A thermodynamical approach to noise in non-linear networks

Abstract

The physical assumptions on which linear fluctuation theory is based do not apply to internal noise in non-linear systems. As a consequence, there is still no complete theory for internal (thermal) noise in non-linear electrical networks. In this paper the authors apply Stratonovich's 'non-linear non-equilibrium thermodynamics' to describe thermal noise in reciprocal non-linear RLC-networks. As an example the (deterministic) Brayton-Moser equations are treated. A stochastic description in terms of master equations for the one-time probability density related to the Markov processes of the fluctuating electrical quantities is obtained. This decription is a generalization of Nyquist's theorem to non-linear resistors. When the non-linear resistances are represented by Taylor polynomials, different master equations are obtained for different degrees of non-linearity. A transformation of variables is used to apply the theory to non-linear dynamical network elements. To consider networks including independent sources, the theory is enlarged to open thermodynamical systems. The results are used to derive approximate noise-equivalent circuits for non-linear resistors. In this sense, this paper proves the approximate validity of 'conventional' noise source models and explicitly fixes the stochastic properties of these noise sources (as far as possible).