Stationary densities in a weakly nonconserving asymmetric exclusion processes with finite resources

TL;DR

This paper investigates the stationary densities and phase transitions in a TASEP model with Langmuir kinetics and finite resources, revealing new phase diagrams and behaviors distinct from traditional open TASEP models.

Contribution

It introduces a TASEP model with Lk connected to reservoirs at both ends, analyzing its stationary states and phase transitions, and compares these with existing models.

Findings

Phase diagrams differ significantly from open TASEP with Lk.

Some phases in open Lk TASEP are not possible in this model.

The model exhibits more phases than a ring TASEP with a defect.

Abstract

Asymmetric exclusion process (TASEP) along a one-dimensional (1D) open channel sets the paradigm for 1D driven models and nonequilibrium phase transitions in open 1D models. Inspired by the phenomenologies of an open TASEP with Langmuir kinetics (Lk) and with finite resources, we study the stationary densities and phase transitions in a TASEP with Lk connected to a particle reservoir at its both ends. We calculate the stationary density profiles and the phase transitions. The resulting phase diagrams in the plane of the control parameters are significantly different from their counterparts in an open TASEP with Lk. In particular, some of the phases admissible in the open TASEP with Lk model are no longer possible. Intriguingly, our model that is closely related to a TASEP coupled with Lk on a ring with a point defect, admits more phases than the latter. Phenomenological implications of our results are discussed.