Asymmetric exclusion processes with fixed resources: Reservoir crowding and steady states

Astik Haldar, Parna Roy, Abhik Basu

Published 2020-06-27Version 1

We study the nonequilibrium steady states of an asymmetric exclusion process (TASEP) coupled to a reservoir of infinite capacity. We elucidate how the steady states are controlled by the interplay between the crowding of the reservoir that dynamically controls both the entry and exit rates of the TASEP, and the total number of particles. We show that the TASEP can be found in the low density, high density, maximal current and shock phases. Interestingly, even with large resources, the phase behaviour and the phase diagram of the TASEP do not approach that of an open TASEP: here, the TASEP can support only localised domain walls for any mean density as a combined consequence of the effects of reservoir crowding on the effective entry and exit rates of the TASEP and the particle number conservation, as opposed to delocalised domain walls in open TASEPs. Furthermore, in the limit of infinite resources, the TASEP can be found in its high density phase only for any finite values of the control parameters, totally in contrast to an open TASEP.