The differential cosmic ray energy flux in the light of an ultrarelativistic generalized Lorentzian thermodynamics

The ultrarelativistic generalized Lorentzian quasi-equilibrium thermodynamic energy distribution is tentatively applied to the energy spectrum of galactic cosmic ray fluxes. It is found that 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 is estimated from the deviation of the fluxes at decreasing energy, presumably throwing light on the cosmic ray acceleration mechanism. A relation between involved turbulent volumina and structure functions is obtained. The conclusions drawn hold only within the realm of applicability of thermodynamics to cosmic ray spectra.