Dynamics of non-Markovian exclusion processes

Abstract

Driven diffusive systems are often used as simple discrete models of collective transport phenomena in physics, biology or social sciences. Restricting attention to one-dimensional geometries, the asymmetric simple exclusion process (ASEP) plays a paradigmatic role to describe noise-activated driven motion of entities subject to an excluded volume interaction and many variants have been studied in recent years. While in the standard ASEP the noise is Poissonian and the process is therefore Markovian, in many applications the statistics of the activating noise has non-standard distribution with possible memory effects resulting from internal degrees of freedom or external sources. This leads to temporal correlations and can significantly affect the shape of the current-density relation as has been studied recently for a number of scenarios. In this paper we report a general framework to derive the fundamental diagram of ASEPs driven by non-Poissonian noise by using effectively only two simple quantities, viz., the mean residual lifetime of the jump distribution and a suitably defined temporal correlation length. We corroborate our results by detailed numerical studies for various noise statistics under periodic boundary conditions and discuss how our approach can be applied to more general driven diffusive systems.

13 pages, 5 figures

References in corpus (11)

• Physics of Transport and Traffic Phenomena in Biology: from molecular motors and cells to organisms
• Steady-state selection in driven diffusive systems with open boundaries
• Intra-cellular transport of single-headed molecular motors KIF1A
• Infinite systems of interacting chains with memory of variable length - a stochastic model for biological neural nets
• Exclusion processes on networks as models for cytoskeletal transport
• Condensation in Temporally Correlated Zero-Range Dynamics
• Dwell time symmetry in random walks and molecular motors
• Spatiotemporally complete condensation in a non-Poissonian exclusion process
• Stepping and crowding of molecular motors: statistical kinetics from an exclusion process perspective
• Renewal processes and fluctuation analysis of molecular motor stepping
• Driven flow with exclusion and transport in graphene-like structures

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• Temporally correlated zero-range process with open boundaries: Steady state and fluctuations
• Limit theorems for a minimal random walk model
• Interacting elephant random walks
• Bidirectional Non-Markovian Exclusion Processes
• Slow melting of a disordered quantum crystal
• First contact percolation