A Lagrangian variational formulation for nonequilibrium thermodynamics

F. Gay-Balmaz, H. Yoshimura

Research output: Contribution to journalArticlepeer-review


We present a variational formulation for nonequilibrium thermodynamics which extends the Hamilton principle of mechanics to include irreversible processes. The variational formulation is based on the introduction of the concept of thermodynamic displacement. This concept makes possible the definition of a nonlinear nonholonomic constraint given by the expression of the entropy production associated to the irreversible processes involved, to which is naturally associated a variational constraint to be used in the variational formulation. We consider both discrete (i.e., finite dimensional) and continuum systems and illustrate the variational formulation with the example of the piston problem and the heat conducting viscous fluid.

Original languageEnglish
Pages (from-to)25-30
Number of pages6
Journal6th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2018
Issue number3
Publication statusPublished - 2018 Jan 1


  • Lagrangian system
  • Nonequilibrium thermodynamics
  • constraints
  • irreversible process
  • variational principle

ASJC Scopus subject areas

  • Control and Systems Engineering


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