Large Deviations in the Symmetric Simple Exclusion Process with Slow Boundaries: A Hydrodynamic Perspective

TL;DR

This paper derives large deviation functions for density and current in a one-dimensional symmetric simple exclusion process with slow boundary reservoirs using hydrodynamic methods, providing explicit solutions and paths for rare fluctuations.

Contribution

It offers an independent hydrodynamic derivation of large deviations functions, incorporating boundary effects and solving the variational problems explicitly.

Findings

Explicit solutions for density large deviations using Euler-Lagrange equations.

Solution for current large deviations via the additivity principle.

Description of the most probable paths for rare fluctuations.

Abstract

We revisit the one-dimensional model of the symmetric simple exclusion process slowly coupled with two unequal reservoirs at the boundaries. In its non-equilibrium stationary state, the large deviations functions of density and current have been recently derived using exact microscopic analysis by Derrida, Hirschberg and Sadhu in J. Stat. Phys. 182, 15 (2021). We present an independent derivation using the hydrodynamic approach of the macroscopic fluctuation theory (MFT). The slow coupling introduces additional boundary terms in the MFT-action, which modifies the spatial boundary conditions for the associated variational problem. For the density large deviations, we explicitly solve the corresponding Euler-Lagrange equations using a simple local transformation of the optimal fields. For the current large deviations, our solution is obtained using the additivity principle. In addition to recovering the expression of the large deviations functions, our solution describes the most probable path for these rare fluctuations.