Rates of Activated Processes with Fluctuating Barriers

We study the ultimate rate of relaxation to equilibrium, as defined by the appropriate master equation, in a bistable potential that is fluctuating in a stationary manner; we obtain results for both dichotomic and Gaussian barrier fluctuations, as a function of the correlation time characterizing the fluctuations. "Resonant activation," previously observed in specific model problems, is shown to be typical and to have a simple physical interpretation. In the slow fluctuation limit we find that the ultimate rate of relaxation—when it exists—differs from the inverse mean first passage time.