A Statistical Theory of Linear Dissipative Systems

Abstract

On the basis of the joint probability for the two states occurring at different times proposed by Onsager, the theory of Brownian motion is generalized to the case of isolated systems such as treated by “the thermodynamics of irreversible processes.” Fokker-Planck's and Langevin's equations are also generalized. When the deviations from thermal equilibrium are so small that the entropy of the system is expressible in a quadratic form with respect to its state variables, these equations are integrated, and the probability distribution for the state variables at each time is obtained. As two examples, the problems of the Brownian motion of a free colloidal particle in a uniform isotropic medium and of the heat conduction along an isolated one-dimensional rod are treated. The result of the former coinsides with the usual one, but that of the latter differs essentially from the Orstein-Milatz theory.