Statistical Mechanics of the Steady State

The description of steady-state phenomena, near equilibrium, in terms of Gibbs ensembles is discussed. The Liouville equation is modified to include external nonconservative forces which prevent the system from reaching equilibrium. The steady state ensembles are then obtained as (approximately) time-independent solutions to the Liouville equation; such ensembles depend linearly on the thermodynamic parameters which characterize the deviation from equilibrium. With the aid of the steady state ensembles the linear relations between the thermodynamic fluxes and forces are obtained.