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

Ultrarelativistic generalized Lorentzian thermodynamics and the differential cosmic ray energy flux