Stability of composite thermodynamic systems with interconnection constraints

In this study, a formulation of thermodynamic systems in terms of contact geometry is proposed. Furthermore, a systematic approach to the description and analysis of composite thermodynamic systems, that is, systems containing a number of interacting thermodynamic subsystems, is developed. In such systems, there are always heat, work or matter flows between the subsystems which, together with constructive restrictions, form the interconnection structure of the composite system. This structure can be described by a set of constraints imposed on the system. In geometric terms, this can be seen as a restriction of the system space to a certain `constraint sub-manifold´. Moreover, there are kinematic (non-holonomic) constraints which restrict the system´s dynamics while imposing no restrictions on the system configuration. Both geometric and kinematic constraints and their influence on the dynamics of the composite system are discussed. Finally, several types of composite thermodynamic system are presented and the LaSalle Invariance Principle is used to analyse the asymptotic dynamical behaviour of one important example.