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Souriau-Casimir Lie Groups Thermodynamics and Machine Learning
Springer Proceedings in Mathematics and Statistics, 2021In 1969, Jean-Marie Souriau introduced a “Lie Groups Thermodynamics” in the framework of Symplectic model of Statistical 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 Lagrange 2-form, and defines in case of non-null cohomology ...
Barbaresco Frédéric +1 more
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Information Geometry, 2021
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Barbaresco Frédéric +1 more
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Koszul information geometry and Souriau Lie group thermodynamics
AIP Conference Proceedings, 2015Koszul Information Geometry and Souriau Lie Group Thermodynamics Frederic Barbaresco1 1,a) Thales Air Systems, Advanced Radar Concepts, Voie Pierre-Gilles de Gennes. 91470 Limours, France a) Frederic.barbaresco@thalesgroup.com Abstract. The Francois Massieu 1869 idea to derive some mechanical and thermal properties of physical systems from ...
Barbaresco Frédéric
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Lecture Notes in Computer Science, 2019
In 1969, Jean-Marie Souriau has 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 Lagrange 2-form, and defines thanks to cohomology (non ...
Barbaresco Frédéric +1 more
exaly +2 more sources
In 1969, Jean-Marie Souriau has 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 Lagrange 2-form, and defines thanks to cohomology (non ...
Barbaresco Frédéric +1 more
exaly +2 more sources
Poly-symplectic Model of Higher Order Souriau Lie Groups Thermodynamics for Small Data Analytics
Lecture Notes in Computer Science, 2017We introduce poly-symplectic extension of Souriau Lie group Thermodynamics based on higher-order model of statistical physics introduced by R.S. Ingarden. This extended model could be used for small data analytics.
Barbaresco Frédéric +1 more
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Method of Orbits of Co-Associated Representation in Thermodynamics of the Lie Non-compact Groups
Lecture Notes in Computer Science, 2017A method of the solution of the main problem of homogeneous spaces thermodynamics for non-compact Lie groups is presented in the work. The method originates from formalism of non-commutative Fourier analysis based on method of coadjoint orbits. A formula that allows efficiently evaluate heat kernel and statistic sum on non-compact Lie group is obtained.
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Polysymplectic Souriau Lie Group Thermodynamics and the Geometric Structure of Its Coadjoint Orbits
Lecture Notes in Computer Science, 2023exaly +2 more sources