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 observables, such as rapidity spectra of the 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-quarkgluon 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.
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