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

Abstract

We study the totally asymmetric exclusion process (TASEP) on a nonuniform one-dimensional ring consisting of two segments having unequal hopping rates, or defects. We allow weak particle nonconservation via Langmuir kinetics (LK), which are parametrized 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 the above phases 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 spatially uniform low- and high-density phases as well, in addition to the inhomogeneous density profiles observed for an extended defect. In all the cases, it is argued that the mean particle density in the steady state is controlled only by the ratio of the LK attachment and detachment rates.

Observation of a non-equilibrium steady state of cold atoms in a moving optical lattice

“…These considerations indicate that our system is in an NESS with characteristics of ASEP with Langmuir kinetics. Therefore, our system can be used to simulate the NESS's in various biochemical systems [14,37]. Interestingly, our system supports quantum internal states of the lattice nodes (vibrational states), which lacks in the standard ASEP model, and thus our system can be regarded as an extended model suitable for low temperature.…”