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

DOI10.1007/978-3-030-77957-3_2OpenAlexW3175546975MaRDI QIDQ5021891

Frédéric Barbaresco

Publication date: 14 January 2022

Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-030-77957-3_2

zbMATH Keywords

symplectic geometryLie groupsthermodynamicsrepresentation theorystatistical physicsmoment map

Mathematics Subject Classification ID

Computer science (68-XX) Statistical mechanics, structure of matter (82-XX) Differential geometry (53-XX)

Related Items (6)

Polysymplectic Souriau Lie group thermodynamics and the geometric structure of its coadjoint orbits ⋮ Polysymplectic Souriau Lie group thermodynamics and entropy geometric structure as Casimir invariant function ⋮ Riemannian geometry of Gibbs cones associated to nilpotent orbits of simple Lie groups ⋮ Symplectic foliation transverse structure and Libermann foliation of heat theory and information geometry ⋮ Souriau's geometric principles for quantum mechanics ⋮ Archetypal model of entropy by Poisson cohomology as invariant Casimir function in coadjoint representation and geometric Fourier heat equation

Cites Work

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• The entropy-based quantum metric
• Maximum d'entropie et problème des moments. (Maximum entropy and the moment problem)
• Structure of dynamical systems. A symplectic view of physics. Transl. from the French by C. H. Cushman-de Vries. Transl. ed.: R. H. Cushman a. G. M. Tuynman
• Koszul lecture related to geometric and analytic mechanics, Souriau's Lie group thermodynamics and information geometry
• Euler-Poincaré equation for Lie groups with non null symplectic cohomology. Application to the mechanics
• Souriau exponential map algorithm for machine learning on matrix Lie groups
• On geometric mechanics
• Les formes extérieures en mécanique
• Introduction to Symplectic Geometry
• Jean-Louis Koszul and the Elementary Structures of Information Geometry

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