Nonequilibrium steady states in coupled asymmetric and symmetric exclusion processes

Abstract

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 in a parameter regime, where hopping along the TASEP lane, diffusion along the SEP lane and the exchange of particles between the TASEP and SEP lanes compete, the SEP diffusivity $D$ appears as a tuning parameter for both the SEP and TASEP densities for a given exchange rate in the nonequilibrium steady states of this model. Indeed, $D$ can be tuned to achieve phase coexistence in the asymmetric exclusion dynamics together with 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. We further define phases in the SEP and obtain phase diagrams, and show their correspondence with the TASEP phases. In addition to its significance as a 1D driven, diffusive model, this model also serves as a simple reduced model for cell biological transport by molecular motors undergoing diffusive and directed motion inside eukaryotic cells.

19 pages, 16 figures

References in corpus (10)

• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
• The Totally Asymmetric Simple Exclusion Process with Langmuir Kinetics
• Traffic of molecular motors through tube-like compartments
• Exclusion Processes with Internal States
• Phase diagram of two-lane driven diffusive systems
• Bulk-driven non-equilibrium phase transitions in a mesoscopic ring
• Generic transport mechanisms for molecular traffic in cellular protrusions
• Domain wall delocalization, dynamics and fluctuations in an exclusion process with two internal states
• Steady states and phase transitions in heterogeneous asymmetric exclusion processes