Stochastic Theory of Environmental Effects in Nonlinear Electrical Circuits

TL;DR

This paper develops a stochastic framework to analyze voltage fluctuations in nonlinear circuits, accounting for circuit feedback and resolving classical paradoxes, with applications to tunnel junctions and diodes.

Contribution

It introduces a novel stochastic method for full statistics of voltage fluctuations in nonlinear circuits, considering feedback effects and thermodynamic consistency.

Findings

Feedback from the circuit influences voltage cumulants.

The approach resolves Brillouin's paradox.

Results applied to tunnel junctions and diodes.

Abstract

We present a stochastic approach to calculate the full statistics of classical voltage fluctuations across an arbitrary, nonlinear, dissipative device embedded in a circuit in the presence of a bias. We show how the feedback resulting from the circuit, made of an ohmic resistor and a capacitor, affects the cumulants of the voltage, and in particular resolves Brillouin's paradox to satisfy thermodynamics. We apply our results to the case of a tunnel junction and a diode.