  The aim of this paper is to investigate the effect of a non-extensive form of
statistical mechanics proposed by Tsallis on the formation of a quark-gluon
plasma (QGP). We suggest to account for the effects of the dominant part of the
{\itshape long-range} interactions among the constituents in the QGP by a
change in the statistics of the system in this phase, and we study the
relevance of this statistics for the phase transition. The results show that
small deviations ($\approx 10%$) from Boltzmann-Gibbs statistics in the QGP
produce a noticeable change in the phase diagram, which can, in principle, be
tested experimentally.
