  We describe some recent applications of Tsallis statistics in fully developed
hydrodynamic turbulence and high energy physics. For many of these applications
nonextensive properties arise from spatial fluctuations of the temperature or
the energy dissipation rate. The entropic index q is related to the relative
magnitude of these fluctuations. We concentrate on a recently derived formula
for the energy dependence of q that is experimentally verified by fits of cross
sections in e+e- annihilation experiments. Evaluating this formula for much
smaller energies E of the order of the recombination temperature, one obtains
the correct order of magnitude of the fluctuations of the cosmic microwave
background. Evaluating it for E going to infinity, one obtains (under certain
assumptions) possible evidence for the existence of 6 compactified dimensions,
as predicted by superstring theory.
