Heriot-Watt Mathematics Report Series
HWM04-3, 16 Jan 2004
The Grand Canonical Asymmetric Exclusion Process and the One Transit Walk
R Blythe, W Janke, D A Johnston and R Kenna
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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