Large deviations in the symmetric simple exclusion process with slow boundaries

TL;DR

This paper derives exact large deviation functions for density and current in a 1D symmetric simple exclusion process with slow boundary rates, revealing how macroscopic fluctuations are affected by boundary rate scaling.

Contribution

It provides the first exact large deviation functions for the process with slow boundary rates, extending previous results to new boundary conditions.

Findings

Large deviation functions are explicitly obtained for slow boundary rates.

Macroscopic fluctuations are significantly altered by boundary rates slower than the bulk.

Results show the impact of boundary rate scaling on non-equilibrium steady states.

Abstract

We obtain the exact large deviation functions of the density profile and of the current, in the non-equilibrium steady state of a one dimensional symmetric simple exclusion process coupled to boundary reservoirs with slow rates. Compared to earlier results, where rates at the boundaries are comparable to the bulk ones, we show how macroscopic fluctuations are modified when the boundary rates are slower by an order of inverse of the system length.