Contact structures: application to interconnected thermodynamical systems

Contact structures and contact vector fields have been used to describe as well reversible as irreversible transformations of thermodynamic systems. The thermodynamic properties are described by a Legendre submanifold of the Thermodynamic Phase Space and the dynamics are described by a contact vector field associated to the transformations. In this paper we shall use the entropy 1-form as the contact form of the Thermodynamic Phase Space. This choice enables us then to derive the contact structure of chemical engineering systems, starting from the balance equations of the conserved extensive quantities. Complex systems often consist in a network of more simple open thermodynamic systems that interact through fluxes of extensive quantities. The contact system of such a complex system can be deduced from the composition of the contact structure of the more simple subsystems.