Lie Group Statistics and Lie Group Machine Learning Based on Souriau Lie Groups Thermodynamics & Koszul-Souriau-Fisher Metric: New Entropy Definition as Generalized Casimir Invariant Function in Coadjoint Representation

Lie Group Statistics and Lie Group Machine Learning Based on Souriau Lie Groups Thermodynamics & Koszul-Souriau-Fisher Metric: New Entropy Definition as Generalized Casimir Invariant Function in Coadjoint Representation

In 1969, Jean-Marie Souriau introduced a “Lie Groups Thermodynamics” in Statistical Mechanics in the framework of Geometric Mechanics. This Souriau’s model considers the statistical mechanics of dynamic systems in their “space of evolution” associated to a homogeneous symplectic manifold by a Lagran...

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Bibliographic Details
Main Author: Frédéric Barbaresco
Format: Article
Language:English
Published: MDPI AG 2020-06-01
Series:Entropy
Subjects:
Lie groups thermodynamics
Lie group machine learning
Kirillov representation theory
coadjoint orbits
moment map
covariant Gibbs density
Online Access:https://www.mdpi.com/1099-4300/22/6/642

Internet

https://www.mdpi.com/1099-4300/22/6/642

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