About Some System-Theoretic Properties of Port-Thermodynamic Systems

Liouville geometry of classical thermodynamics

“…In particular, this property implies that if the homogeneous Hamiltonians K 1 , K 2 are zero on the Liouville submanifold L, and thus by Proposition 3.10 the homogeneous Hamiltonian vector fields X K1 , X K2 are tangent to L, then also [X K1 , X K2 ] is tangent to L, and therefore the Poisson bracket {K 1 , K 2 } is also zero on L. Together with Proposition 3.9 this was crucially used in the controllability and observability analysis of port-thermodynamic systems in [38].…”

Classical Thermodynamics Revisited: A Systems and Control Perspective

“…Finally we mention, see again [36] for details, that the Poisson bracket of two homogeneous Hamiltonian functions is homogeneous, and that the Lie bracket of two homogeneous Hamiltonian vector fields on T * Z is homogeneous. This allows to set up a Lie-algebraic theory for verifying controllability and observability [46,36] for port-thermodynamic systems.…”

Contact geometry for simple thermodynamical systems with friction

“…Other approaches like in [3] use similar techniques, called single generation formalism introducing a generalized bracket which is naturally divided into two parts: a non-canonical Poisson bracket and a new dissipation bracket. The derived structures are capable of reproducing both reversible and irreversible evolutions providing a unifying formalism for many systems ruled by the laws of thermodynamics (see also [4]). These approaches have proved to be very useful for the description of complex thermodynamical systems and also facilitate their numerical integration.…”