Weak reservoirs are superexponentially irrelevant for misanthrope processes

2023/10/25 by Julian Kern, Kern, Julian
Mathematics · Physics and Astronomy · #60J27 #60K35 #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2310.17038

openalex publication_date 2023/10/25 · openalex created_date 2023/10/28 · openalex updated_date 2026/07/28

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.

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• Strong Asymmetric Limit of the Quasi-Potential of the Boundary Driven Weakly Asymmetric Exclusion Process
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