Homogeneous Hamiltonian Control Systems Part II: Application to thermodynamic systems

Abstract

In this paper, we give several examples of the formulation of the dynamics of open physical systems in terms of homogeneous Hamiltonian control systems. Therefore we have systematically used Gibbs-Massieu equations in the entropy form for the definition of the Lagrangian submanifold associated with the thermodynamical properties of the system. Accordingly we have used the total entropy function of the system to define the generating function of this Lagrange submanifold and have used the canonical lifting of systems of balance equations of the remaining independent extensive variables. In the first part we consider two examples of thermodynamic systems: two cells exchanging a heat flow and the Continuous Stirred Tank Reactor (CSTR). In the second part, we consider an elementary dissipative mechanical, the mass-spring-damper system and then embed it into the gas-piston system.