  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.
