  We have explored a simple microscopic model to simulate a thermally activated
rate process where the associated bath which comprises a set of relaxing modes
is not in an equilibrium state. The model captures some of the essential
features of non-Markovian Langevin dynamics with a fluctuating barrier. Making
use of the Fokker-Planck description we calculate the barrier dynamics in the
steady state and non-stationary regimes. The Kramers-Grote-Hynes reactive
frequency has been computed in closed form in the steady state to illustrate
the strong dependence of the dynamic coupling of the system with the relaxing
modes. The influence of nonequilibrium excitation of the bath modes and its
relaxation on the kinetics of activation of the system mode is demonstrated. We
derive the dressed time-dependent Kramers rate in the nonstationary regime in
closed analytical form which exhibits strong non-exponential relaxation
kinetics of the reaction co-ordinate. The feature can be identified as a
typical non-Markovian dynamical effect.
