Ultrarelativistic generalized Lorentzian thermodynamics and the differential cosmic ray energy flux

We apply the ultrarelativistic generalized Lorentzian quasi-equilibrium thermodynamic energy distribution to the energy spectrum of galactic cosmic ray fluxes. The inferred power law slopes contain a component which evolves with cosmic ray energy in steps of thirds, resembling the sequence of structure functions in fully developed Kolmogorov turbulence. Within the generalized thermodynamics the chemical potential can be estimated from the deviation of the fluxes at decreasing energy. Both may throw some light on the cosmic ray acceleration mechanism to very high energies.