VIII. The Brownian movement of linear and non-linear systems

Abstract

It has not so far proved possible to extend the conventional Brownian movement analysis to a system with an intrinsically non-linear relaxation mechanism (e.g. viscosity or electrical conductivity). In this paper a new statistical hypothesis is proposed which for the ideally linear circuit yields results in agreement with those already accepted and enables a calculation to be made of the Brownian movement (and corresponding frequency-spectrum) of a non-linear system. The results may be of interest in a number of practical problems, particularly in relation to proposals for the use of electrical ‘noise’ as an absolute thermometer at high temperatures.