  Following the basic prescriptions of the relativistic Tsallis' non-extensive
thermostatistics, we investigate from a phenomenological point of view the
relevance of non-extensive statistical effects on relativistic heavy-ion
collisions observable, such as rapidity spectra of net proton production,
transverse momentum distributions and transverse momentum fluctuations.
Moreover, we study the nuclear and the subnuclear equation of state,
investigating the critical densities of a phase transition to a
hadron-quark-gluon mixed phase by requiring the Gibbs conditions on the global
conservation of the electric and the baryon charges. The relevance of small
deviations from the standard extensive statistics is studied in the context of
intermediate and high energy heavy-ion collisions.
