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Fluxes of cosmic rays: A delicately balanced anomalous stationary state

By Constantino Tsallis, Joao C. Anjos and Ernesto P. Borges


The analysis of cosmic rays fluxes reveals a knee slightly below 1016 eV and an ankle close to 1019 eV. Their physical origins remain up to now quite enigmatic, essentially because no elementary process is known which occurs at energies close to 1016 eV. We propose a phenomenological approach along the lines of nonextensive statistical mechanics, a formalism which contains Boltzmann-Gibbs statistical mechanics as a particular case. The knee then appears as a crossover between two fractal-like thermal regimes, the crossover being caused by process occurring at energies ten million times lower than that of the knee, in the region of the quark hadron transition ( ≃ 109 eV). This opens the door to an unexpected standpoint for further clarifying the phenomenon

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