  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.
