Non-linear irreversible thermodynamics of Brownian motion

Abstract

Irreversible thermodynamics is studied for a special system far from equilibrium. Kramers' theory of Brownian motion leads to a diffusion equation in phase space. The distribution function resulting from this equation is used for the definition of free energy as a function of time. A system of non-linear irreversible thermodynamics is developed on this basis. Relations which are analogous to the Onsager relations are found. The formalism appears to be applicable to a much wider class of diffusion equations. For these more general cases also, Onsager's relations appear automatically, while microscopic irreversibility has not been introduced explicitly.