Nonequilibrium steady states in a closed inhomogeneous asymmetric exclusion process with particle nonconservation

TL;DR

This paper investigates the steady states of a nonuniform asymmetric exclusion process with particle nonconservation, revealing phase transitions and density profiles influenced by inhomogeneity and Langmuir kinetics.

Contribution

It introduces a detailed analysis of inhomogeneous TASEP with particle nonconservation, highlighting how defects and LK rates shape steady state phases and density profiles.

Findings

Extended defect leads to inhomogeneous density profiles with phase transitions.

Slower segment maintains uniform density, akin to maximal current phase.

Particle density is governed solely by LK attachment and detachment rate ratio.

Abstract

We study asymmetric exclusion processes (TASEP) on a nonuniform one-dimensional ring consisting of two segments having unequal hopping rates, or {\em defects}. We allow weak particle nonconservation via Langmuir kinetics (LK), that are parameterised by generic unequal attachment and detachment rates. For an extended defect, in the thermodynamic limit the system generically displays inhomogeneous density profiles in the steady state - the faster segment is either in a phase with spatially varying density having no density discontinuity, or a phase with a discontinuous density changes. Nonequilibrium phase transitions between them are controlled by the inhomogeneity and LK. The slower segment displays only macroscopically uniform bulk density profiles in the steady states, reminiscent of the maximal current phase of TASEP but with a bulk density generally different from half. With a point defect, there are low and high density spatially uniform phases as well, in addition to the inhomogeneous density profiles observed for an extended defect. In all the cases, it is argued that the the mean particle density in the steady state is controlled only by the ratio of the LK attachment and detachment rates.