Dirac structures in nonequilbrium thermodynamics

Hiroaki Yoshimura, François Gay-Balmaz

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Abstract

    In this paper, we show that the evolution equations for nonequilibrium thermodynamics can be formulated in terms of Dirac structures on the Pontryagin bundle P =TQ ⊕ T*Q, where Q = Q ×s R denotes the thermodynamic configuration manifold. In particular, we extend the use of Dirac structures from the case of linear nonholonomic constraints to the case of nonlinear nonholonomic constraints. Such a nonlinear constraint comes from the entropy production associated with irreversible processes in nonequilibrium thermodynamics. We also develop the induced Dirac structure on N=T*Q × R and the associated Lagrange-Dirac and Hamilton-Dirac dynamical formulations.

    Original languageEnglish
    Title of host publicationGeometric Science of Information - 3rd International Conference, GSI 2017, Proceedings
    PublisherSpringer-Verlag
    Pages410-417
    Number of pages8
    ISBN (Print)9783319684444
    DOIs
    Publication statusPublished - 2017 Jan 1
    Event3rd International Conference on Geometric Science of Information, GSI 2017 - Paris, France
    Duration: 2017 Nov 72017 Nov 9

    Publication series

    NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
    Volume10589 LNCS
    ISSN (Print)0302-9743
    ISSN (Electronic)1611-3349

    Other

    Other3rd International Conference on Geometric Science of Information, GSI 2017
    CountryFrance
    CityParis
    Period17/11/717/11/9

    Fingerprint

    Dirac Structures
    Nonholonomic Constraints
    Non-equilibrium Thermodynamics
    Thermodynamics
    Nonlinear Constraints
    Paul Adrien Maurice Dirac
    Irreversible Processes
    Entropy Production
    Linear Constraints
    Lagrange
    Evolution Equation
    Bundle
    Entropy
    Denote
    Configuration
    Formulation

    Keywords

    • Dirac structures
    • Implicit systems
    • Irreversible processes
    • Nonequilibrium thermodynamics
    • Nonlinear constraints

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Computer Science(all)

    Cite this

    Yoshimura, H., & Gay-Balmaz, F. (2017). Dirac structures in nonequilbrium thermodynamics. In Geometric Science of Information - 3rd International Conference, GSI 2017, Proceedings (pp. 410-417). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10589 LNCS). Springer-Verlag. https://doi.org/10.1007/978-3-319-68445-1_48

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

    Geometric Science of Information - 3rd International Conference, GSI 2017, Proceedings. Springer-Verlag, 2017. p. 410-417 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10589 LNCS).

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Yoshimura, H & Gay-Balmaz, F 2017, Dirac structures in nonequilbrium thermodynamics. in Geometric Science of Information - 3rd International Conference, GSI 2017, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10589 LNCS, Springer-Verlag, pp. 410-417, 3rd International Conference on Geometric Science of Information, GSI 2017, Paris, France, 17/11/7. https://doi.org/10.1007/978-3-319-68445-1_48
    Yoshimura H, Gay-Balmaz F. Dirac structures in nonequilbrium thermodynamics. In Geometric Science of Information - 3rd International Conference, GSI 2017, Proceedings. Springer-Verlag. 2017. p. 410-417. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-319-68445-1_48
    Yoshimura, Hiroaki ; Gay-Balmaz, François. / Dirac structures in nonequilbrium thermodynamics. Geometric Science of Information - 3rd International Conference, GSI 2017, Proceedings. Springer-Verlag, 2017. pp. 410-417 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
    @inproceedings{25fe92f10eb2424a80dd944459b7ad39,
    title = "Dirac structures in nonequilbrium thermodynamics",
    abstract = "In this paper, we show that the evolution equations for nonequilibrium thermodynamics can be formulated in terms of Dirac structures on the Pontryagin bundle P =TQ ⊕ T*Q, where Q = Q ×s R denotes the thermodynamic configuration manifold. In particular, we extend the use of Dirac structures from the case of linear nonholonomic constraints to the case of nonlinear nonholonomic constraints. Such a nonlinear constraint comes from the entropy production associated with irreversible processes in nonequilibrium thermodynamics. We also develop the induced Dirac structure on N=T*Q × R and the associated Lagrange-Dirac and Hamilton-Dirac dynamical formulations.",
    keywords = "Dirac structures, Implicit systems, Irreversible processes, Nonequilibrium thermodynamics, Nonlinear constraints",
    author = "Hiroaki Yoshimura and Fran{\cc}ois Gay-Balmaz",
    year = "2017",
    month = "1",
    day = "1",
    doi = "10.1007/978-3-319-68445-1_48",
    language = "English",
    isbn = "9783319684444",
    series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
    publisher = "Springer-Verlag",
    pages = "410--417",
    booktitle = "Geometric Science of Information - 3rd International Conference, GSI 2017, Proceedings",

    }

    TY - GEN

    T1 - Dirac structures in nonequilbrium thermodynamics

    AU - Yoshimura, Hiroaki

    AU - Gay-Balmaz, François

    PY - 2017/1/1

    Y1 - 2017/1/1

    N2 - In this paper, we show that the evolution equations for nonequilibrium thermodynamics can be formulated in terms of Dirac structures on the Pontryagin bundle P =TQ ⊕ T*Q, where Q = Q ×s R denotes the thermodynamic configuration manifold. In particular, we extend the use of Dirac structures from the case of linear nonholonomic constraints to the case of nonlinear nonholonomic constraints. Such a nonlinear constraint comes from the entropy production associated with irreversible processes in nonequilibrium thermodynamics. We also develop the induced Dirac structure on N=T*Q × R and the associated Lagrange-Dirac and Hamilton-Dirac dynamical formulations.

    AB - In this paper, we show that the evolution equations for nonequilibrium thermodynamics can be formulated in terms of Dirac structures on the Pontryagin bundle P =TQ ⊕ T*Q, where Q = Q ×s R denotes the thermodynamic configuration manifold. In particular, we extend the use of Dirac structures from the case of linear nonholonomic constraints to the case of nonlinear nonholonomic constraints. Such a nonlinear constraint comes from the entropy production associated with irreversible processes in nonequilibrium thermodynamics. We also develop the induced Dirac structure on N=T*Q × R and the associated Lagrange-Dirac and Hamilton-Dirac dynamical formulations.

    KW - Dirac structures

    KW - Implicit systems

    KW - Irreversible processes

    KW - Nonequilibrium thermodynamics

    KW - Nonlinear constraints

    UR - http://www.scopus.com/inward/record.url?scp=85033723035&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=85033723035&partnerID=8YFLogxK

    U2 - 10.1007/978-3-319-68445-1_48

    DO - 10.1007/978-3-319-68445-1_48

    M3 - Conference contribution

    AN - SCOPUS:85033723035

    SN - 9783319684444

    T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

    SP - 410

    EP - 417

    BT - Geometric Science of Information - 3rd International Conference, GSI 2017, Proceedings

    PB - Springer-Verlag

    ER -