On perturbation around closed exclusion processes

TL;DR

This paper derives a general formula for the stationary states of inhomogeneously perturbed exclusion processes, extending previous conjectures and enabling detailed phase diagram analysis of related models.

Contribution

It provides a new, generalized formula for stationary states in inhomogeneous exclusion processes, expanding theoretical understanding and application scope.

Findings

Derived a formula for stationary states with inhomogeneous adsorption/desorption.

Validated the formula by reproducing known phase diagrams.

Extended previous conjectures to more general inhomogeneous cases.

Abstract

We derive the formula for the stationary states of particle-number conserving exclusion processes infinitesimally perturbed by inhomogeneous adsorption and desorption. The formula not only proves but also generalises the conjecture proposed in arXiv:1711.06949 to account for inhomogeneous adsorption and desorption. As an application of the formula, we draw part of the phase diagrams of the open asymmetric simple exclusion process with and without Langmuir kinetics, correctly reproducing known results.