The Grand-Canonical Asymmetric Exclusion Process and the One-Transit Walk
R. A. Blythe, W. Janke, D. A. Johnston, R. Kenna
TL;DR
This paper explores the grand-canonical partition function of the ASEP, revealing its simplicity and enabling new insights into the asymptotic behavior and its connection to One-Transit Walks, advancing understanding of nonequilibrium systems.
Contribution
It introduces a simple form of the grand-canonical partition function for ASEP and links it to One-Transit Walks, providing new analytical tools for nonequilibrium statistical mechanics.
Findings
Derived asymptotics of the canonical normalization in various phases
Established a direct connection between ASEP and One-Transit Walks
Simplified the analysis of ASEP in the grand-canonical ensemble
Abstract
The one-dimensional Asymmetric Exclusion Process (ASEP) is a paradigm for nonequilibrium dynamics, in particular driven diffusive processes. It is usually considered in a canonical ensemble in which the number of sites is fixed. We observe that the grand-canonical partition function for the ASEP is remarkably simple. It allows a simple direct derivation of the asymptotics of the canonical normalization in various phases and of the correspondence with One-Transit Walks recently observed by Brak et.al.
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