Hamiltonian Variational Formulation for Non-simple Thermodynamic Systems

A Lagrangian variational formulation for nonequilibrium thermodynamics was proposed in [2–4]. In this paper, we develop a Hamiltonian analogue of the Lagrangian variational formulation for non-simple thermodynamic systems [6, 8]. We start with the Lagrangian variational formulation for simple systems, where the Lagrangian is degenerate. Under some assumption, we show how to construct the Hamiltonian variational formulation for nonequilibrium thermodynamics for the simple case. Then, we extend it to the case of adiabatically closed non-simple systems, in which there exists several entropy variables in addition to the mechanical variables. Finally, we illustrate our theory of the Hamiltonian variational formulation by an example of the adiabatic piston problem.