Finite-Volume Non-extensive statistical in QCD phase

Abstract

Recently, some research has emerged that used the Tsallis statistics in Quantum Chromodynamics (QCD). In Tsallis statistics, the Tsallis parameter $\mathfrak{q}$ reflects long-range interactions, non-Markovian memory, and multifractal boundary effects, linking directly to temperature variance in fluctuating systems, which vanish in the Boltzmann-Gibbs limit. This is our motivation to investigate the thermodynamical variables of a hot and dense system. Within a non-extensive color QCD MIT-Bag Model and using the Tsallis distributions to describe the thermal response functions related to the equation of state. The study focuses on the deconfinement phase transition from a hadronic gas to a quark-gluon plasma in order to analyze the behavior of thermodynamical quantities of the system, such as the energy density, the pressure and the interaction measure at finite volume under Tsallis statistics. Furthermore, the effect of the $\mathfrak{q}$-parameter on the phase transition point is investigated. We find that the transition point is significantly affected by the $\mathfrak{q}$-parameter in the framework of non-extensive statistics.