Superstatistics in high energy physics: Application to cosmic ray energy spectra and e+e- annihilation

We work out a superstatistical description of high-energy scattering processes that takes into account temperature fluctuations in small volume elements. For Gamma-distributed fluctuations of the inverse temperature one effectively obtains formulas similar to those used in nonextensive statistical mechanics, whereas for other temperature distributions more general superstatistical models arise. We consider two main examples: Scattering processes of cosmic ray particles and e+e- annihilation processes. In both cases one obtains excellent fits of experimentally measured energy spectra and cross sections.