Tunneling and Metastability of continuous time Markov chains II, the nonreversible case

TL;DR

This paper extends the theoretical framework for analyzing metastability from reversible to nonreversible continuous-time Markov chains, utilizing potential theory and Dirichlet principles.

Contribution

It introduces a new approach to study metastability in nonreversible Markov chains, building on previous methods for reversible cases.

Findings

Extended potential theory to nonreversible dynamics

Developed new tools for analyzing metastability

Provided rigorous proofs for nonreversible case behavior

Abstract

We proposed in \cite{bl2} a new approach to prove the metastable behavior of reversible dynamics based on potential theory and local ergodicity. In this article we extend this theory to nonreversible dynamics based on the Dirichlet principle proved in \cite{gl2}.