Variational discretization of the nonequilibrium thermodynamics of simple systems

Francois Gay-Balmaz, Hiroaki Yoshimura

    Research output: Contribution to journalArticle

    3 Citations (Scopus)

    Abstract

    In this paper, we develop variational integrators for the nonequilibrium thermodynamics of simple closed systems. These integrators are obtained by a discretization of the Lagrangian variational formulation of nonequilibrium thermodynamics developed in (Gay-Balmaz and Yoshimura 2017a J. Geom. Phys. part I 111 169-93; Gay-Balmaz and Yoshimura 2017b J. Geom. Phys. part II 111 194-212) and thus extend the variational integrators of Lagrangian mechanics, to include irreversible processes. In the continuous setting, we derive the structure preserving property of the flow of such systems. This property is an extension of the symplectic property of the flow of the Euler-Lagrange equations. In the discrete setting, we show that the discrete flow solution of our numerical scheme verifies a discrete version of this property. We also present the regularity conditions which ensure the existence of the discrete flow. We finally illustrate our discrete variational schemes with the implementation of an example of a simple and closed system.

    Original languageEnglish
    Pages (from-to)1673-1705
    Number of pages33
    JournalNonlinearity
    Volume31
    Issue number4
    DOIs
    Publication statusPublished - 2018 Mar 12

    Fingerprint

    Non-equilibrium Thermodynamics
    nonequilibrium thermodynamics
    integrators
    Discretization
    Thermodynamics
    Variational Integrators
    Mechanics
    Euler-Lagrange equation
    irreversible processes
    Lagrangian Mechanics
    Irreversible Processes
    Closed
    regularity
    preserving
    Euler-Lagrange Equations
    Variational Formulation
    Regularity Conditions
    Numerical Scheme
    formulations
    Verify

    Keywords

    • discrete Lagrangian formulation
    • entropy
    • nonequilibrium thermodynamics
    • structure preserving discretization
    • variational integrators

    ASJC Scopus subject areas

    • Statistical and Nonlinear Physics
    • Mathematical Physics
    • Physics and Astronomy(all)
    • Applied Mathematics

    Cite this

    Variational discretization of the nonequilibrium thermodynamics of simple systems. / Gay-Balmaz, Francois; Yoshimura, Hiroaki.

    In: Nonlinearity, Vol. 31, No. 4, 12.03.2018, p. 1673-1705.

    Research output: Contribution to journalArticle

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