Dirac Structures in Thermodynamics of Non-simple Systems

Hiroaki Yoshimura*, François Gay-Balmaz

*Corresponding author for this work

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


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 languageEnglish
Title of host publicationGeometric Science of Information - 5th International Conference, GSI 2021, Proceedings
EditorsFrank Nielsen, Frédéric Barbaresco
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages8
ISBN (Print)9783030802080
Publication statusPublished - 2021
Event5th International Conference on Geometric Science of Information, GSI 2021 - Paris, France
Duration: 2021 Jul 212021 Jul 23

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12829 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference5th International Conference on Geometric Science of Information, GSI 2021


  • Adiabatic piston
  • Dirac structures
  • Non-simple systems
  • Thermodynamics

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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