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

Abstract

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

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• Macroscopic fluctuation theory for stationary non equilibrium states
• Fluctuations in Stationary non Equilibrium States
• Large Deviation of the Density Profile in the Steady State of the Open Symmetric Simple Exclusion Process
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