Irreversible port-Hamiltonian systems : a general formulation of irreversible processes with application to the CSTR

In this paper we suggest a class of quasi-port Hamiltonian systems called Irreversible port Hamiltonian Systems, that expresses simultaneously the first and second principle of thermodynamics as a structural property. These quasi-port Hamiltonian systems are defined with respect to a structure matrix and a modulating function which depends on the thermodynamic relation between state and co-state variables of the system. This modulating function itself is the product of some positive function γ and the Poisson bracket of the entropy and the energy function. This construction guarantees that the Hamiltonian function is a conserved quantity and simultaneously that the entropy function satisfies a balance equation containing an irreversible entropy creation term. In the second part of the paper, we suggest a lift of the Irreversible Port Hamiltonian Systems to control contact systems defined on the Thermodynamic Phase Space which is canonically endowed with a contact Preprint submitted to Chemical Engineering Science November 19, 2012 ha l-0 08 72 27 4, v er si on 1 14 O ct 2 01 3 Author manuscript, published in "Chemical Engineering Science 89 (2013) 223-234"