Abstract. We propose a new definition of metastability of Markov processes on countable state spaces. We obtain sufficient conditions for a sequence of processes to be metastable. In the reversible case these conditions are expressed in terms of the capacity and of the stationary measure of the metastable states.

Abstract. Let r : S × S → R + be the jump rates of an irreducible random walk on a finite set S, reversible with respect to some probability measure m.Consider a zero range process on S in which a particle jumps from a site x, occupied by k particles, to a site y at rate g(k)r(x, y). Let N stand for the total number of particles. In the stationary state, as N ↑ ∞, all particles but a finite number accumulate on one single site. We show in this article that in the time scale N 1+α the site which concentrates almost all particles evolves as a random walk on S whose transition rates are proportional to the capacities of the underlying random walk.

We presented in [1,5] an approach to derive the metastable behavior of continuous-time Markov chains. We assumed in these articles that the Markov chains visit points in the time scale in which it jumps among the metastable sets. We replace this condition here by assumtpions on the mixing times and on the relaxation times of the chains reflected at the boundary of the metastable sets.

We proposed in [1] 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 [11].