Generalized Statistics and the Formation a Quark-Gluon Plasma

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.