Volume effects on the QCD critical end point from thermal fluctuations within the super statistics framework

We investigate the impact of the finite volume and the thermal fluctuations on the critical end point of the QCD phase diagram. To do so, we implement the super statistics framework with gamma, F, and log-normal distributions and their relation with the Tsallis nonextensive thermodynamics. We compute an effective thermodynamic potential as a function of the inverse temperature fluctuations and explicit dependence on the system volume. To find an analytic expression for the effective potential, we expand the modified Boltzmann factor by using the equilibrium thermodynamic potential computed in the linear sigma model coupled to quarks. We find that the pseudocritical temperature of transition at vanishing baryon chemical potential is modified by the size of the system being about 7% lower for small volumes. Additionally, the critical end point moves to higher densities and lower temperatures (about 12% in both cases). Interestingly, the results are quantitatively the same when the parameter that models the out-of -equilibrium situation is modified, indicating that the chiral symmetry restoration is robust against the thermal fluctuations in this approximation.

Automated summary

This study investigates the impact of finite volume and thermal fluctuations on the critical end point of the QCD phase diagram. The results show that the temperature at the pseudocritical point decreases by about 7% for small volumes, and the critical end point shifts towards higher densities and lower temperatures by approximately 12%. Furthermore, the results indicate that chiral symmetry restoration is robust against thermal fluctuations in this approximation.