Non extensive self-consistent thermodynamics

A well-known feature of High Energy Physics (HEP) experimental data is the power-law behavior of some of the distributions, as for instance the transverse momentum (pT) distribution. This behavior was not predicted by the Hagedorn self-consistent approach to the thermodynamical description of HEP data.
In recent years however it has been shown that using Tsallis distribution instead of Boltzmann distribution it is possible to get a non extensive version of Hagedorn self-consistent principle, resulting in power-law distributions that can describe well the available experimental data even at energies as high as those found at LHC.
In this talk a review of the Non Extensive Self-Consistent Thermodynamics is given, as well as the experimental verification of the predictions obtained through this theory. Recent developments will also be presented and some applications will be discussed. Finally, the possible origins of non extensivity in HEP will be discussed.