Current Fluctuations in One Dimensional Diffusive Systems with a Step Initial Density Profile

Abstract

We show how to apply the macroscopic fluctuation theory (MFT) of Bertini, De Sole, Gabrielli, Jona-Lasinio, and Landim to study the current fluctuations of diffusive systems with a step initial condition. We argue that one has to distinguish between two ways of averaging (the annealed and the quenched cases) depending on whether we let the initial condition fluctuate or not. Although the initial condition is not a steady state, the distribution of the current satisfies a symmetry very reminiscent of the fluctuation theorem. We show how the equations of the MFT can be solved in the case of non-interacting particles. The symmetry of these equations can be used to deduce the distribution of the current for several other models, from its knowledge for the symmetric simple exclusion process. In the range where the integrated current $Q_t\sim \sqrt{t}$, we show that the non-Gaussian decay $\exp [-Q_t^3/t]$ of the distribution of $Q_t$ is generic.

17 pages, 2 figures

References in corpus (12)

• The large deviation approach to statistical mechanics
• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Fluctuation theorems for stochastic dynamics
• Asymptotics in ASEP with Step Initial Condition
• A Fredholm Determinant Representation in ASEP
• Mapping out of equilibrium into equilibrium in one-dimensional transport models
• Cumulants and large deviations of the current through non-equilibrium steady states
• Current Fluctuations and Statistics During a Large Deviation Event in an Exactly-Solvable Transport Model
• Equilibrium-like fluctuations in some boundary-driven open diffusive systems
• Current Fluctuations in the exclusion process and Bethe Ansatz
• Cumulants of the current in the weakly asymmetric exclusion process
• Strong asymmetric limit of the quasi-potential of the boundary driven weakly asymmetric exclusion process

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