Nonextensive Statistical Mechanics

226 7 Thermodynamical and Nonthermodynamical Applications10 410 110 –210 –5[≈1 particle/(m 2 s)]Flux50004000300020001000Flux [m 2 sr s Gev] −110 –810 –1110 –1410 –1701/β = 1.67 10 8 eV KneeA = 3.0 10 −13 [≈1 particle/(m 2 year)]0 2 4 6 8Energy [GeV]Boltzmann−Gibbs[E crossover = 8.32 10 15 ]10 –2010 –2310 –26q = 1.2251/β q = 9.615 10 7 eVq′ = 1.1851/β q′ = 1.562 10 9 eVA = 5.3 10 −13Ankle[≈1 particle/(km 2 year)]10 –2910 8 10 9 10 10 10 11 10 12 10 13 10 14 10 15 10 16 10 17 10 18 10 19 10 20 10 21Energy [eV]Fig. 7.4 Fluxes of cosmic rays. The red curve comes from a crossover statistics (see [415]).Fig. 7.5 Experimental tests, with data of scattering of pions by various nuclei ( 4 He, 12 C, 16 Oand 40 Ca), of the theoretically allowed bands (grey regions) of the angular entropy (S θ )andtheangle-momentum entropy (S L )forq = 1, q = 0.75, and q = 1.5 (from [418]).