Generalized Hamiltonian representation of thermo-mechanical systems based on an entropic formulation

In this work, we present an approach to construct generalized Hamiltonian representations for thermo-mechanical systems. Using entropic formulation of thermodynamic systems, the construction is applied to a class of thermo-mechanical systems. The proposed approach leads to an explicit expression of the dissipation along the trajectories of the dynamics. The considered thermo-mechanical systems are, in a thermodynamical sense, systems for which the dynamics of the extensive variables are functions of the intensive variables with respect to an entropic formulation. Using the entropy as the storage function, the dissipative structures of an analogue to a port-controlled Hamiltonian (PCH) representation are identified with irreversible phenomena, while the conservative structures are identified with reversible or isentropic phenomena. Examples are presented to illustrate the application of the proposed methodology, including a reacting system.