Nonextensive methods in turbulence and particle physics

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.