A theory of spontaneous fluctuations in macroscopic systems

Abstract

A theory is developed for the dynamics of spontaneous fluctuations in systems which, on the average, obey nonlinear transport equations. The theory is a generalization of the Ornstein–Uhlenbeck theory of near equilibrium fluctuations (Langevin‐type theories) and yields a stochastic process which is nonstationary with a Gaussian conditional probability. The three assumptions on which the theory is based are predominately kinetic in nature and in order to apply the theory it is necessary to formulate rate equations in terms of elementary events. Examples of this are given for nonlinear chemical reactions and the complete nonlinear Boltzmann equation.