  In this paper we prove a version of the Berman-Konsowa principle for
reversible Markov jump processes on Polish spaces. The Berman-Konsowa principle
provides a variational formula for the capacity of a pair of disjoint
measurable sets. There are two versions, one involving a class of probability
measures for random finite paths from one set to the other, the other involving
a class of finite unit flows from one set to the other. The Berman-Konsowa
principle complements the Dirichlet principle and the Thomson principle, and
turns out to be especially useful for obtaining sharp estimates on crossover
times in metastable interacting particle systems.
