Cluster approximations for the TASEP: stationary state and dynamical transition

Abstract

We develop and test cluster approximations, which generalize simple mean--field by taking into account more and more local correlations, for the Totally Asymmetric Simple Exclusion Process with open boundaries. We consider in detail the pair and triplet approximations, discussing the improvements with respect to mean field in various steady state properties. Moreover, we analyze the recently discovered dynamical transition, describing how the spectrum of the relaxation matrix changes at the transition.

arXiv comment8 pages, 9 figures

References in corpus (23)

• Phase transitions in an exactly soluble one-dimensional exclusion process
• Non-equilibrium statistical mechanics: From a paradigmatic model to biological transport
• Discrete stochastic models for traffic flow
• Phase Coexistence in Driven One Dimensional Transport
• Bethe Ansatz Solution of the Asymmetric Exclusion Process with Open Boundaries
• The Totally Asymmetric Simple Exclusion Process with Langmuir Kinetics
• Cluster Variation Method in Statistical Physics and Probabilistic Graphical Models
• A message-passing approach for recurrent-state epidemic models on networks
• Dynamic message-passing equations for models with unidirectional dynamics
• The role of clustering and gridlike ordering in epidemic spreading
• Relaxation times in the ASEP model using a DMRG method
• Majority dynamics on trees and the dynamic cavity method
• Slowest relaxation mode of the partially asymmetric exclusion process with open boundaries
• The Cavity Approach to Parallel Dynamics of Ising Spins on a Graph
• Cluster approximations for probabilistic systems: a new perspective of epidemiological modelling
• Dynamic mean-field and cavity methods for diluted Ising systems
• A message-passing scheme for non-equilibrium stationary states
• Dynamical Transition in the Open-boundary Totally Asymmetric Exclusion Process
• Rigorous results on the local equilibrium kinetics of a protein folding model
• Variational approximations for stationary states of Ising-like models
• A simple analytical description of the non-stationary dynamics in Ising spin systems
• Neighborhood approximations for non-linear voter models
• Variational approximations for stochastic dynamics on graphs

Cited by in corpus (4)

• Dynamical transition in the TASEP with Langmuir kinetics: mean-field theory
• Unbalanced Langmuir kinetics affects TASEP dynamical transitions: mean-field theory
• The fast and the slow axonal transport: a unified approach based on cargo and molecular motors coupled dynamics
• Dynamical transitions in a driven diffusive model with interactions