  Boundary controlled irreversible port-Hamiltonian systems (BC-IPHS) on
1-dimensional spatial domains are defined by extending the formulation of
reversible BC-PHS to irreversible thermodynamic systems controlled at the
boundaries of their spatial domains. The structure of BC-IPHS has clear
physical interpretation, characterizing the coupling between energy storing and
energy dissipating elements. By extending the definition of boundary port
variables of BC-PHS to deal with the dissipative terms, a set of boundary port
variables are defined such that BC-IPHS are passive with respect to a given set
of conjugated inputs and outputs. As for finite dimensional IPHS, the first and
second principle are satisfied as a structural property. Several examples are
given to illustrate the proposed approach.
