  Stochastic evolution of various dynamic systems and reaction networks is
commonly described in terms of noise assisted escape of an overdamped particle
from a potential well, as devised by the paradigmatic Langevin equation in
which additive Gaussian stochastic force reproduces effects of thermal
fluctuations from the reservoir. When implemented for systems close to
equilibrium, the approach correctly explains emergence of Boltzmann
distribution for the ensemble of trajectories generated by Langevin equation
and relates intensity of the noise strength to the mobility.
  This scenario can be further generalized to include effects of non-Gaussian,
burst-like forcing modeled by L\'evy noise. In this case however, the pulsatile
additive noise cannot be treated as the internal (thermal), since the relation
between the strength of the friction and variance of the noise is violated.
  Heavy tails of L\'evy noise distributions not only facilitate escape
kinetics, but more importantly, change the escape protocol by altering final
stationary state to a non-Boltzmann, non-equilibrium form. As a result,
  contrary to the kinetics induced by a Gaussian white noise, escape rates in
environments with L\'evy noise are determined not by the barrier height, but
instead, by the barrier width.
  We further discuss consequences of simultaneous action of thermal and L\'evy
noises on statistics of passage times and population of reactants in
double-well potentials.
