On-site residence time in a driven diffusive system: violation and recovery of mean-field

TL;DR

This paper studies the average time particles spend on sites in driven diffusive systems, revealing limitations of mean-field theory and demonstrating improved accuracy using domain wall theory across various models.

Contribution

It introduces an analytical approach combining mean-field and domain wall theory to accurately estimate residence times in driven diffusive systems, surpassing previous mean-field limitations.

Findings

Mean-field theory underestimates residence times near shock positions.

Domain wall theory provides highly accurate residence time estimates.

Analytical predictions match well with Monte Carlo simulations.

Abstract

We investigate simple one-dimensional driven diffusive systems with open boundaries. We are interested in the average on-site residence time defined as the time a particle spends on a given site before moving on to the next site. Using mean-field theory, we obtain an analytical expression for the on-site residence times. By comparing the analytic predictions with numerics, we demonstrate that the mean-field significantly underestimates the residence time due to the neglect of time correlations in the local density of particles. The temporal correlations are particularly long-lived near the average shock position, where the density changes abruptly from low to high. By using Domain wall theory (DWT), we obtain highly accurate estimates of the residence time for different boundary conditions. We apply our analytical approach to residence times in a totally asymmetric exclusion process (TASEP), TASEP coupled to Langmuir kinetics (TASEP + LK), and TASEP coupled to mutually interactive LK (TASEP + MILK). The high accuracy of our predictions is verified by comparing these with detailed Monte Carlo simulations.