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.
Derrida
B
B
Laboratoire de Physique Statistique, 24 rue Lhomond, 75231 Paris Cedex 05, France. derrida@lps.ens.fr
Lebowitz
J L
JL
Speer
E R
ER