Fluctuations in interacting particle systems with memory

TL;DR

This paper investigates how long-range temporal correlations and memory effects influence fluctuations and rare events in many-particle systems, revealing superdiffusive behavior and modifying large deviation principles.

Contribution

It introduces a framework for analyzing memory-dependent particle systems and demonstrates superdiffusive phenomena in a modified exclusion process.

Findings

Memory dependence alters large deviation behavior.

Superdiffusive behavior can emerge due to memory effects.

Connections to recent related research.

Abstract

We consider the effects of long-range temporal correlations in many-particle systems, focusing particularly on fluctuations about the typical behaviour. For a specific class of memory dependence we discuss the modification of the large deviation principle describing the probability of rare currents and show how superdiffusive behaviour can emerge. We illustrate the general framework with detailed calculations for a memory-dependent version of the totally asymmetric simple exclusion process as well as indicating connections to other recent work.