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Entropy 2016, 18(7), 254; doi:10.3390/e18070254

Link between Lie Group Statistical Mechanics and Thermodynamics of Continua

Laboratoire de Mécanique de Lille, CNRS FRE 3723, Université de Lille 1, Villeneuve d’Ascq F59655, France
Academic Editors: Frédéric Barbaresco and Frank Nielsen
Received: 29 April 2016 / Revised: 17 June 2016 / Accepted: 7 July 2016 / Published: 12 July 2016
(This article belongs to the Special Issue Differential Geometrical Theory of Statistics)
View Full-Text   |   Download PDF [293 KB, uploaded 12 July 2016]

Abstract

In this work, we consider the value of the momentum map of the symplectic mechanics as an affine tensor called momentum tensor. From this point of view, we analyze the underlying geometric structure of the theories of Lie group statistical mechanics and relativistic thermodynamics of continua, formulated by Souriau independently of each other. We bridge the gap between them in the classical Galilean context. These geometric structures of the thermodynamics are rich and we think they might be a source of inspiration for the geometric theory of information based on the concept of entropy. View Full-Text
Keywords: Lie groups; symplectic geometry; affine tensors; continuum thermodynamics; statistical mechanics Lie groups; symplectic geometry; affine tensors; continuum thermodynamics; statistical mechanics
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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de Saxcé, G. Link between Lie Group Statistical Mechanics and Thermodynamics of Continua. Entropy 2016, 18, 254.

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