An approach to the study of the thermally driven deconfinement phase transition in a finite volume through the order parameter, its derivatives, and cumulants of the probability distribution

We describe the temperature driven deconfining phase transition between hadronic and quark-gluon plasma (QGP) phases coexisting in a finite volume by means of a probability distribution using a simple thermodynamic model. The equations of state of both phases are calculated, where the colour singletness requirement is considered for the QGP phase with massless up and down quarks. We emphasize in this work the probability distribution and try to deeply analyze it to extract information about the transition. Also, the mean values of some response functions, which are mainly the order parameter, its three first thermal derivatives, and the second, third, and fourth cumulants of the probability distribution, are calculated and their behavior with temperature at vanishing chemical potential and at different volumes is examined. The striking result is the large similarity noted between the behavior of the order parameter derivatives and that of their homologous cumulants of the probability density. This similarity is worked out, and particularly the linearity between the thermal susceptibility and the variance is probed.