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Jean-Marie Souriau’s Symplectic Model of Statistical Physics: Seminal Papers on Lie Groups Thermodynamics - Quod Erat Demonstrandum

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Geometric Structures of Statistical Physics, Information Geometry, and Learning (SPIGL 2020)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 361))

Abstract

The objective of this chapter is to make better known Jean-Marie Souriau works, more particularly his symplectic model of statistical physics, called “Lie groups thermodynamics”. This model was initially described in chapter IV “Statistical Mechanics” of his book “Structure of dynamical systems” published in 1969. We have translated in English some parts of three Souriau’s publications which provide more details about this geometric model of Thermodynamics. Entropy acquires a geometric foundation as a function parameterized by mean of moment map in dual Lie algebra, and in term of foliations. Souriau established the generalized Gibbs laws when the manifold has a symplectic form and a connected Lie group G operates on this manifold by symplectomorphisms. Souriau Entropy is invariant under the action of the group acting on the homogeneous symplectic manifold. As quoted by Souriau, these equations are universal and could be also of great interest in Mathematics.

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Authors and Affiliations

  1. Thales Land and Air Systems, Voie Pierre-Gilles de Gennes, 91470, Limours, France

    Frédéric Barbaresco

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  1. Frédéric Barbaresco
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Correspondence to Frédéric Barbaresco .

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  1. Thales Land & Air Systems, Technical Directorate, Thales, Limours, France

    Frédéric Barbaresco

  2. Sony Computer Science Laboratories Inc., Tokyo, Japan

    Frank Nielsen

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Barbaresco, F. (2021). Jean-Marie Souriau’s Symplectic Model of Statistical Physics: Seminal Papers on Lie Groups Thermodynamics - Quod Erat Demonstrandum. In: Barbaresco, F., Nielsen, F. (eds) Geometric Structures of Statistical Physics, Information Geometry, and Learning. SPIGL 2020. Springer Proceedings in Mathematics & Statistics, vol 361. Springer, Cham. https://doi.org/10.1007/978-3-030-77957-3_2

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