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 …
Contact geometry and thermodynamics
A Bravetti - International Journal of Geometric Methods in Modern …, 2019 - World Scientific
These are the lecture notes for the course given at the “XXVII International Fall Workshop on
Geometry and Physics” held in Seville (Spain) in September 2018. We review the geometric …
Geometry and Physics” held in Seville (Spain) in September 2018. We review the geometric …
Lie group statistics and Lie group machine learning based on Souriau Lie groups thermodynamics & Koszul-Souriau-Fisher metric: New entropy definition as …
F Barbaresco - Entropy, 2020 - mdpi.com
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 …
Mechanics in the framework of Geometric Mechanics. This Souriau's model considers the …
Lie group cohomology and (multi) symplectic integrators: new geometric tools for Lie group machine learning based on Souriau geometric statistical mechanics
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 …
Geometry of non-standard Hamiltonian structures of Liénard equations and contact structure
We start with a self-contained brief review of the construction of non-standard Lagrangian
and Hamiltonian structures for the Liénard equations satisfying Chiellini condition, we apply …
and Hamiltonian structures for the Liénard equations satisfying Chiellini condition, we apply …
Contact variational integrators
We present geometric numerical integrators for contact flows that stem from a discretization
of Herglotz'variational principle. First we show that the resulting discrete map is a contact …
of Herglotz'variational principle. First we show that the resulting discrete map is a contact …
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 …
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 …
Kernel density estimation on the Siegel space with an application to radar processing
This paper studies probability density estimation on the Siegel space. The Siegel space is a
generalization of the hyperbolic space. Its Riemannian metric provides an interesting …
generalization of the hyperbolic space. Its Riemannian metric provides an interesting …
Differential Geometric Aspects of Parametric Estimation Theory for States on Finite-Dimensional C∗-Algebras
A geometrical formulation of estimation theory for finite-dimensional C∗-algebras is
presented. This formulation allows to deal with the classical and quantum case in a single …
presented. This formulation allows to deal with the classical and quantum case in a single …