Phase space compression and entropy of nonequilibrium steady states

We show that the variational principle of Evans and Baranyai [Phys. Rev. Lett. 67, 2597 (1991)] can be derived from a macroscopic entropy definition of nonequilibrium steady states. This definition claims that the entropy of nonequilibrium steady states is the sum of the equilibrium entropy of the system under the same external conditions (fixed internal energy, E, volume, V, and number of particles N), and an additional term which can be measured by the minimum excess work performed on the system by the external field, F-e, by bringing it from its equilibrium state to the final steady state. (C) 1996 American Institute of Physics.