Feedback and Fluctuations in a Totally Asymmetric Simple Exclusion Process with Finite Resources

TL;DR

This paper studies a modified TASEP model with feedback from a finite reservoir, improving predictions of density profiles and understanding shock localization through a generalized theory.

Contribution

It introduces a generalized domain wall theory that accounts for feedback fluctuations, enhancing the accuracy of predictions in TASEP with finite resources.

Findings

Improved density profile predictions

Better understanding of shock localization

Enhanced modeling of feedback fluctuations

Abstract

We revisit a totally asymmetric simple exclusion process (TASEP) with open boundaries and a global constraint on the total number of particles [Adams, et. al. 2008 J. Stat. Mech. P06009]. In this model, the entry rate of particles into the lattice depends on the number available in the reservoir. Thus, the total occupation on the lattice feeds back into its filling process. Although a simple domain wall theory provided reasonably good predictions for Monte Carlo simulation results for certain quantities, it did not account for the fluctuations of this feedback. We generalize the previous study and find dramatically improved predictions for, e.g., the density profile on the lattice and provide a better understanding of the phenomenon of "shock localization."