I'm working on an API for simulation of port-Hamiltonian systems. As far as I understand it, a Hamiltonian system is symplectic if it is power conserving, and so including resistive elements would thus destroy the symplectic nature. My question is, if I add an extra state variable, the dissipated heat, along with its adjoint, does this restore its symplecticity?
Further, if I didn't include the extra state variable, would I still benefit from using symplectic integrators? And do systems lying on a contact manifold still benefit from symplectic integrators?