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Entropy 2017, 19(8), 381; https://doi.org/10.3390/e19080381

Kinetic Theory beyond the Stosszahlansatz

1
Department of Computer Science, University of Geneva, Route de Drize 7, 1227 Geneva, Switzerland
2
Department of Theoretical Physics, University of Geneva, Quai Ernest-Ansermet 24, 1211 Geneva, Switzerland
*
Author to whom correspondence should be addressed.
Received: 8 June 2017 / Revised: 20 July 2017 / Accepted: 21 July 2017 / Published: 25 July 2017
(This article belongs to the Special Issue Entropy, Time and Evolution)
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Abstract

In a recent paper (Chliamovitch, et al., 2015), we suggested using the principle of maximum entropy to generalize Boltzmann’s Stosszahlansatz to higher-order distribution functions. This conceptual shift of focus allowed us to derive an analog of the Boltzmann equation for the two-particle distribution function. While we only briefly mentioned there the possibility of a hydrodynamical treatment, we complete here a crucial step towards this program. We discuss bilocal collisional invariants, from which we deduce the two-particle stationary distribution. This allows for the existence of equilibrium states in which the momenta of particles are correlated, as well as for the existence of a fourth conserved quantity besides mass, momentum and kinetic energy. View Full-Text
Keywords: kinetic theory; non-equilibrium statistical mechanics; maximum entropy principle kinetic theory; non-equilibrium statistical mechanics; maximum entropy principle
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Chliamovitch, G.; Malaspinas, O.; Chopard, B. Kinetic Theory beyond the Stosszahlansatz. Entropy 2017, 19, 381.

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