A message-passing scheme for non-equilibrium stationary states

Abstract

We study stationary states in a diluted asymmetric (kinetic) Ising model. We apply the recently introduced dynamic cavity method to compute magnetizations of these stationary states. Depending on the update rule, different versions of the dynamic cavity method apply. We here study synchronous updates and random sequential updates, and compare local properties computed by the dynamic cavity method to numerical simulations. Using both types of updates, the dynamic cavity method is highly accurate at high enough temperatures. At low enough temperatures, for sequential updates the dynamic cavity method tends to a fixed point, but which does not agree with numerical simulations, while for parallel updates, the dynamic cavity method may display cyclic behavior. When it converges and is accurate, the dynamic cavity method offers a huge speed-up compared to Monte Carlo, particularly for large systems.

12 pages, 5 figures

References in corpus (6)

• Mean Field Theory For Non-Equilibrium Network Reconstruction
• Dynamical TAP equations for non-equilibrium Ising spin glasses
• Network inference using asynchronously updated kinetic Ising Model
• Parallel dynamics of disordered Ising spin systems on finitely connected directed random graphs with arbitrary degree distributions
• Dynamical replica analysis of processes on finitely connected random graphs I: vertex covering
• Dynamics of an Ising Spin Glass on the Bethe Lattice

Cited by in corpus (20)

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• Dynamic mean-field and cavity methods for diluted Ising systems
• Inference of kinetic Ising model on sparse graphs
• A Cavity Master Equation for the continuous time dynamics of discrete spins models
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• Generalized mean field approximation for parallel dynamics of the Ising model
• Variational approximations for stationary states of Ising-like models
• A simple analytical description of the non-stationary dynamics in Ising spin systems
• Dynamics of asymmetric kinetic Ising systems revisited
• A matrix product algorithm for stochastic dynamics on networks, applied to non-equilibrium Glauber dynamics
• Cluster approximations for the TASEP: stationary state and dynamical transition
• The matrix product approximation for the dynamic cavity method
• Variational approximations for stochastic dynamics on graphs
• Dynamics of sparse Boolean networks with multi-node and self-interactions
• Inferring entropy production in many-body systems using nonequilibrium maximum entropy
• Small-Coupling Dynamic Cavity: a Bayesian mean-field framework for epidemic inference
• Three lemmas on the dynamic cavity method
• Minority Takeover in Majority Dynamics: Searching for Rare Initializations via the History Passing Algorithm
• Uncovering the non-equilibrium stationary properties in sparse Boolean networks
• Dynamic message-passing approach for kinetic spin models with reversible dynamics