Nonextensive methods in turbulence and particle physics

We describe some recent applications of Tsallis statistics in fully developed hydrodynamic turbulence and in 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→∞, one obtains (under certain assumptions) possible evidence for the existence of six compactified dimensions, as predicted by superstring theory.