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

Soumyabrata Saha, Tridib Sadhu

Published 2023-10-17Version 1

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 et al. 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 equation 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 deviation functions, our solution describes the most probable path for these rare fluctuations.