DECAY OF METASTABLE STATES .1. A GENERAL-CASE WITHOUT MANIFEST DETAILED BALANCE

The equilibration process, activated by noise, is considered as an eigenproblem of the Fokker-Planck operator. The rate of escape from quite general metastable states is calculated analytically via Rayleigh's identity. Its usefulness is demonstrated with an example of the escape of a Brownian particle across a multidimensional potential barrier. Our result is shown to provide a unified treatment of the whole range of frictional dissipation. For the case with an unknown equilibrium distribution a correction formula is derived. Its relative error decreases with decreasing noise intensity epsilon as epsilon-2, instead Of epsilon as is the case for the standard formulae. Our results generalize the known expressions for transition rates in a very natural way. Possible limitations of their validity are discussed, and a way to overcome them is proposed.