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Two of the most influential exact results for classical one-dimensional diffusive transport are the exact results of current statistics for the symmetric simple exclusion process in the stationary state on a finite line coupled with two unequal reservoirs at the boundary and in the non-stationary state on an infinite line. We present the corresponding result for the intermediate geometry of a semi-infinite line coupled with a single reservoir. These results are obtained using the fluctuating hydrodynamics framework of the macroscopic fluctuation theory and confirmed by rare event simulations using a cloning algorithm. Our exact result enables us to address the corresponding problem on an infinite line in the presence of a slow region and several related problems.
Sharma et al. (Wed,) studied this question.