An entropy-based formulation of irreversible processes based on contact structures

In this paper we propose an analytical formulation of the dynamical behaviour of complex and open physical systems which is formulated on the total thermodynamic phase space using the contact form associated with Gibbs’ relation. Starting from balance equations we construct control contact systems by using the entropy function to represent the thermodynamic properties. The contact Hamiltonian function generating the dynamical behaviour has then the units of an entropy variation. We consider complex thermodynamic systems, described by compartmental systems, and we construct the associated control contact system by composing the control contact formulation of every compartment. The contact Hamiltonian functions generating the dynamical behaviour are discussed with respect to two alternative formalisms used for describing coupled sets of reversible and irreversible processes, namely the GENERIC formulation and the Matrix formulation. This analysis is then illustrated on the elementary example of a coupled mechanical and thermodynamic system.