exponential kinetics is essentially an offshoot of a dynamic modification of the fluctuation-dissipation theorem appropriately carried over to a nonstationary regime. This nonequilibrium nature of activated process is reflected in the nonstationary kinetics that we derive here.

The non - exponential relaxation kinetics had been explored earlier in different occasions in relation to disordered systems$^{13}$, viscous liquids$^{19}$, oxygen binding to h$\mbox{\ae}$moglobin$^{16}$, where phenomenological fluctuating barrier models have been employed (barriers arising from the collective motions of many degrees of freedom). The present model although oversimplified in many respects captures the essential nature of influence of an initial non-thermal mode density distribution on the relaxation kinetics of the system.

**[VI.Conclusions]{}**

In conclusion, we consider a simple microscopic system-nonequilibrium bath model to simulate nonstationary thermally activated processes. The nonequilibrium bath is effectively realized in terms of a semi-infinite dimensional broad-band reservoir which is subsequently kept in contact with a thermal reservoir which allows the nonthermal bath to relax with a characteristic time. A systematic separation of timescales is then used to construct the appropriate Langevin equation for the particle, which is nonlinear and non-Markovian in character. Based on a strategy of Van Kampen’s expansion in $\epsilon \tau_{c}$ of the relevant physical quantity where $\epsilon$ is the strength and $\tau_{c}$ is the correlation time of fluctuations of the relaxing modes, we show that this Langevin equation can be recast into the form of a generalized Fokker-Planck equation, when the correlation time is short but finite. Adelman’s form of the Fokker-Planck equation \[ Eq.(8) \] as well as the standard Markovian description can be recovered in the appropriate limits. We now summarize the main conclusions of this study:

\(i) The model proposed here captures the essential features of Langevin dynami