On the association of power-flow with circuit terminals

In classical circuit theory, the question of how much power flows into a circuit through a set of terminals only makes sense if these terminals form a port, i.e., if the sum of the terminal currents is zero all of the time. On the other hand, looking from a field theory perspective, it can make sense to associate a power flow even to a set of terminals which do not form a port, especially to single terminals. This can be done by integrating the Poynting vector over those parts of a closed surface around the circuit,which points are geometrically more close to one terminal than any other terminal. We argue that, under certain conditions, the product of terminal current with the difference of the terminal potential and the average potential of all port terminals can serve as power assigned to this terminal in the field theoretic sense stated above.