By means of an effective relativistic nuclear equation of state in the framework of the nonextensive statistical mechanics, characterized by power-law quantum distributions, we study the phase transition from hadronic matter to quark-gluon plasma at finite temperature and baryon density. The analysis is performed by requiring the Gibbs conditions on the global conservation of baryon number, electric charge fraction and zero net strangeness. We show that nonextensive statistical effects strongly influence the strangeness production during the pure hadronic phase and the hadron-quark-gluon mixed phase transition, also for small deviations from the standard Boltzmann-Gibbs statistics.
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