The mathematical representation of driven thermodynamic systems

A general framework for the treatment of driven systems in nonequilibrium thermodynamics is discussed for two selected theories and a simple model system. The framework is based upon the of modeling and control of general physical systems proposed by van der Schaft and co-workers. The crucial concept is the notion of a Dirac structure representing the dynamical equations of motion as well as the power conserving interconnection structure of the system. We applied the framework to two existing theories and a very simple model system. The two selected theories are the “General Equation for the Non-Equilibrium Reversible-Irreversible Coupling” (GENERIC) formalism of Grmela and Öttinger and the Matrix model of Jongschaap; the model system is a viscous gas in a cylinder and an externally driven piston. It is shown that the new approach provides not only a common framework for both theories, but also useful extensions, in particular, an extended GENERIC treatment of driven systems.