Towards a theory of linear nonequilibrium statistical mechanics

Abstract

A unified and comprehensive presentation is given of a treatment suitable for the description, in terms of classical statistical mechanics, of the approach to thermodynamic equilibrium of an ensemble of systems displaced macroscopically from equilibrium. The method apes, as far as possible, the Gibbs treatment of equilibrium ensembles. The selection of thermodynamic variables that fluctuage independently, chosen so that the second derivatives of the entropy are diagonal and normalized, correspond to functions in the coordinate momentum space (gamma space) that are normalized and mutually orthogonal. A further (unitary) transformation diagonalizes the Onsager Matrix connecting thermodynamic flux and displacement forces. The probability density in phase space describing an ensemble of systems displaced by a sinusoidal unit amplitude from equilibrium along one such thermodynamic variable can be described as the equilibrium function times unity plus a displacement function. These displacement functions are normalized and mutually orthogonal. Their decay with time are independent and can be analyzed in terms of spectral functions giving the amplitudes of eigenfunctions of the Liouville operator which compose them.