Stationary densities in a weakly nonconserving asymmetric exclusion processes with finite resources

Asymmetric exclusion process (TASEP) along a one-dimensional (1D) open channel sets the paradigm for 1D driven models and nonequilibrium phase transitions in open 1D models. Inspired by the phenomenologies of an open TASEP with Langmuir kinetics (Lk) and with finite resources, we study the stationary densities and phase transitions in a TASEP with Lk connected to a particle reservoir at its both ends. We calculate the stationary density profiles and the phase transitions. The resulting phase diagrams in the plane of the control parameters are significantly different from their counterparts in an open TASEP with Lk. In particular, some of the phases admissible in the open TASEP with Lk model are no longer possible. Intriguingly, our model that is closely related to a TASEP coupled with Lk on a ring with a point defect, admits more phases than the latter. Phenomenological implications of our results are discussed.

💡 Research Summary

In this work the authors investigate a totally asymmetric simple exclusion process (TASEP) that is coupled both to Langmuir kinetics (Lk) in the bulk and to finite particle reservoirs at its two boundaries. The novelty lies in the simultaneous presence of two weakly non‑conserving mechanisms: (i) particles can attach to or detach from any bulk site with rates that scale as ω = Ω/L, ensuring that Langmuir attachment/detachment competes with the unit hopping rate; (ii) the entry and exit rates at the left and right boundaries are not fixed external parameters but depend on the instantaneous number of particles NR in a shared reservoir of capacity L. The effective entry and exit rates are taken as α_eff(NR)=α f(NR) and β_eff(NR)=β