The Road from Molecules to Onsager

Abstract

Our starting point consists of the microscopic dynamical equations of motion for the molecules, either classical or quantum mechanical. Subsequently the repeated randomness assumption is introduced, which breaks the time symmetry and produces the mesoscopic description in the form of a master equation for the probability distribution. Thereafter an expansion in the reciprocal system size leads to a macroscopic description, which may take one of two forms. Either it takes the form of a (nonlinear) deterministic rate equation for the macroscopic variables, tending to an equilibrium state; in this case the linearization around equilibrium produces the familiar Onsager reciprocal relations. Or it takes the form of a Fokker–Planck equation for the same variables; in that case a second expansion, this time in the temperature, leads to a nonlinear rate equation plus a dissipative term. The latter constitutes a nonlinear version of the Onsager equations.