1. Theoretical framework of Tsallis entropy and its non-extensive
statistics is introduced as well as the q−probability distribution.
With respect to its self-referential problem we firstly add one more
constraint and generalize the corresponding ensemble theory. Modified
q-BED and q-FDD are then well set-up.
2. Tsallis’ particle-hole symmetry breaks for its q-exponential
functions. Two deformed distributions are proposed and well satisfy it.
Furthermore, κ−exponential in Kaniadakis statistics is investigated as
a better solution.
3. The p_T spectra are well fitted with non-extensive distributions for
not pp but also AA collisions. The fitting parameters are not
independent at all, and their connections are nicely built up in our
models.