Hamiltonian variational formulation for nonequilibrium thermodynamics of simple closed systems

Hiroaki Yoshimura*, Frangois Gay-Balmaz

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

3 Citations (Scopus)


In this paper, we develop a Hamiltonian variational formulation for the nonequilibrium thermodynamics of simple adiabatically closed systems that is an extension of Hamilton's phase space principle in mechanics. We introduce the Hamilton-d'Alembert principle for thermodynamic systems by considering nonlinear nonholonomic constraints of thermodynamic type. In particular, for the case in which the given Lagrangian is degenerate, we construct the Hamiltonian by incorporating the primary constraints via Dirac's theory of constraints. We illustrate our Hamiltonian variational formulation with some examples of systems with friction, with internal matter transfer as well as with chemical reactions.

Original languageEnglish
Pages (from-to)81-86
Number of pages6
Issue number18
Publication statusPublished - 2022 Jul 1
Event4th IFAC Workshop on Thermodynamics Foundations of Mathematical Systems Theory, TFMST 2022 - Montreal, Canada
Duration: 2022 Jul 252022 Jul 27


  • Dirac's theory of constraints
  • Hamilton-d'Alembert principle
  • Hamiltonian variational formulation
  • nonequilibrium thermodynamics
  • nonlinear nonholonomic constraints

ASJC Scopus subject areas

  • Control and Systems Engineering


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