  We consider the motion of a particle in a force field subjected to adiabatic,
fluctuations of external origin. We do not put the restriction on the type of
stochastic process that the noise is Gaussian. Based on a method developed
earlier by us [ J. Phys. A {\bf 31} (1998) 3937, 7301] we have derived the
equation of motion for probability distribution function for the particle on a
coarse-grained timescale $\Delta t$ assuming that it satisfies the separation
of timescales; $|\mu |^{-1} \ll \Delta t \ll \tau_c$, where $\tau_c$ is the
correlation time of fluctuations. $|\mu |^{-1}$ refers to the inverse of the
damping rate (or, the largest of the eigenvalues of the unperturbed system) and
sets the shortest timescale in the dynamics in contrast to the conventional
theory of fast fluctuations. The equation includes a third order noise term. We
solve the equation for a Kramers' type potential and show that although the
system is thermodynamically open, appropriate boundary conditions allow the
distinct steady states. Based on the exact solution of the third order equation
for the linearized potential and the condition for attainment of the steady
states we calculate the adiabatic noise-induced rate of escape of a particle
confined in a well. A typical variation of the escape rate as a function of
dissipation which is reminiscent of Kramers' turn-over problem, has been
demonstrated.
