Current fluctuations in a semi-infinite line

Abstract

We present the application of a fluctuating hydrodynamic theory to study current fluctuations in diffusive systems on a semi-infinite line in contact with a reservoir with slow coupling. We show that the distribution of the time-integrated current across the boundary at large times follows a large deviation principle with a rate function that depends on the coupling strength with the reservoir. The system exhibits a long-term memory of its initial state, which was earlier reported on an infinite line and can be described using quenched and annealed averages of the initial state. We present an explicit expression of the rate function for independent particles, which we verify using an exact solution of the microscopic dynamics. For the symmetric simple exclusion process, we present expressions for the first three cumulants of both quenched and annealed averages.

27 pages, 5 figures. Several corrections done in the first draft. Published in J Stat Mech

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Cited by in corpus (6)

• Large Deviations in the Symmetric Simple Exclusion Process with Slow Boundaries: A Hydrodynamic Perspective
• Semi-infinite simple exclusion process: from current fluctuations to target survival
• Current fluctuations in the symmetric exclusion process beyond the one-dimensional geometry
• Large deviations of current for the symmetric simple exclusion process on a semi-infinite line, and on an infinite line with a slow bond
• Lecture notes on large deviations in non-equilibrium diffusive systems
• Macroscopic fluctuation theory of interacting Brownian particles