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 = 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 = +/- 1/10 kT(H) approximate to +/- 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* approximate to 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.