Weak reservoirs are superexponentially irrelevant for misanthrope processes
Julian Kern
TL;DR
The paper addresses boundary-driven misanthrope/exclusion processes with weak reservoirs and proves an exponential equivalence to the corresponding impermeable-boundary systems under a precise scaling condition. This equivalence enables transferring hydrodynamic limits and large deviation principles from impermeable models to weak-reservoir models, notably for the TASEP and TALJEP with long jumps, without requiring vanishing viscosity. The method relies on an attractive misanthrope coupling and a speed-up criterion, providing a practical tool to analyze non-reversible boundary-driven dynamics. The results unify and extend hydrodynamic and LDP analyses for boundary-driven exclusion processes, including long-range jump regimes, with potential applications to a broader class of lattice systems.
Abstract
We provide a short proof for the exponential equivalence between misanthrope processes in contact with weak reservoirs and those with impermeable boundaries. As a consequence, we can derive both the hydrodynamic limit and the large deviations of the totally asymmetric simple exclusion process (TASEP) in contact with weak reservoirs. This extends a recent result which proved the hydrodynamic behaviour of a vanishing viscocity approximation of the TASEP in contact with weak reservoirs. Further applications to a class of asymmetric exclusion processes with long jumps are discussed.