Fluctuations in meta-population exclusion processes

TL;DR

This paper develops a systematic approach to analyze fluctuations in meta-population exclusion processes, extending traditional models by considering patches of finite size and deriving effective Langevin descriptions.

Contribution

It introduces a meta-population framework with patch size expansion, providing a first-principles derivation of fluctuation dynamics in exclusion models.

Findings

Semi-analytical spectral properties derived

Numerical simulations confirm theoretical predictions

Good approximation to conventional exclusion models

Abstract

We introduce a meta-population version of models of asymmetric exclusion models, consisting of a spatial arrangement of patches. Patches are of a specific size, indicating the maximal number of particles they can hold. We use an expansion in the inverse patch size to calculate the spectral properties of fluctuations in such systems. This provides a systematic derivation from first principles of effective Langevin descriptions discussed in the literature. We apply our approach to the totally asymmetric simple exclusion process, to variants with an overall constraint on the total particle number and to a two-species exclusion model. The theory provides semi-analytical results, these are confirmed in numerical simulations, and give good approximations to conventional exclusion models. These are recovered when the patch size is set to unity.