Koszul lecture related to geometric and analytic mechanics, Souriau's Lie group thermodynamics and information geometry
F Barbaresco - Information Geometry, 2021 - Springer
This paper deals with Jean-Louis Koszul's works related to Geometric and Analytic
Mechanics, and to Souriau's Lie Group Thermodynamics that have appeared over time as …
Mechanics, and to Souriau's Lie Group Thermodynamics that have appeared over time as …
Lie group cohomology and (multi) symplectic integrators: new geometric tools for Lie group machine learning based on Souriau geometric statistical mechanics
F Barbaresco, F Gay-Balmaz - Entropy, 2020 - mdpi.com
In this paper, we describe and exploit a geometric framework for Gibbs probability densities
and the associated concepts in statistical mechanics, which unifies several earlier works on …
and the associated concepts in statistical mechanics, which unifies several earlier works on …
From tools in symplectic and poisson geometry to J.-M. Souriau's theories of statistical mechanics and thermodynamics
CM Marle - Entropy, 2016 - mdpi.com
I present in this paper some tools in symplectic and Poisson geometry in view of their
applications in geometric mechanics and mathematical physics. After a short discussion of …
applications in geometric mechanics and mathematical physics. After a short discussion of …
Geometric theory of heat from Souriau Lie groups thermodynamics and Koszul Hessian geometry: Applications in information geometry for exponential families
F Barbaresco - Entropy, 2016 - mdpi.com
We introduce the symplectic structure of information geometry based on Souriau's Lie group
thermodynamics model, with a covariant definition of Gibbs equilibrium via invariances …
thermodynamics model, with a covariant definition of Gibbs equilibrium via invariances …
Symplectic theory of heat and information geometry
F Barbaresco - Handbook of statistics, 2022 - Elsevier
We present in this chapter a new formulation of heat theory and Information Geometry
through symplectic and Poisson structures based on Jean-Marie Souriau's symplectic model …
through symplectic and Poisson structures based on Jean-Marie Souriau's symplectic model …
On Gibbs states of mechanical systems with symmetries
CM Marle - 2020 - projecteuclid.org
The French mathematician and physicist Jean-Marie Souriau studied Gibbs states for the
Hamiltonian action of a Lie group on a symplectic manifold and considered their possible …
Hamiltonian action of a Lie group on a symplectic manifold and considered their possible …
Souriau-Casimir Lie groups thermodynamics and machine learning
F Barbaresco - Workshop on Joint Structures and Common …, 2020 - Springer
Abstract In 1969, Jean-Marie Souriau introduced a “Lie Groups Thermodynamics” in the
framework of Symplectic model of Statistical Mechanics. This Souriau's model considers the …
framework of Symplectic model of Statistical Mechanics. This Souriau's model considers the …
Jean-Marie Souriau's symplectic model of statistical physics: seminal papers on Lie groups thermodynamics-Quod Erat demonstrandum
F Barbaresco - Workshop on Joint Structures and Common …, 2020 - Springer
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” …
particularly his symplectic model of statistical physics, called “Lie groups thermodynamics” …
Euler-Poincaré equation for Lie groups with non null symplectic cohomology. Application to the mechanics
G de Saxcé - Geometric Science of Information: 4th International …, 2019 - Springer
Let G be a symplectic group on a symplectic manifold N N. To any momentum map ψ: N →
g^* ψ: N→ g∗, one can associate a class of symplectic cohomology cocs. It does not depend …
g^* ψ: N→ g∗, one can associate a class of symplectic cohomology cocs. It does not depend …
On the use of multidimensional differential geometry to model covariant behaviors of viscoelastic or hyperelastic structures, illustrated with numerical simulations using …
B Panicaud, E Rouhaud - International Journal of Solids and Structures, 2024 - Elsevier
In the present article, a covariant spacetime formalism is used to model the behavior of
viscoelastic and hyperelastic solids, within a thermodynamical framework. The latter aims to …
viscoelastic and hyperelastic solids, within a thermodynamical framework. The latter aims to …