The present study explores how the quadratic form of the Generalized Uncertainty Principle (GUP) modifies the thermodynamic and transport properties of an ideal Quark–Gluon Plasma (QGP). By incorporating GUP-induced minimal length effects into the statistical framework, we analyze the behavior of the entropy density, the speed of sound, and the ratio between bulk and shear viscosities. Our findings show that, in the limit of a vanishing deformation parameter ( \(\varvec{\beta \rightarrow 0}\) ), the standard results for an ideal gas of massless, noninteracting particles are naturally recovered: the entropy scales as \(\varvec{s \propto T^3}\) , the squared speed of sound approaches \(\varvec{c_s^2 = 1/3}\) , and the bulk viscosity tends to zero. However, when GUP corrections become significant at high temperatures, the thermodynamic response of the plasma changes markedly. The modified dispersion relations lead to a reduction in the speed of sound, approaching \(\varvec{c_s^2 \simeq 1/5}\) in the asymptotic regime, while the bulk-to-shear viscosity ratio increases according to \(\varvec{\zeta /\eta \propto \beta ^2 T^4}\) . These results suggest that the quadratic GUP introduces an intrinsic quantum-gravitational scale that explicitly breaks conformal symmetry in the QGP and could imprint observable signatures in the high-temperature phase of strongly interacting matter.
