A variational formulation of nonequilibrium thermodynamics for discrete open systems with mass and heat transfer

François Gay-Balmaz, Hiroaki Yoshimura

    Research output: Contribution to journalArticle

    3 Citations (Scopus)

    Abstract

    We propose a variational formulation for the nonequilibrium thermodynamics of discrete open systems, i.e., discrete systems which can exchange mass and heat with the exterior. Our approach is based on a general variational formulation for systems with time-dependent nonlinear nonholonomic constraints and time-dependent Lagrangian. For discrete open systems, the time-dependent nonlinear constraint is associated with the rate of internal entropy production of the system. We show that this constraint on the solution curve systematically yields a constraint on the variations to be used in the action functional. The proposed variational formulation is intrinsic and provides the same structure for a wide class of discrete open systems. We illustrate our theory by presenting examples of open systems experiencing mechanical interactions, as well as internal diffusion, internal heat transfer, and their cross-effects. Our approach yields a systematic way to derive the complete evolution equations for the open systems, including the expression of the internal entropy production of the system, independently on its complexity. It might be especially useful for the study of the nonequilibrium thermodynamics of biophysical systems.

    Original languageEnglish
    Article number163
    JournalEntropy
    Volume20
    Issue number3
    DOIs
    Publication statusPublished - 2018 Mar 1

    Fingerprint

    nonequilibrium thermodynamics
    mass transfer
    heat transfer
    formulations
    entropy
    heat
    curves
    interactions

    Keywords

    • Discrete open systems
    • Lagrangian variational formulation
    • Nonequilibrium thermodynamics
    • Nonlinear nonholonomic constraint

    ASJC Scopus subject areas

    • Physics and Astronomy(all)

    Cite this

    A variational formulation of nonequilibrium thermodynamics for discrete open systems with mass and heat transfer. / Gay-Balmaz, François; Yoshimura, Hiroaki.

    In: Entropy, Vol. 20, No. 3, 163, 01.03.2018.

    Research output: Contribution to journalArticle

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