Fluctuations in interacting particle systems with memory

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.

22 pages, 9 figures. v2+: Minor changes. This is an author-created, un-copyedited version of an article published in JSTAT. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at http://dx.doi.org/10.1088/1742-5468/2015/07/P07021 . Note also erratum to fix errors in production!

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• Large deviations in models of growing clusters with symmetry-breaking transitions
• Nonequilibrium steady state of trapped active particles
• Optimizing thermodynamic trajectories using evolutionary and gradient-based reinforcement learning
• Large deviations in statistics of the convex hull of passive and active particles: A theoretical study
• Nonequilibrium steady state of Brownian motion in an intermittent potential
• Current fluctuations of a self-interacting diffusion on a ring
• Accelerated first-passage dynamics in a non-Markovian feedback Ornstein--Uhlenbeck process
• Effective bandwidth of non-Markovian packet traffic
• Towards neural reinforcement learning for large deviations in nonequilibrium systems with memory