Availability, storage capacity, and diffusion: Stationary states of an asymmetric exclusion process connected to two reservoirs

TL;DR

This paper models a one-dimensional particle transport system with finite reservoirs and diffusion, revealing how resource limitations and exchange mechanisms influence steady states and phase behavior, differing from traditional open TASEP models.

Contribution

It introduces a minimal model connecting two finite reservoirs via TASEP and diffusion, analyzing how resource constraints and exchange parameters shape steady states and phase diagrams.

Findings

Steady state density profiles can be uniform or piecewise continuous.

Reservoir populations can be tuned to be preferentially filled or emptied.

Phase diagrams differ significantly from open TASEP models.

Abstract

We explore how the interplay of finite availability, carrying capacity of particles at different parts of a spatially extended system and particle diffusion between them control the steady state currents and density profiles in a one-dimensional current-carrying channel connecting the different parts of the system. To study this, we construct a minimal model consisting of two particle reservoirs of finite carrying capacities connected by a totally asymmetric simple exclusion process (TASEP). In addition to particle transport via TASEP between the reservoirs, the latter can also directly exchange particles, modeling particle diffusion between them that can maintain a steady current in the system. We investigate the steady state density profiles and the associated particle currents in the TASEP lane. The resulting phases and the phase diagrams are quite different from an open TASEP, and are characterised by the model parameters defining particle exchanges between the TASEP and the reservoirs, direct particle exchanges between the reservoirs, and the filling fraction of the particles that determines the total resources available. These parameters can be tuned to make the density on the TASEP lane globally uniform or piecewise continuous, and can make the two reservoirs preferentially populated or depopulated.