Toward a Statistical Thermodynamics of Steady States

The rate of change of the entropy S and free energy 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 $\dot{S}=0\mathrm{}$ and $\dot{A}=0\mathrm{}$ are obtained, results that are consistent with the assumption of a smooth, differentiable phase space distribution function.