On the Association of Power-Flow With Circuit Terminals

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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.