Port maps of Irreversible Port Hamiltonian Systems

Irreversible Port Hamiltonian Systems are departure of Port Hamiltonian Systems as they are generated not only by a Hamiltonian function but also by an entropy function and defined with respect to a quasi-Poisson bracket which embeds the definition of the irreversible phenomena taking place in the system. However the port map, consisting in the input map and the output map were poorly justified and lacked any physical consistency. In this paper, we suggest a novel definition of the port maps which allows to recover not only the energy balance equation (when the Hamiltonian equals the total energy of the system) but also a entropy balance equation including the irreversible entropy creation at the interface (the port) of the system in addition to the entropy creation term due to internal irreversible phenomena.