Thermodynamics with time: Exergy and passivity

Abstract

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 exergy11The term exergy was coined by Zoran Rant in the 1950s. We choose to use it here instead of one of the other possible names such as available work, available energy, utilizable energy, etc. because it has a single precise meaning. Willems uses the term available energy in his major work on dissipative systems (Willems1972a, 1972b) but in a generic way. (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.