We consider systems that possess a local but non-global port-Hamiltonian representation. We show that non-globality is a consequence of the phase-space topology and that local port-Hamiltonian systems may transgress the dissipation inequality satisfied by their global counterparts. Far from being a defect, non-globality extends the modeling power of port-Hamiltonian systems by providing a framework to model cyclic physical processes for energy conversion and extraction.