Dirac structures in nonequilibrium thermodynamics

François Gay-Balmaz*, Hiroaki Yoshimura

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)


Dirac structures are geometric objects that generalize both Poisson structures and presymplectic structures on manifolds. They naturally appear in the formulation of constrained mechanical systems. In this paper, we show that the evolution equations for nonequilibrium thermodynamics admit an intrinsic formulation in terms of Dirac structures, both on the Lagrangian and the Hamiltonian settings. In the absence of irreversible processes, these Dirac structures reduce to canonical Dirac structures associated with canonical symplectic forms on phase spaces. Our geometric formulation of nonequilibrium thermodynamic thus consistently extends the geometric formulation of mechanics, to which it reduces in the absence of irreversible processes. The Dirac structures are associated with the variational formulation of nonequilibrium thermodynamics developed in the work of Gay-Balmaz and Yoshimura, J. Geom. Phys. 111, 169-193 (2017a) and are induced from a nonlinear nonholonomic constraint given by the expression of the entropy production of the system.

Original languageEnglish
Article number012701
JournalJournal of Mathematical Physics
Issue number1
Publication statusPublished - 2018 Jan 1

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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