Mixed population of competing TASEPs with a shared reservoir of particles

TL;DR

This paper develops a mean-field theoretical framework to analyze multiple TASEPs competing for a finite particle reservoir, revealing complex phase behaviors and enabling parameter extraction from single-lattice measurements.

Contribution

It introduces a novel mean-field model for multiple TASEPs with diverse parameters sharing a finite reservoir, including relations for particle partitioning and phase behavior analysis.

Findings

Competition affects phase transitions and current independence from total particles.

Single-lattice current measurements can infer the entire distribution of lattice parameters.

The framework is extendable beyond mean-field approximations.

Abstract

We introduce a mean-field theoretical framework to describe multiple totally asymmetric simple exclusion processes (TASEPs) with different lattice lengths, entry and exit rates, competing for a finite reservoir of particles. We present relations for the partitioning of particles between the reservoir and the lattices: these relations allow us to show that competition for particles can have non-trivial effects on the phase behavior of individual lattices. For a system with non-identical lattices, we find that when a subset of lattices undergoes a phase transition from low to high density, the entire set of lattice currents becomes independent of total particle number. We generalize our approach to systems with a continuous distribution of lattice parameters, for which we demonstrate that measurements of the current carried by a single lattice type can be used to extract the entire distribution of lattice parameters. Our approach applies to populations of TASEPs with any distribution of lattice parameters, and could easily be extended beyond the mean-field case.