A message-passing scheme for non-equilibrium stationary states

Abstract

We study stationary states in a diluted asymmetric (kinetic) Ising model. We apply therecently introduced dynamic cavity method to compute magnetizations of these stationarystates. Depending on the update rule, different versions of the dynamic cavity methodapply. We here study synchronous updates and random sequential updates, and comparelocal properties computed by the dynamic cavity method to numerical simulations.Using both types of updates, the dynamic cavity method is highly accurate athigh enough temperatures. At low enough temperatures, for sequential updatesthe dynamic cavity method tends to a fixed point, but this does not agree withnumerical simulations, while for parallel updates, the dynamic cavity method maydisplay oscillatory behavior. When it converges and is accurate, the dynamic cavitymethod offers a huge speed-up compared to Monte Carlo, particularly for largesystems.