Sum of exit times in a series of two metastable states

TL;DR

This paper analyzes the expected exit times in a chain of metastable states within finite Markov chains, providing sharp estimates and an addition rule, with applications to the Blume-Capel model.

Contribution

It introduces a precise estimate of exit times and an addition rule for metastable states in Markov chains, with application to a specific physical model.

Findings

Sharp estimate of exit time from higher-energy metastable state

Addition rule for combined metastable states on exponential time scale

Application to the Blume-Capel model in zero chemical potential case

Abstract

We consider the problem of non degenerate in energy metastable states forming a series in the framework of reversible finite state space Markov chains. We assume that starting from the state at higher energy the system necessarily visits the second one before reaching the stable state. In this framework, we give a sharp estimate of the exit time from the metastable state at higher energy and, on the proper exponential time scale, we prove an addition rule. As an application of the theory, we study the Blume-Capel model in the zero chemical potential case.