Generalized statistical mechanics of high energy scattering processes

Very  recently  we  have  applied q-generalized  statistical  mechanics  methods  to  high  energy scattering processes, which lie at the root of the production process of cosmic rays.
It  is  known  that  the Boltzmann-Gibbs  formalism  has  severe  restrictions:  It  is  not  valid  for nonequilibrium  systems,  it  is  not  valid  for  systems  with  long-range  interactions  (such  as gravity), and it is not valid for systems with a very small volume and fluctuating temperature (as  probed  in  scattering  processes  of  cosmic  ray  particles  at  very  high  energies).  For  these types  of  complex  systems  it  is  useful  to  generalize the  formalism  to  a  more  general  setting,
based  on  the  maximization  of  more  general  entropy  measures  which  contain  the  Shannon entropy as a special case.
In  this  talk  we  present  how  to  apply  these  techniques  borrowed  from  generalized  statistical mechanics to analyse the AMS-02 (the Alpha Magnetic Spectrometer) data sets. To conclude, we have shown  that  the  different  energy  dependences  of  the  spectral  indices  of  positron  and electron cosmic rays are well explained by a q-generalized Hagedorn theory.
Also  we  compare  our  ongoing  analysis  for  DAMPE(DArk  Matter  Particle  Explore) and CALET (The CALorimetric Electron Telescope), showing that they may be good candidates to  keep  investigating  high  energy  scattering  processes  by  using  generalized  statistical mechanics.