Thermodynamics with time: Exergy and passivity

In this paper we continue the exploration started in the joint paper Brockett and Willems (1978) with a view toward the further development of models for characterizing the limits on energy flow in mixed thermal-mechanical systems. We put the thermodynamic concept of exergy1 (available energy) in system theoretic terms and discuss its use as a storage function in the context of input-output models. In important cases the reachable sets for the systems considered here are not closed and of course this complicates any discussion of optimality. Only through the consideration of the closure of the reachable sets can the connection between optimal trajectories of dynamical systems and the basic results of classical thermodynamics be made tight.