  The noise driven motion in a bistable potential acts as the archetypal model
of various physical phenomena. Here, we contrast the overdamped dynamics with
the full (underdamped) dynamics. For the overdamped particle driven by a
non-equilibrium, $\alpha$-stable noise the ratio of forward and backward
transition rates depends only on the width of a potential barrier separating
both minima. Using analytical and numerical methods, we show that in the regime
of full dynamics, contrary to the overdamped case, the ratio of transition
rates depends both on widths and heights of the potential barrier. The
analytical formula for the ratio of transition rates is corroborated by
extensive numerical simulations.
