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 a generalized statistical mechanics of Tsallis type, 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.