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Definition and Time Evolution of Correlations in Classical Statistical Mechanics

The study of dense gases and liquids requires consideration of the interactions between the particles and the correlations created by these interactions. In this article, the N-variable distribution function which maximizes the Uncertainty (Shannon’s information entropy) and admits as marginals a se...

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Autor principal: Dufour, Claude G.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2018
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7512483/
https://www.ncbi.nlm.nih.gov/pubmed/33266622
http://dx.doi.org/10.3390/e20120898
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author Dufour, Claude G.
author_facet Dufour, Claude G.
author_sort Dufour, Claude G.
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description The study of dense gases and liquids requires consideration of the interactions between the particles and the correlations created by these interactions. In this article, the N-variable distribution function which maximizes the Uncertainty (Shannon’s information entropy) and admits as marginals a set of (N−1)-variable distribution functions, is, by definition, free of N-order correlations. This way to define correlations is valid for stochastic systems described by discrete variables or continuous variables, for equilibrium or non-equilibrium states and correlations of the different orders can be defined and measured. This allows building the grand-canonical expressions of the uncertainty valid for either a dilute gas system or a dense gas system. At equilibrium, for both kinds of systems, the uncertainty becomes identical to the expression of the thermodynamic entropy. Two interesting by-products are also provided by the method: (i) The Kirkwood superposition approximation (ii) A series of generalized superposition approximations. A theorem on the temporal evolution of the relevant uncertainty for molecular systems governed by two-body forces is proved and a conjecture closely related to this theorem sheds new light on the origin of the irreversibility of molecular systems. In this respect, the irreplaceable role played by the three-body interactions is highlighted.
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spelling pubmed-75124832020-11-09 Definition and Time Evolution of Correlations in Classical Statistical Mechanics Dufour, Claude G. Entropy (Basel) Article The study of dense gases and liquids requires consideration of the interactions between the particles and the correlations created by these interactions. In this article, the N-variable distribution function which maximizes the Uncertainty (Shannon’s information entropy) and admits as marginals a set of (N−1)-variable distribution functions, is, by definition, free of N-order correlations. This way to define correlations is valid for stochastic systems described by discrete variables or continuous variables, for equilibrium or non-equilibrium states and correlations of the different orders can be defined and measured. This allows building the grand-canonical expressions of the uncertainty valid for either a dilute gas system or a dense gas system. At equilibrium, for both kinds of systems, the uncertainty becomes identical to the expression of the thermodynamic entropy. Two interesting by-products are also provided by the method: (i) The Kirkwood superposition approximation (ii) A series of generalized superposition approximations. A theorem on the temporal evolution of the relevant uncertainty for molecular systems governed by two-body forces is proved and a conjecture closely related to this theorem sheds new light on the origin of the irreversibility of molecular systems. In this respect, the irreplaceable role played by the three-body interactions is highlighted. MDPI 2018-11-23 /pmc/articles/PMC7512483/ /pubmed/33266622 http://dx.doi.org/10.3390/e20120898 Text en © 2018 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Dufour, Claude G.
Definition and Time Evolution of Correlations in Classical Statistical Mechanics
title Definition and Time Evolution of Correlations in Classical Statistical Mechanics
title_full Definition and Time Evolution of Correlations in Classical Statistical Mechanics
title_fullStr Definition and Time Evolution of Correlations in Classical Statistical Mechanics
title_full_unstemmed Definition and Time Evolution of Correlations in Classical Statistical Mechanics
title_short Definition and Time Evolution of Correlations in Classical Statistical Mechanics
title_sort definition and time evolution of correlations in classical statistical mechanics
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7512483/
https://www.ncbi.nlm.nih.gov/pubmed/33266622
http://dx.doi.org/10.3390/e20120898
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