Analytic theory of extrema. IV. Relaxation from metastable and unstable states

The exact and asymptotic results for mean first passage times of master equation processes obtained in the companion paper are here applied to the study of relaxation times from metastable and unstable states. It is shown that the use of a master equation necessarily leads to an exponential system size dependence of the relaxation time from a metastable state. It is also a general consequence of the structure of the master equation that the relaxation from an unstable state occurs on a much shorter time scale than from a metastable state.