  We study the generic problem of the escape of a classical particle over a
fluctuating barrier under the influence of non-Gaussian noise mimicking the
effects of not-fully equilibrated bath. Our attention focuses on the effect of
the stable noises on the mean escape time and on the phenomenon of resonant
activation (RA). Possible physical interpretation of the occurrence of L\'evy
noises in the system of interest is discussed and the connection between the
Tsallis statistics and the Fractional Fokker Planck Equation is addressed.
