Cosmic ray energy spectra exhibit power law distributions over many orders of magnitude that are very well described by the predictions of q -generalized statistical mechanics , based on a q -generalized Hagedorn theory for transverse momentum spectra and hard QCD scattering processes .
QCD at largest center of mass energies predicts the entropic index to be q = \frac { 13 } { 11 } .
Here we show that the escort duality of the nonextensive thermodynamic formalism predicts an energy split of effective temperature given by \Delta kT = \pm \frac { 1 } { 10 } kT _ { H } \approx \pm 18 MeV , where T _ { H } is the Hagedorn temperature .
We carefully analyse the measured data of the AMS-02 collaboration and provide evidence that the predicted temperature split is indeed observed , leading to a different energy dependence of the e ^ { + } and e ^ { - } spectral indices .
We also observe a distinguished energy scale E ^ { * } \approx 50 GeV where the e ^ { + } and e ^ { - } spectral indices differ the most .
Linear combinations of the escort and non-escort q -generalized canonical distributions yield excellent agreement with the measured AMS-02 data in the entire energy range .