Polysymplectic Souriau Lie group thermodynamics and entropy geometric structure as Casimir invariant function

DOI10.1007/978-3-031-38299-4_15OpenAlexW4385435007MaRDI QIDQ6138223

Mohamed El Morsalani

Publication date: 16 January 2024

Published in: Lecture Notes in Computer Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-031-38299-4_15

zbMATH Keywords

Lie groups thermodynamicsextended Lie-Poisson bracketpoly-symplectic manifolds

Mathematics Subject Classification ID

Symplectic manifolds (general theory) (53D05) Applications of differential geometry to physics (53Z05) Classical and relativistic thermodynamics (80A10) Foundations of thermodynamics and heat transfer (80A05) Coadjoint orbits; nilpotent varieties (17B08) Differential geometric aspects of statistical manifolds and information geometry (53B12) General theory of finite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, invariants (37J06) Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) (37J39)

Cites Work

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• Poly-Poisson structures
• Koszul lecture related to geometric and analytic mechanics, Souriau's Lie group thermodynamics and information geometry
• Introduction to Symplectic Geometry
• Jean-Marie Souriau’s Symplectic Model of Statistical Physics: Seminal Papers on Lie Groups Thermodynamics - Quod Erat Demonstrandum
• Souriau-Casimir Lie Groups Thermodynamics and Machine Learning

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