  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.
