A Switching-Function Approach to Parametrizing the Temperature-Driven Deconfinement Phase Transition, at Zero Chemical Potential, in a Finite Volume

In this work, we investigate the temperature-driven deconfinement phase transition for a strongly interacting system in a finite volume, at zero chemical potential. The transition is described from a low-temperature hadronic gas phase consisting of pions to a high-temperature quark–gluon plasma phase with 2+1 quark flavors. To model the occurring transition, we use a phenomenological switching-function approach, which continuously interpolates between the hadronic gas and quark–gluon plasma phases around the transition temperature. The pressure of the mixed system is constructed as a weighted combination of the partial pressures of the two phases, while the energy density is obtained through the standard thermodynamic relation involving the entropy density. From these quantities, we determine the squared speed of sound, cs² = ∂P/∂e, which provides an important measure of the dynamical response of the medium across the transition region. The model parameters, including the transition temperature, the width of the transition region and the bag constant, are chosen to describe the thermal evolution of the system and to reproduce the smooth crossover behavior observed in finite systems, since finite-size effects are known to smooth out the sharp behavior expected in the thermodynamic limit. The obtained temperature dependence of the studied physical quantities is compared with lattice QCD results for (2+1) quark flavors. The comparison shows good qualitative agreement, and the obtained results indicate that the switching-function model provides a simple and effective framework for parametrizing the deconfinement phase transition in a finite volume and for describing the thermodynamic behavior of strongly interacting matter.