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In this work we compute the entropy density, speed of sound, and theresulting impact on the bulk viscosity to shear viscosity ratio of an idealQuark Gluon Plasma when the effects of a generalized uncertainty principle aretaken into consideration. When the parameter of the generalized uncertaintyprinciple tends to zero, i.e., $\alpha \rightarrow 0$, we obtain the value ofthe speed of sound for the ideal gas of massless particles, i.e.,$c^{2}_{s}\rightarrow 1/3$, and we recover the expected result that the bulkviscosity $\zeta \rightarrow 0$ when $\alpha \rightarrow 0$. In addition, inthe high temperature limit, i.e., $T\rightarrow \infty$, the speed of soundsatisfies the equation $c^{2}_{s}\rightarrow 1/4$. The consequence this has onthe bulk viscosity is that in the high temperature limit, the ratio of the bulkto shear viscosity $\zeta/\eta \rightarrow 5/48$. Our results suggest that theGUP introduces a scale into the system breaking the a priori conformalinvariance of a system of massless noninteracting particles.

Effect of the GUP on the Entropy, Speed of Sound, and Bulk to Shear Viscosity Ratio of an ideal QGP