A port-Dirac formulation for thermodynamics of non-simple systems

The paper presents a port-Dirac formulation for thermodynamics of non-simple systems, in which we consider a non-simple system whose thermodynamic states may be represented by several entropy variables. Here we regard such a non-simple system as an interconnected system with ports that can be represented by a port-Dirac system in the context of Dirac structures. We first show some extension of the Lagrange-d'Alembert principle for obtaining the evolution equations of such non-simple systems. Then, a Dirac structure is constructed on the Pontryagin bundle over a thermodynamic configuration manifold. Further, a port-Dirac dynamical formulation for such non-simple systems is demonstrated, where the developed evolution equations are to be equivalent with the generalized Lagrange-d'Alembert equations. The validity of the proposed approach is finally illustrated by two examples of an adiabatic piston and a resistive circuit with entropy production.