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Entropy, Volume 13, Issue 11 (November 2011), Pages 1904-1966

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Research

Open AccessArticle Generalized Hamilton’s Principle for Inelastic Bodies Within Non-Equilibrium Thermodynamics
Entropy 2011, 13(11), 1904-1915; doi:10.3390/e13111904
Received: 5 September 2011 / Revised: 20 October 2011 / Accepted: 25 October 2011 / Published: 26 October 2011
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Abstract
Within the thermodynamic framework with internal variables, the classical Hamilton’s principle for elastic bodies is extended to inelastic bodies composed of materials whose free energy densities are point functions of internal variables, or the so‑termed Green-inelastic bodies, subject to finite deformation and non-conservative
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Within the thermodynamic framework with internal variables, the classical Hamilton’s principle for elastic bodies is extended to inelastic bodies composed of materials whose free energy densities are point functions of internal variables, or the so‑termed Green-inelastic bodies, subject to finite deformation and non-conservative external forces. Yet this general result holds true even without the Green-inelasticity presumption under a more general interpretation of the infinitesimal internal rearrangement. Three special cases are discussed following the generalized form: (a) the Green-elastic bodies whose free energy can be identified with the strain energy; (b) the Green-inelastic bodies composed of materials compliant with the additive decomposition of strain; and (c) the Green-inelastic bodies undergoing isothermal relaxation processes where the thermodynamic forces conjugate to internal variables, or the so-termed internal forces prove to be potential forces. This paper can be viewed as an extension of Yang et al. [1]. Full article
Open AccessArticle A Generalized Maximum Entropy Stochastic Frontier Measuring Productivity Accounting for Spatial Dependency
Entropy 2011, 13(11), 1916-1927; doi:10.3390/e13111916
Received: 29 September 2011 / Revised: 17 October 2011 / Accepted: 24 October 2011 / Published: 28 October 2011
Cited by 1 | PDF Full-text (259 KB) | HTML Full-text | XML Full-text
Abstract
In this paper, a stochastic frontier model accounting for spatial dependency is developed using generalized maximum entropy estimation. An application is made for measuring total factor productivity in European agriculture. The empirical results show that agricultural productivity growth in Europe is driven by
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In this paper, a stochastic frontier model accounting for spatial dependency is developed using generalized maximum entropy estimation. An application is made for measuring total factor productivity in European agriculture. The empirical results show that agricultural productivity growth in Europe is driven by upward movements of technology over time through technological developments. Results are then compared for a situation in which spatial dependency in the technical inefficiency effects is not accounted. Full article
Open AccessArticle Classes of N-Dimensional Nonlinear Fokker-Planck Equations Associated to Tsallis Entropy
Entropy 2011, 13(11), 1928-1944; doi:10.3390/e13111928
Received: 4 October 2011 / Accepted: 21 October 2011 / Published: 1 November 2011
Cited by 20 | PDF Full-text (302 KB) | HTML Full-text | XML Full-text
Abstract
Several previous results valid for one-dimensional nonlinear Fokker-Planck equations are generalized to N-dimensions. A general nonlinear N-dimensional Fokker-Planck equation is derived directly from a master equation, by considering nonlinearitiesin the transition rates. Using nonlinear Fokker-Planck equations, the H-theorem is proved;for that, an important
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Several previous results valid for one-dimensional nonlinear Fokker-Planck equations are generalized to N-dimensions. A general nonlinear N-dimensional Fokker-Planck equation is derived directly from a master equation, by considering nonlinearitiesin the transition rates. Using nonlinear Fokker-Planck equations, the H-theorem is proved;for that, an important relation involving these equations and general entropic forms is introduced. It is shown that due to this relation, classes of nonlinear N-dimensional Fokker-Planck equations are connected to a single entropic form. A particular emphasis is given to the class of equations associated to Tsallis entropy, in both cases of the standard, and generalized definitions for the internal energy. Full article
(This article belongs to the Special Issue Tsallis Entropy)
Open AccessArticle A Characterization of Entropy in Terms of Information Loss
Entropy 2011, 13(11), 1945-1957; doi:10.3390/e13111945
Received: 11 October 2011 / Revised: 18 November 2011 / Accepted: 21 November 2011 / Published: 24 November 2011
Cited by 17 | PDF Full-text (246 KB) | HTML Full-text | XML Full-text
Abstract
There are numerous characterizations of Shannon entropy and Tsallis entropy as measures of information obeying certain properties. Using work by Faddeev and Furuichi, we derive a very simple characterization. Instead of focusing on the entropy of a probability measure on a finite set,
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There are numerous characterizations of Shannon entropy and Tsallis entropy as measures of information obeying certain properties. Using work by Faddeev and Furuichi, we derive a very simple characterization. Instead of focusing on the entropy of a probability measure on a finite set, this characterization focuses on the “information loss”, or change in entropy, associated with a measure-preserving function. Information loss is a special case of conditional entropy: namely, it is the entropy of a random variable conditioned on some function of that variable. We show that Shannon entropy gives the only concept of information loss that is functorial, convex-linear and continuous. This characterization naturally generalizes to Tsallis entropy as well. Full article
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Open AccessArticle Loop Entropy Assists Tertiary Order: Loopy Stabilization of Stacking Motifs
Entropy 2011, 13(11), 1958-1966; doi:10.3390/e13111958
Received: 1 October 2011 / Revised: 10 November 2011 / Accepted: 18 November 2011 / Published: 24 November 2011
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Abstract
The free energy of an RNA fold is a combination of favorable base pairing and stacking interactions competing with entropic costs of forming loops. Here we show how loop entropy, surprisingly, can promote tertiary order. A general formula for the free energy of
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The free energy of an RNA fold is a combination of favorable base pairing and stacking interactions competing with entropic costs of forming loops. Here we show how loop entropy, surprisingly, can promote tertiary order. A general formula for the free energy of forming multibranch and other RNA loops is derived with a polymer-physics based theory. We also derive a formula for the free energy of coaxial stacking in the context of a loop. Simulations support the analytic formulas. The effects of stacking of unpaired bases are also studied with simulations. Full article
(This article belongs to the Special Issue Loop Entropy)
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