From Lagrangian mechanics to nonequilibrium thermodynamics: A variational perspective

François Gay-Balmaz*, Hiroaki Yoshimura

*Corresponding author for this work

Research output: Contribution to journalReview articlepeer-review

27 Citations (Scopus)


In this paper, we survey our recent results on the variational formulation of nonequilibrium thermodynamics for the finite-dimensional case of discrete systems, as well as for the infinite-dimensional case of continuum systems. Starting with the fundamental variational principle of classical mechanics, namely, Hamilton's principle, we show, with the help of thermodynamic systems with gradually increasing complexity, how to systematically extend it to include irreversible processes. In the finite dimensional cases, we treat systems experiencing the irreversible processes of mechanical friction, heat, and mass transfer in both the adiabatically closed cases and open cases. On the continuum side, we illustrate our theory using the example of multicomponent Navier-Stokes-Fourier systems.

Original languageEnglish
Article number8
Issue number1
Publication statusPublished - 2019 Jan 1


  • Continuum thermodynamic systems
  • Discrete thermodynamic systems
  • Irreversible processes
  • Nonequilibrium thermodynamics
  • Nonholonomic constraints
  • Variational formulation

ASJC Scopus subject areas

  • Information Systems
  • Mathematical Physics
  • Physics and Astronomy (miscellaneous)
  • Electrical and Electronic Engineering


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