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
EditorsFrank Nielsen, Frederic Barbaresco, Frank Nielsen
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

Keywords

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

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Yoshimura, H., & Gay-Balmaz, F. (2017). Dirac structures in nonequilbrium thermodynamics. In F. Nielsen, F. Barbaresco, & F. Nielsen (Eds.), 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