  We provide evidence that the small-scale statistics of the acceleration of a
test particle in high-Reynolds number Lagrangian turbulence is correctly
described by Tsallis statistics with entropic index q=3/2. We present
theoretical arguments why Tsallis statistics can naturally arise in Lagrangian
turbulence and why at the smallest scales q=3/2 is relevant. A generalized
Heisenberg-Yaglom formula is derived from the nonextensive model.
