Eur. Phys. J. B 50, 57-61 (2006)
https://doi.org/10.1140/epjb/e2006-00097-9

A definition of metastability for Markov processes with detailed balance

Centro de Ciencias Físicas, UNAM; Apartado postal 48-3, CP, 62251 Cuernavaca Morelos, Mexico

Corresponding author: ^a leyvraz@ce.fis.unam.mx

Received: 29 September 2005
Revised: 17 November 2005
Published online: 12 April 2006

Abstract

A definition of metastable states applicable to arbitrary finite state Markov processes satisfying detailed balance is discussed. In particular, we identify a crucial condition that distinguishes genuine metastable states from other types of slowly decaying modes and which leads to properties similar to those postulated in the restricted ensemble approach [1]. The intuitive physical meaning of this condition is simply that the total equilibrium probability of finding the system in the metastable state is negligible. As a concrete application of our formalism we present preliminary results on a 2D kinetic Ising model.