Dirac Structures in Thermodynamics of Non-simple Systems

Hiroaki Yoshimura; François Gay-Balmaz

doi:10.1007/978-3-030-80209-7_98

Dirac Structures in Thermodynamics of Non-simple Systems

Hiroaki Yoshimura^*, François Gay-Balmaz

^*Corresponding author for this work

School of Fundamental Science and Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

We present the Dirac structures and the associated Dirac system formulations for non-simple thermodynamic systems by focusing upon the cases that include irreversible processes due to friction and heat conduction. These systems are called non-simple since they involve several entropy variables. We review the variational formulation of the evolution equations of such non-simple systems. Then, based on this, we clarify that there exists a Dirac structure on the Pontryagin bundle over a thermodynamic configuration space and we develop the Dirac dynamical formulation of such non-simple systems. The approach is illustrated with the example of an adiabatic piston.

Original language	English
Title of host publication	Geometric Science of Information - 5th International Conference, GSI 2021, Proceedings
Editors	Frank Nielsen, Frédéric Barbaresco
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	918-925
Number of pages	8
ISBN (Print)	9783030802080
DOIs	https://doi.org/10.1007/978-3-030-80209-7_98
Publication status	Published - 2021
Event	5th International Conference on Geometric Science of Information, GSI 2021 - Paris, France Duration: 2021 Jul 21 → 2021 Jul 23

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	12829 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	5th International Conference on Geometric Science of Information, GSI 2021
Country/Territory	France
City	Paris
Period	21/7/21 → 21/7/23

Keywords

Adiabatic piston
Dirac structures
Non-simple systems
Thermodynamics

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/978-3-030-80209-7_98

Cite this

Yoshimura, H., & Gay-Balmaz, F. (2021). Dirac Structures in Thermodynamics of Non-simple Systems. In F. Nielsen, & F. Barbaresco (Eds.), Geometric Science of Information - 5th International Conference, GSI 2021, Proceedings (pp. 918-925). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12829 LNCS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-030-80209-7_98

Dirac Structures in Thermodynamics of Non-simple Systems. / Yoshimura, Hiroaki; Gay-Balmaz, François.
Geometric Science of Information - 5th International Conference, GSI 2021, Proceedings. ed. / Frank Nielsen; Frédéric Barbaresco. Springer Science and Business Media Deutschland GmbH, 2021. p. 918-925 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12829 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Yoshimura, H & Gay-Balmaz, F 2021, Dirac Structures in Thermodynamics of Non-simple Systems. in F Nielsen & F Barbaresco (eds), Geometric Science of Information - 5th International Conference, GSI 2021, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 12829 LNCS, Springer Science and Business Media Deutschland GmbH, pp. 918-925, 5th International Conference on Geometric Science of Information, GSI 2021, Paris, France, 21/7/21. https://doi.org/10.1007/978-3-030-80209-7_98

Yoshimura H, Gay-Balmaz F. Dirac Structures in Thermodynamics of Non-simple Systems. In Nielsen F, Barbaresco F, editors, Geometric Science of Information - 5th International Conference, GSI 2021, Proceedings. Springer Science and Business Media Deutschland GmbH. 2021. p. 918-925. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-80209-7_98

Yoshimura, Hiroaki ; Gay-Balmaz, François. / Dirac Structures in Thermodynamics of Non-simple Systems. Geometric Science of Information - 5th International Conference, GSI 2021, Proceedings. editor / Frank Nielsen ; Frédéric Barbaresco. Springer Science and Business Media Deutschland GmbH, 2021. pp. 918-925 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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