Nonequilibrium steady states in coupled asymmetric and symmetric exclusion processes

Atri Goswami, Utsa Dey, Sudip Mukherjee

Published 2023-06-26Version 1

We propose and study a one-dimensional (1D) model consisting of two lanes with open boundaries. One of the lanes executes diffusive and the other lane driven unidirectional or asymmetric exclusion dynamics, which are mutually coupled through particle exchanges in the bulk. We elucidate the generic nonuniform steady states in this model. We show that the nonequilibrium steady states of this model can be controlled by the ratio of the diffusive and directed motion time-scales, which can be tuned to achieve phase coexistence in the asymmetric exclusion dynamics and spatially smoothly varying density in the diffusive dynamics in the steady state. We obtain phase diagrams of the model by using mean field theories, and corroborate and complement the results by stochastic Monte Carlo simulations. This model reduces to an isolated open totally asymmetric exclusion process (TASEP) and an open TASEP with bulk particle nonconserving Langmuir kinetics (LK), respectively, in the limits of vanishing and diverging particle diffusivity in the lane executing diffusive dynamics. Thus this model works as an overarching general model, connecting both pure TASEPs and TASEPs with LK in different asymptotic limits.