Fluxes of cosmic rays: A delicately balanced stationary state

The analysis of cosmic rays fluxes as a function of energy reveals a {\it knee} slightly below ${10}^{16}$ eV and an {\it ankle} close to ${10}^{19}$ eV. Their physical origins remain up to now quite enigmatic; in particular, no elementary process is known which occurs at energies close to ${10}^{16}$ 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 ($\simeq {10}^9$ eV). This opens the door to an unexpected standpoint for further clarifying the phenomenon.