecosystems represent a research paradigm both for studies of complex systems dynamics as well as to unveil the mechanisms responsible for the assembly of species-rich communities. The more classical equilibrium approaches are compared versus non-equilibrium ones and in particular I discuss a recently introduced cellular automaton model in which species compete both locally in physical space and along a niche axis. Full article
(This article belongs to the collection Advances in Applied Statistical Mechanics)
Open AccessReview Physical Properties of High Entropy Alloys
Entropy 2013, 15(12), 5338-5345; doi:10.3390/e15125338
Received: 26 September 2013 / Revised: 20 November 2013 / Accepted: 24 November 2013 / Published: 3 December 2013
Cited by 14 | PDF Full-text (752 KB) | HTML Full-text | XML Full-text
Abstract
The majority of studies on high-entropy alloys are focused on their phase, microstructure, and mechanical properties. However, the physical properties of these materials are also encouraging. This paper provides a brief overview of the physical properties of high-entropy alloys. Emphasis is laid [...] Read more.
The majority of studies on high-entropy alloys are focused on their phase, microstructure, and mechanical properties. However, the physical properties of these materials are also encouraging. This paper provides a brief overview of the physical properties of high-entropy alloys. Emphasis is laid on magnetic, electrical, and thermal properties. Full article
(This article belongs to the Special Issue High Entropy Alloys)

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