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In this paper, we develop a Hamiltonian variational formulation for thenonequilibrium thermodynamics of simple adiabatically closed systems that is anextension of Hamilton's phase space principle in mechanics. We introduce theHamilton-d'Alembert principle for thermodynamic systems by consideringnonlinear nonholonomic constraints of thermodynamic type. In particular, forthe case in which the given Lagrangian is degenerate, we construct theHamiltonian by incorporating the primary constraints via Dirac's theory ofconstraints. We illustrate our Hamiltonian variational formulation with someexamples of systems with friction, with internal matter transfer as well aswith chemical reactions.

Hamiltonian variational formulation for nonequilibrium thermodynamics of simple closed systems