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Open AccessArticle

Definition and Time Evolution of Correlations in Classical Statistical Mechanics

Formerly Department of Physics, Université de Mons-UMONS, Place du Parc 20, B-7000 Mons, Belgium
Entropy 2018, 20(12), 898; https://doi.org/10.3390/e20120898
Received: 3 October 2018 / Revised: 19 November 2018 / Accepted: 19 November 2018 / Published: 23 November 2018
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. View Full-Text
Keywords: information theory; high order correlations; entropy; many-body interactions; irreversibility information theory; high order correlations; entropy; many-body interactions; irreversibility
MDPI and ACS Style

Dufour, C.G. Definition and Time Evolution of Correlations in Classical Statistical Mechanics. Entropy 2018, 20, 898.

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