Contact topology and non-equilibrium thermodynamics

Michael Entov; Leonid Polterovich

doi:10.1088/1361-6544/acd1ce

Contact topology and non-equilibrium thermodynamics

Michael Entov, Leonid Polterovich

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We describe a method, based on contact topology, of showing the existence of semi-infinite trajectories of contact Hamiltonian flows which start on one Legendrian submanifold and asymptotically converge to another Legendrian submanifold. We discuss a mathematical model of non-equilibrium thermodynamics where such trajectories play a role of relaxation processes, and illustrate our results in the case of the Glauber dynamics for the mean field Ising model.

Original language	English
Pages (from-to)	3349-3375
Number of pages	27
Journal	Nonlinearity
Volume	36
Issue number	6
DOIs	https://doi.org/10.1088/1361-6544/acd1ce
State	Published - 17 May 2023

Keywords

Hamiltonian flow
Ising model
Legendrian submanifold
contact manifold
contact thermodynamics
non-equilibrium thermodynamics

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
General Physics and Astronomy
Applied Mathematics

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10.1088/1361-6544/acd1ce

Cite this

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title = "Contact topology and non-equilibrium thermodynamics",

abstract = "We describe a method, based on contact topology, of showing the existence of semi-infinite trajectories of contact Hamiltonian flows which start on one Legendrian submanifold and asymptotically converge to another Legendrian submanifold. We discuss a mathematical model of non-equilibrium thermodynamics where such trajectories play a role of relaxation processes, and illustrate our results in the case of the Glauber dynamics for the mean field Ising model.",

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AU - Polterovich, Leonid

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AB - We describe a method, based on contact topology, of showing the existence of semi-infinite trajectories of contact Hamiltonian flows which start on one Legendrian submanifold and asymptotically converge to another Legendrian submanifold. We discuss a mathematical model of non-equilibrium thermodynamics where such trajectories play a role of relaxation processes, and illustrate our results in the case of the Glauber dynamics for the mean field Ising model.

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KW - Ising model

KW - Legendrian submanifold

KW - contact manifold

KW - contact thermodynamics

KW - non-equilibrium thermodynamics

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Contact topology and non-equilibrium thermodynamics

Abstract

Keywords

ASJC Scopus subject areas

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