Hamiltonian variational formulation for nonequilibrium thermodynamics of simple closed systems

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