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

B. Derrida·J. L. Lebowitz·E. R. Speer
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Abstract

We obtain the exact probability $\exp[-L {\cal F}(\{ρ(x)\})]$ of finding a macroscopic density profile $ρ(x)$ 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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B. Derrida, J. L. Lebowitz, E. R. Speer. 2002-03-07. Exact Free Energy Functional for a Driven Diffusive Open Stationary Nonequilibrium System. https://doi.org/10.1103/physrevlett.89.030601

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