  We consider a system-reservoir model where the reservoir is modulated by an
external noise. Both the internal noise of the reservoir and the external noise
are stationary, Gaussian and are characterized by arbitrary decaying
correlation functions. Based on a relation between the dissipation of the
system and the response function of the reservoir driven by external noise we
numerically examine the model using a full bistable potential to show that one
can recover the turn-over features of the usual Kramers' dynamics when the
external noise modulates the reservoir rather than the system directly. We
derive the generalized Kramers' rate for this nonequilibrium open system. The
theoretical results are verified by numerical simulation.
