Entropy

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Thermodynamics and Fluctuations Far From Equilibrium

by John Ross and Alejandro Fernández Villaverde

Entropy 2010, 12(10), 2199-2243; https://doi.org/10.3390/e12102199 - 21 Oct 2010

Cited by 17 | Viewed by 9727

We review a coherent mesoscopic presentation of thermodynamics and fluctuations far from and near equilibrium, applicable to chemical reactions, energy transfer and transport processes, and electrochemical systems. Both uniform and spatially dependent systems are considered. The focus is on processes leading to and [...] Read more.

We review a coherent mesoscopic presentation of thermodynamics and fluctuations far from and near equilibrium, applicable to chemical reactions, energy transfer and transport processes, and electrochemical systems. Both uniform and spatially dependent systems are considered. The focus is on processes leading to and in non‑equilibrium stationary states; on systems with multiple stationary states; and on issues of relative stability of such states. We establish thermodynamic state functions, dependent on the irreversible processes, with simple physical interpretations that yield the work available from these processes and the fluctuations. A variety of experiments are cited that substantiate the theory. The following topics are included: one-variable systems, linear and nonlinear; connection of thermodynamic theory with stochastic theory; multivariable systems; relative stability of different phases; coupled transport processes; experimental determination of thermodynamic and stochastic potentials; dissipation in irreversible processes and nonexistence of extremum theorems; efficiency of oscillatory reactions, including biochemical systems; and fluctuation-dissipation relations. Full article

(This article belongs to the Special Issue Nonequilibrium Thermodynamics)

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119 KiB

Open AccessArticle

Black Hole Entropy for Two Higher Derivative Theories of Gravity

by Emilio Bellini, Roberto Di Criscienzo, Lorenzo Sebastiani and Sergio Zerbini

Entropy 2010, 12(10), 2186-2198; https://doi.org/10.3390/e12102186 - 21 Oct 2010

Cited by 12 | Viewed by 7808

Abstract

The dark energy issue is attracting the attention of an increasing number of physicists all over the world. Among the possible alternatives to explain what as been named the “Mystery of the Millennium” are the so-called Modified Theories of Gravity. A crucial test [...] Read more.

The dark energy issue is attracting the attention of an increasing number of physicists all over the world. Among the possible alternatives to explain what as been named the “Mystery of the Millennium” are the so-called Modified Theories of Gravity. A crucial test for such models is represented by the existence and (if this is the case) the properties of their black hole solutions. Nowadays, to our knowledge, only two non-trivial, static, spherically symmetric, solutions with vanishing cosmological constant are known by Barrow & Clifton (2005) and Deser, Sarioglu & Tekin (2008). The aim of the paper is to discuss some features of such solutions, with emphasis on their thermodynamic properties such as entropy and temperature. Full article

(This article belongs to the Special Issue Entropy in Quantum Gravity)

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229 KiB

Open AccessArticle

Incorporating Spatial Structures in Ecological Inference: An Information Theory Approach

by Rosa Bernardini Papalia

Entropy 2010, 12(10), 2171-2185; https://doi.org/10.3390/e12102171 - 14 Oct 2010

Cited by 6 | Viewed by 6149

Abstract

This paper introduces an Information Theory-based method for modeling economic aggregates and estimating their sub-group (sub-area) decomposition when no individual or sub-group data are available. This method offers a flexible framework for modeling the underlying variation in sub-group indicators, by addressing the spatial [...] Read more.

This paper introduces an Information Theory-based method for modeling economic aggregates and estimating their sub-group (sub-area) decomposition when no individual or sub-group data are available. This method offers a flexible framework for modeling the underlying variation in sub-group indicators, by addressing the spatial dependency problem. A basic ecological inference problem, which allows for spatial heterogeneity and dependence, is presented with the aim of first estimating the model at the aggregate level, and then of employing the estimated coefficients to obtain the sub-group level indicators. Full article

(This article belongs to the Special Issue Advances in Information Theory)

853 KiB

Open AccessArticle

Increasing and Decreasing Returns and Losses in Mutual Information Feature Subset Selection

by Gert Van Dijck and Marc M. Van Hulle

Entropy 2010, 12(10), 2144-2170; https://doi.org/10.3390/e12102144 - 11 Oct 2010

Cited by 6 | Viewed by 8915

Abstract

Mutual information between a target variable and a feature subset is extensively used as a feature subset selection criterion. This work contributes to a more thorough understanding of the evolution of the mutual information as a function of the number of features selected. [...] Read more.

Mutual information between a target variable and a feature subset is extensively used as a feature subset selection criterion. This work contributes to a more thorough understanding of the evolution of the mutual information as a function of the number of features selected. We describe decreasing returns and increasing returns behavior in sequential forward search and increasing losses and decreasing losses behavior in sequential backward search. We derive conditions under which the decreasing returns and the increasing losses behavior hold and prove the occurrence of this behavior in some Bayesian networks. The decreasing returns behavior implies that the mutual information is concave as a function of the number of features selected, whereas the increasing returns behavior implies this function is convex. The increasing returns and decreasing losses behavior are proven to occur in an XOR hypercube. Full article

(This article belongs to the Special Issue Advances in Information Theory)

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301 KiB

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On the Microscopic Perspective of Black Branes Thermodynamic Geometry

by Stefano Bellucci and Bhupendra Nath Tiwari

Entropy 2010, 12(10), 2097-2143; https://doi.org/10.3390/e12102097 - 30 Sep 2010

Cited by 20 | Viewed by 6999

Abstract

We study thermodynamic state-space geometry of the black holes in string theory and M-theory. For a large number of microstates, we analyze the intrinsic state-space geometry for (i) extremal and non-extremal black branes in string theory, (ii) multi-centered black brane configurations, (iv) small [...] Read more.

We study thermodynamic state-space geometry of the black holes in string theory and M-theory. For a large number of microstates, we analyze the intrinsic state-space geometry for (i) extremal and non-extremal black branes in string theory, (ii) multi-centered black brane configurations, (iv) small black holes with fractional branes, and (v) fuzzy rings in the setup of Mathur’s fuzzballs and subensemble theory. We extend our analysis for the black brane foams and bubbling black brane solutions in M-theory. We discuss the nature of state-space correlations of various black brane configurations, and show that the notion of state-space manifolds describes the associated coarse-grained interactions of the corresponding microscopic CFT data. Full article

933 KiB

Open AccessArticle

Information Driven Ecohydrologic Self-Organization

by Praveen Kumar and Benjamin L. Ruddell

Entropy 2010, 12(10), 2085-2096; https://doi.org/10.3390/e12102085 - 29 Sep 2010

Cited by 44 | Viewed by 7999

Abstract

Variability plays an important role in the self-organized interaction between vegetation and its environment, yet the principles that characterize the role of the variability in these interactions remain elusive. To address this problem, we study the dependence between a number of variables measured [...] Read more.

Variability plays an important role in the self-organized interaction between vegetation and its environment, yet the principles that characterize the role of the variability in these interactions remain elusive. To address this problem, we study the dependence between a number of variables measured at flux towers by quantifying the information flow between the different variables along with the associated time lag. By examining this network of feedback loops for seven ecosystems in different climate regions, we find that: (1) the feedback tends to maximize information production in the entire system, and the latter increases with increasing variability within the whole system; and (2) variables that participate in feedback exhibit moderated variability. Self-organization arises as a tradeoff where the ability of the total system to maximize information production through feedback is limited by moderate variability of the participating variables. This relationship between variability and information production leads to the emergence of ordered organization. Full article

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64 KiB

Open AccessArticle

A Microeconomic Interpretation of the Maximum Entropy Estimator of Multinomial Logit Models and Its Equivalence to the Maximum Likelihood Estimator

by Pedro Donoso and Louis de Grange

Entropy 2010, 12(10), 2077-2084; https://doi.org/10.3390/e12102077 - 29 Sep 2010

Cited by 13 | Viewed by 7251

Abstract

Maximum entropy models are often used to describe supply and demand behavior in urban transportation and land use systems. However, they have been criticized for not representing behavioral rules of system agents and because their parameters seems to adjust only to modeler-imposed constraints. [...] Read more.

Maximum entropy models are often used to describe supply and demand behavior in urban transportation and land use systems. However, they have been criticized for not representing behavioral rules of system agents and because their parameters seems to adjust only to modeler-imposed constraints. In response, it is demonstrated that the solution to the entropy maximization problem with linear constraints is a multinomial logit model whose parameters solve the likelihood maximization problem of this probabilistic model. But this result neither provides a microeconomic interpretation of the entropy maximization problem nor explains the equivalence of these two optimization problems. This work demonstrates that an analysis of the dual of the entropy maximization problem yields two useful alternative explanations of its solution. The first shows that the maximum entropy estimators of the multinomial logit model parameters reproduce rational user behavior, while the second shows that the likelihood maximization problem for multinomial logit models is the dual of the entropy maximization problem. Full article

(This article belongs to the Special Issue Maximum Entropy 2010)

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Entropy, Volume 12, Issue 10 (October 2010) – 7 articles , Pages 2077-2243

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