Exact Free Energy Functional for a Driven Diffusive Open Stationary Nonequilibrium System

Physics – Condensed Matter – Statistical Mechanics

Scientific paper

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LaTeX2e, RevTeX4, PiCTeX. Four pages, one PiCTeX figure included in TeX source file

Scientific paper

10.1103/PhysRevLett.89.030601

We obtain the exact probability $\exp[-L {\cal F}(\{\rho(x)\})]$ 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 $L \to \infty$. $\cal F$, which plays the role of a nonequilibrium free energy, has a very different structure from that found in the purely diffusive case. As there, $\cal F$ is nonlocal, but the shocks and dynamic phase transitions of the driven system are reflected in non-convexity of $\cal F$, in discontinuities in its second derivatives, and in non-Gaussian fluctuations in the steady state.

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