Nonequilibrium steady states in a closed inhomogeneous asymmetric exclusion process with particle nonconservation

Abstract

We study asymmetric exclusion processes (TASEP) on a nonuniform one-dimensional ring consisting of two segments having unequal hopping rates, or {\em defects}. We allow weak particle nonconservation via Langmuir kinetics (LK), that are parameterised by generic unequal attachment and detachment rates. For an extended defect, in the thermodynamic limit the system generically displays inhomogeneous density profiles in the steady state - the faster segment is either in a phase with spatially varying density having no density discontinuity, or a phase with a discontinuous density changes. Nonequilibrium phase transitions between them are controlled by the inhomogeneity and LK. The slower segment displays only macroscopically uniform bulk density profiles in the steady states, reminiscent of the maximal current phase of TASEP but with a bulk density generally different from half. With a point defect, there are low and high density spatially uniform phases as well, in addition to the inhomogeneous density profiles observed for an extended defect. In all the cases, it is argued that the the mean particle density in the steady state is controlled only by the ratio of the LK attachment and detachment rates.

arXiv comment10 pages, 14 figures

References in corpus (21)

• Traffic and Related Self-Driven Many-Particle Systems
• Statistical Physics of Vehicular Traffic and Some Related Systems
• Non-equilibrium statistical mechanics: From a paradigmatic model to biological transport
• The Totally Asymmetric Simple Exclusion Process with Langmuir Kinetics
• Modeling Translation in Protein Synthesis with TASEP: A Tutorial and Recent Developments
• Driven Lattice Gases with Quenched Disorder: Exact Results and Different Macroscopic Regimes
• Fluctuation-Driven Molecular Transport in an Asymmetric Membrane Channel
• Towards a model for protein production rates
• Bottleneck-induced transitions in a minimal model for intracellular transport
• Towards a model for protein production rates
• Phase diagram and edge effects in the ASEP with bottlenecks
• Asymmetric coupling in two-lane simple exclusion process with Langmuir kinetics: phase diagrams and boundary layers
• Nonequilibrium Criticality at Shock Formation in Steady States
• Bulk and surface transitions in asymmetric simple exclusion process: Impact on boundary layers
• Disordered exclusion process revisited: some exact results in the low-current regime
• Nonequilibrium steady states in asymmetric exclusion processes on a ring with bottlenecks
• Fixed points and boundary layers in exclusion processes
• Phase coexistences and particle non-conservation in a closed asymmetric exclusion process with inhomogeneities
• Generic nonequilibrium steady states in an exclusion process on an inhomogeneous ring
• Duality and phase diagram of one dimensional transport
• Multi-shocks in asymmetric simple exclusions processes: Insights from fixed-point analysis of the boundary-layers

Cited by in corpus (3)

• Observation of a non-equilibrium steady state of cold atoms in a moving optical lattice
• Interference of two co-directional exclusion processes in the presence of a static bottleneck: a biologically motivated model
• Defect versus defect: stationary states of single file marching in periodic landscapes with road blocks