  Transport of overdamped particles in an asymmetrically periodic potential is
investigated in the presence of L\'{e}vy noise and ac-driving forces. The group
velocity is used to measure the transport driven by the nonthermal noise. It is
found that the L\'{e}vy flights and ac-driving forces are the two different
driving factors that can break thermodynamical equilibrium. The competition
between the two factors will induce some peculiar phenomena. For example,
multiple transport reversals occur on changing the noise intensity.
Additionally, we also find that the group velocity as a function of L\'{e}vy
index is nonmonotonic for small values of the noise intensity.

Statistical Mechanics