One-transit paths and steady-state of a non-equilibrium process in a discrete-time update

TL;DR

This paper establishes a connection between the partition function of the ASEP with open boundaries under sublattice-parallel update and a two-dimensional one-transit walk model, revealing their physical quantities are related.

Contribution

It introduces a novel equivalence between the ASEP with specific updating and a one-transit walk model, providing new insights into their steady-state properties.

Findings

Partition function of ASEP equals that of the walk model.

Physical quantities are related via a similarity transformation.

Provides a new perspective on non-equilibrium processes.

Abstract

We have shown that the partition function of the Asymmetric Simple Exclusion Process with open boundaries in a sublattice-parallel updating scheme is equal to that of a two-dimensional one-transit walk model defined on a diagonally rotated square lattice. It has been also shown that the physical quantities defined in these systems are related through a similarity transformation.