2020 Examples of Gibbs States of Mechanical Systems with Symmetries
Charles-Michel Marle
J. Geom. Symmetry Phys. 58: 55-79 (2020). DOI: 10.7546/jgsp-58-2020-55-79

Abstract

In a previous paper, the notion of Gibbs state for the Hamiltonian action of a Lie group on a symplectic manifold was given, together with its applications in Statistical Mechanics, and the works in this field of the French mathematician and physicist Jean-Marie Souriau were presented. Using an adaptation of the cross product for pseudo-Euclidean three-dimensional vector spaces, we present several examples of such Gibbs states, together with the associated thermodynamic functions, for various two-dimensional symplectic manifolds, including the pseudo-spheres, the Poincaré disk and the Poincaré half-plane.

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Charles-Michel Marle. "Examples of Gibbs States of Mechanical Systems with Symmetries." J. Geom. Symmetry Phys. 58 55 - 79, 2020. https://doi.org/10.7546/jgsp-58-2020-55-79

Information

Published: 2020
First available in Project Euclid: 10 February 2021

Digital Object Identifier: 10.7546/jgsp-58-2020-55-79

Rights: Copyright © 2020 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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