Toward a Statistical Thermodynamics of Steady States

The rate of change of the entropy {ital S} and free energy {ital A} with respect to time for a nonequilibrium system in a steady state is considered. A modified Liouville equation is derived to account for the phase space Jacobian arising from nontrivial phase space compression. With due allowance for this factor, the relations {dot S}=0 and {dot A}=0 are obtained, results that are consistent with the assumption of a smooth, differentiable phase space distribution function. {copyright} {ital 1997} {ital The American Physical Society}