Power-law partition and entropy production of high-energy cosmic rays: Knee-ankle structure of the all-particle spectrum

Abstract

A statistical description of the all-particle cosmic-ray spectrum is given in the 10 14 eV to 10 20 eV interval. The high-energy cosmic-ray flux is modeled as an ultra-relativistic multicomponent plasma, whose components constitute a mixture of nearly ideal but nonthermal gases of low density and high temperature. Each plasma component is described by an ultra-relativistic power-law density manifested as spectral peak in the wideband fit. The "knee" and "ankle" features of the high-and ultra-high-energy spectrum turn out to be the global and local extrema of the double-logarithmic E 3-scaled flux representation in which the spectral fit is performed. The all-particle spectrum is covered by recent data sets from several air shower arrays, and can be modeled as three-component plasma in the indicated energy range extending over six decades. The temperature, specific number density, internal energy and entropy of each plasma component are extracted from the partial fluxes in the broadband fit. The grand partition function and the extensive entropy functional of a non-equilibrated gas mixture with power-law components are derived in phase space by ensemble averaging.