Dynamical transition in the TASEP with Langmuir kinetics: mean-field theory

TL;DR

This paper develops a mean-field theoretical framework to analyze the dynamical transition in TASEP with Langmuir kinetics, revealing a singularity in relaxation rates without steady-state changes.

Contribution

It extends mean-field analysis to TASEP with Langmuir kinetics, predicting a dynamical transition characterized by relaxation rate singularities.

Findings

Relaxation rate becomes independent of boundary rates at critical points.

Rigorous bounds for relaxation rates are established and become tight in the thermodynamic limit.

Dynamical transition predicted in TASEP with Langmuir kinetics, generalizing previous results.

Abstract

We develop a mean-field theory for the totally asymmetric simple exclusion process (TASEP) with open boundaries, in order to investigate the so-called dynamical transition. The latter phenomenon appears as a singularity in the relaxation rate of the system toward its non-equilibrium steady state. In the high-density (low-density) phase, the relaxation rate becomes independent of the injection (extraction) rate, at a certain critical value of the parameter itself, and this transition is not accompanied by any qualitative change in the steady-state behavior. We characterize the relaxation rate by providing rigorous bounds, which become tight in the thermodynamic limit. These results are generalized to the TASEP with Langmuir kinetics, where particles can also bind to empty sites or unbind from occupied ones, in the symmetric case of equal binding/unbinding rates. The theory predicts a dynamical transition to occur in this case as well.