Lucas Désoppi : Thermodynamic consistency of noise models in electrical circuits: From Brillouin’s paradox to nonlinear stochastic networks

The description of noise and dissipation in electrical circuits is a long-standing problem. Fluctuations induced by an ohmic resistor are well described by the Johnson-Nyquist model, leading to a relationship analogous to Einstein’s for Brownian motion, linking the diffusion coefficient to the value of the resistance.
However, when considering a resistive component with a nonlinear current-voltage characteristic, adding a fluctuation term is not as simple as in the linear case. In fact, the naive approach of writing the simplest possible Langevin equation will generally lead to a conflict with the second law of thermodynamics: this is Brillouin’s paradox. However, it is possible to construct and classify an entire landscape of thermodynamically consistent models by reexamining the principle of detailed balance.