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Quantum Fluctuations in Electrical Multiport Linear Systems

We present an extension of the classical Nyquist-Thevenin theorem for multiport classical electrical networks by Twiss to the quantum case. Conversely, we extend the quantum fluctuation-dissipation result for one port electrical systems to the multiport case, both reciprocal and nonreciprocal. Our results are extended to lossy systems by depicting resistive components as continuous limits of purely lossless lumped-element networks. Simple circuit examples are analyzed, including a linear system lacking a direct impedance representation.