Limits to the fluctuation-dissipation theorem for nonlinear circuits

It is well known that the equilibrium thermal noise behavior at the terminals of any linear time-invariant (LTI) RLC circuit can be predicted from knowledge of the driving-point impedance and temperature alone. This paper examines the conjecture that similar results hold if the capacitors and inductors are nonlinear. We refine the conjecture by analyzing the behavior of an RLC bridge circuit with the nonlinear inductor and capacitor carefully matched so the terminal behavior reduces to that of a linear resistor R. We show that the terminal noise current is not that predicted by the Nyquist-Johnson model for R if the driving voltage is time dependent or the inductor and capacitor are time varying. This counterexample disproves the conjecture, which does hold, however, for the bridge circuit with nonlinear (but time invariant) devices if the driving voltage is zero or constant. This paper makes exact calculations using techniques from stochastic differential equations and using reversibility arguments.