https://ens.hal.science/hal-03872244Yoshimura, HiroakiHiroakiYoshimuraGay-Balmaz, FrançoisFrançoisGay-BalmazENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettresCNRS - Centre National de la Recherche ScientifiqueHamiltonian variational formulation for nonequilibrium thermodynamics of simple closed systemsHAL CCSD2022[MATH.MATH-MP] Mathematics [math]/Mathematical Physics [math-ph]Gay-Balmaz, François2022-11-25 15:39:242023-03-24 14:53:292022-11-25 15:39:24enJournal articles1In 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.