Thermodynamically Consistent Noise Modeling in Non-Linear Circuits

Traditional attempts to extend the Nyquist Johnson formula for thermal fluctuations to non-linear dissipative elements have led to thermodynamically inconsistent models. In this work, we present a Langevin model for thermal noise in non-linear dissipative elements, that is fully consistent with the main requirements of thermodynamics. The model accurately predicts the Gibbs (Maxwell Boltzmann) distribution at thermal equilibrium and ensures zero expected voltages and currents, thereby resolving the well-known Brillouin's paradox and confirming compliance with the second law of thermodynamics.