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

TL;DR

This study explores how finite volume and thermal fluctuations influence the QCD critical end point using super statistics and non-extensive thermodynamics, revealing significant shifts in transition temperatures and critical point location.

Contribution

It introduces an analytic framework combining super statistics with the Linear Sigma Model to analyze volume and fluctuation effects on the QCD phase diagram.

Findings

Pseudo-critical temperature decreases by about 7% in small volumes.

Critical endpoint shifts to higher densities and lower temperatures by approximately 12%.

Results are robust against changes in out-of-equilibrium parameters.

Abstract

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 non-extensive 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 pseudo-critical 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 endpoint 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.