Sum of exit times in series of metastable states in Probabilistic Cellular Automata

TL;DR

This paper investigates the long-term behavior of reversible Probabilistic Cellular Automata with multiple metastable states, analyzing the sum of exit times and their implications for understanding metastability in statistical mechanics.

Contribution

It introduces a model with a series of two metastable states and proposes a rule for combining their exit times, advancing the understanding of metastability dynamics.

Findings

The system exhibits two distinct metastable states with long trapping times.

A rule for combining exit times from each metastable state is proposed.

The model provides insights into the metastability phenomena in probabilistic cellular automata.

Abstract

Reversible Probabilistic Cellular Automata are a special class of automata whose stationary behavior is described by Gibbs-like measures. For those models the dynamics can be trapped for a very long time in states which are very different from the ones typical of stationarity. This phenomenon can be recasted in the framework of metastability theory which is typical of Statistical Mechanics. In this paper we consider a model presenting two not degenerate in energy metastable states which form a series, in the sense that, when the dynamics is started at one of them, before reaching stationarity, the system must necessarily visit the second one. We discuss a rule for combining the exit times from each of the metastable states.