Variational discretization of the nonequilibrium thermodynamics of simple systems

Francois Gay-Balmaz, Hiroaki Yoshimura

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


In this paper, we develop variational integrators for the nonequilibrium thermodynamics of simple closed systems. These integrators are obtained by a discretization of the Lagrangian variational formulation of nonequilibrium thermodynamics developed in (Gay-Balmaz and Yoshimura 2017a J. Geom. Phys. part I 111 169-93; Gay-Balmaz and Yoshimura 2017b J. Geom. Phys. part II 111 194-212) and thus extend the variational integrators of Lagrangian mechanics, to include irreversible processes. In the continuous setting, we derive the structure preserving property of the flow of such systems. This property is an extension of the symplectic property of the flow of the Euler-Lagrange equations. In the discrete setting, we show that the discrete flow solution of our numerical scheme verifies a discrete version of this property. We also present the regularity conditions which ensure the existence of the discrete flow. We finally illustrate our discrete variational schemes with the implementation of an example of a simple and closed system.

Original languageEnglish
Pages (from-to)1673-1705
Number of pages33
Issue number4
Publication statusPublished - 2018 Mar 12


  • discrete Lagrangian formulation
  • entropy
  • nonequilibrium thermodynamics
  • structure preserving discretization
  • variational integrators

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics


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