Conservative and dissipative phenomena in thermodynamical systems stability

The entropy production of thermodynamical systems with reversible (conservative) and irreversible (dissipative) phenomena is used as a Lyapunov candidate function to address stability properties. First, based on the conjugated variables of the extensive properties, the dissipative and conservative phenomena are identified, then, the dynamic behavior of entropy production is obtained. Based on the properties of the entropy function Hessian, it is found that dissipative phenomena contribute to stability and attraction of the thermodynamical equilibrium. In particular, when only dissipative phenomena are present, the entropy production is a Lyapunov function that guarantees global or local stability, depending on the nonlinearities. Complex behaviors, for instance transitory increments of the entropy production, are due to both conservative phenomena and, far from equilibrium, non linearities of dissipative phenomena. Finally, a case study consisting in a gas-piston system is presented to illustrate these ideas.