Results 1 to 10 of about 4,029 (181)

Higher Order Geometric Theory of Information and Heat Based on Poly-Symplectic Geometry of Souriau Lie Groups Thermodynamics and Their Contextures: The Bedrock for Lie Group Machine Learning [PDF]

Entropy, 2018
We introduce poly-symplectic extension of Souriau Lie groups thermodynamics based on higher-order model of statistical physics introduced by Ingarden. This extended model could be used for small data analytics and machine learning on Lie groups.
Frédéric Barbaresco
doaj   +8 more sources

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 [PDF]

Entropy, 2020
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
Frédéric Barbaresco
doaj   +5 more sources

Link between Lie Group Statistical Mechanics and Thermodynamics of Continua [PDF]

Entropy, 2016
In this work, we consider the value of the momentum map of the symplectic mechanics as an affine tensor called momentum tensor. From this point of view, we analyze the underlying geometric structure of the theories of Lie group statistical mechanics and ...
Géry de Saxcé
doaj   +4 more sources

Koszul Information Geometry and Souriau Geometric Temperature/Capacity of Lie Group Thermodynamics [PDF]

Entropy, 2014
The François Massieu 1869 idea to derive some mechanical and thermal properties of physical systems from “Characteristic Functions”, was developed by Gibbs and Duhem in thermodynamics with the concept of potentials, and introduced by Poincaré in ...
Frédéric Barbaresco
doaj   +5 more sources

Geometric Theory of Heat from Souriau Lie Groups Thermodynamics and Koszul Hessian Geometry: Applications in Information Geometry for Exponential Families [PDF]

Entropy, 2016
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 through co-adjoint action of a group on its moment space, defining physical ...
Frédéric Barbaresco
doaj   +4 more sources

Jean-Marie Souriau’s Symplectic Foliation Model of Sadi Carnot’s Thermodynamics [PDF]

Entropy
The explanation of thermodynamics through geometric models was initiated by seminal figures such as Carnot, Gibbs, Duhem, Reeb, and Carathéodory. Only recently, however, has the symplectic foliation model, introduced within the domain of geometric ...
Frédéric Barbaresco
doaj   +4 more sources

Thermodynamics à la Souriau on Kähler Non-Compact Symmetric Spaces for Cartan Neural Networks [PDF]

Entropy
In this paper, we clarify several issues concerning the abstract geometrical formulation of thermodynamics on non-compact symmetric spaces U/H that are the mathematical model of hidden layers in the new paradigm of Cartan Neural Networks.
Pietro G. Fré, Alexander S. Sorin, Mario Trigiante   +2 more
doaj   +2 more sources

Lie groups in nonequilibrium thermodynamics: Geometric structure behind viscoplasticity [PDF]

Journal of Non-Newtonian Fluid Mechanics, 2010
11 pages, 1 figure, accepted for publication in J. Non-Newtonian Fluid Mech. Keywords: Elastic-viscoplastic materials, Nonequilibrium thermodynamics, GENERIC, Lie groups, Reference ...
Hans Christian Öttinger
exaly   +4 more sources

Multi-symplectic Lie Group Thermodynamics for Covariant Field Theories [PDF]

Lecture Notes in Computer Science, 2019
We propose a multi-symplectic generalisation of Souriau’s Lie group thermodynamics for first order parametrised classical field theories. A new notion of general covariant Gibbs state functional is defined in terms of the multi-momentum map associated to the lifted action of the diffeomorphisms group on the fields extended phase space.
Goffredo Chirco, Fabio Maria Mele, Marco Laudato   +2 more
exaly   +3 more sources

Symplectic Foliation Structures of Non-Equilibrium Thermodynamics as Dissipation Model: Application to Metriplectic Nonlinear Lindblad Quantum Master Equation

Entropy, 2022
The idea of a canonical ensemble from Gibbs has been extended by Jean-Marie Souriau for a symplectic manifold where a Lie group has a Hamiltonian action.
Frédéric Barbaresco
doaj   +1 more source