A Lagrangian variational formulation for nonequilibrium thermodynamics. Part I

Discrete systems

François Gay-Balmaz, Hiroaki Yoshimura

    Research output: Contribution to journalArticle

    16 Citations (Scopus)

    Abstract

    In this paper, we present a Lagrangian variational formulation for nonequilibrium thermodynamics. This formulation is an extension of Hamilton's principle of classical mechanics that allows the inclusion of irreversible phenomena. The irreversibility is encoded into a nonlinear phenomenological constraint given by the expression of the entropy production associated to all the irreversible processes involved. From a mathematical point of view, our variational formulation may be regarded as a generalization to nonequilibrium thermodynamics of the Lagrange–d'Alembert principle used in nonlinear nonholonomic mechanics, where the conventional Lagrange–d'Alembert principle cannot be applied since the nonlinear phenomenological constraint and its associated variational constraint must be treated separately. In our approach, to deal with the nonlinear nonholonomic constraint, we introduce a variable called the thermodynamic displacement associated to each irreversible process. This allows us to systematically define the corresponding variational constraint. In Part I, our variational theory is illustrated with various examples of discrete systems such as mechanical systems with friction, matter transfer, electric circuits, chemical reactions, and diffusion across membranes. In Part II of the present paper, we will extend our variational formulation of discrete systems to the case of continuum systems.

    Original languageEnglish
    Pages (from-to)169-193
    Number of pages25
    JournalJournal of Geometry and Physics
    Volume111
    DOIs
    Publication statusPublished - 2017 Jan 1

    Fingerprint

    Non-equilibrium Thermodynamics
    nonequilibrium thermodynamics
    Nonlinear Constraints
    Variational Formulation
    Discrete Systems
    Irreversible Processes
    formulations
    Nonholonomic Mechanics
    irreversible processes
    Nonholonomic Constraints
    Hamilton's Principle
    Irreversibility
    Entropy Production
    Classical Mechanics
    Chemical Reaction
    Mechanical Systems
    Friction
    Thermodynamics
    Continuum
    Membrane

    Keywords

    • Discrete systems
    • Irreversible processes
    • Lagrangian formulation
    • Nonequilibrium thermodynamics
    • Nonholonomic constraints
    • Variational formulation

    ASJC Scopus subject areas

    • Mathematical Physics
    • Physics and Astronomy(all)
    • Geometry and Topology

    Cite this

    A Lagrangian variational formulation for nonequilibrium thermodynamics. Part I : Discrete systems. / Gay-Balmaz, François; Yoshimura, Hiroaki.

    In: Journal of Geometry and Physics, Vol. 111, 01.01.2017, p. 169-193.

    Research output: Contribution to journalArticle

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