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

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."

11 pages, 3 figures, v2: Minor changes

References in corpus (6)

• Phase Coexistence in Driven One Dimensional Transport
• Traffic of molecular motors through tube-like compartments
• Exact Spectral Gaps of the Asymmetric Exclusion Process with Open Boundaries
• Inhomogeneous exclusion processes with extended objects: The effect of defect locations
• Far-from-equilibrium transport with constrained resources
• Dynamic correlation functions and Boltzmann Langevin approach for driven one dimensional lattice gas