Dirac structures in nonequilibrium thermodynamics

Hiroaki Yoshimura, François Gay-Balmaz

    Research output: Contribution to journalArticle

    Abstract

    In this paper, it is shown that the evolution equations for nonequilibrium thermodynamics admit an intrinsic formulation in terms of Dirac structures, both on the Lagrangian and the Hamiltonian settings. The Dirac structures are constructed on the Pontryagin bundle P = TQ ⊕ TQ, where Q = Q × ℝ is the thermodynamic configuration manifold. In particular, it is illustrated how one can develop Dirac structures that include nonlinear nonholonomic constraints originated from the entropy production in each irreversible process. Lastly, we also present the induced Dirac structure on N = TQ × ℝ together with the associated Lagrange-Dirac and Hamilton-Dirac dynamical formulations in analogy with nonholonomic mechanics.

    Original languageEnglish
    Pages (from-to)31-37
    Number of pages7
    JournalIFAC-PapersOnLine
    Volume51
    Issue number3
    DOIs
    Publication statusPublished - 2018 Jan 1

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    Thermodynamics
    Hamiltonians
    Mechanics
    Entropy

    Keywords

    • Dirac structures
    • Hamilton-Dirac systems
    • irreversible processes
    • Lagrange-Dirac systems
    • Nonequilibrium thermodynamics
    • nonlinear nonholonomic constraints

    ASJC Scopus subject areas

    • Control and Systems Engineering

    Cite this

    Dirac structures in nonequilibrium thermodynamics . / Yoshimura, Hiroaki; Gay-Balmaz, François.

    In: IFAC-PapersOnLine, Vol. 51, No. 3, 01.01.2018, p. 31-37.

    Research output: Contribution to journalArticle

    Yoshimura, Hiroaki ; Gay-Balmaz, François. / Dirac structures in nonequilibrium thermodynamics In: IFAC-PapersOnLine. 2018 ; Vol. 51, No. 3. pp. 31-37.
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