Derivation of the phenomenological equations from the master equation. I. Even variables only

Abstract

The ‘master equation’ describes the behaviour of a macroscopic system in terms of a time dependent probability distribution. It is here shown that, if the initial distribution is concentrated in a small region, it moves toward equilibrium without spreading. Thus the stochastic process described by the master equation is observed as a deterministic process by an observer whose observations are too coarse to observe the fluctuations. This is the process to which the usual phenomenological equations refer. With the aid of appropriate approximations one finds in this way the well-known linear regression equations, including Onsager's reciprocal relations.