Exact free energy functional for a driven diffusive open stationary nonequilibrium system

We obtain the exact probability exp[-LF({rho(x)}) ] of finding a macroscopic density profile rho(x) in the stationary nonequilibrium state of an open driven diffusive system, when the size of the system L-->infinity .F, which plays the role of a nonequilibrium free energy, has a very different structure from that found in the purely diffusive case. As there, F is nonlocal, but the shocks and dynamic phase transitions of the driven system are reflected in nonconvexity of F , in discontinuities in its second derivatives, and in non-Gaussian fluctuations in the steady state.