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

TL;DR

This paper investigates how the generalized uncertainty principle (GUP) influences thermodynamic properties and viscosity ratios of an ideal Quark Gluon Plasma, revealing deviations from standard behavior at high temperatures.

Contribution

It provides the first analysis of GUP effects on entropy, speed of sound, and viscosity ratios in an ideal QGP, highlighting scale introduction and conformal invariance breaking.

Findings

Speed of sound approaches 1/3 as GUP parameter tends to zero.

At high temperature, speed of sound approaches 1/4.

Bulk to shear viscosity ratio tends to 5/48 at high temperature.

Abstract

In this work we compute the entropy density, speed of sound, and the resulting impact on the bulk viscosity to shear viscosity ratio of an ideal Quark Gluon Plasma when the effects of a generalized uncertainty principle are taken into consideration. When the parameter of the generalized uncertainty principle tends to zero, i.e., $\alpha \rightarrow 0$, we obtain the value of the 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 bulk viscosity $\zeta \rightarrow 0$ when $\alpha \rightarrow 0$. In addition, in the high temperature limit, i.e., $T\rightarrow \infty$, the speed of sound satisfies the equation $c^{2}_{s}\rightarrow 1/4$. The consequence this has on the bulk viscosity is that in the high temperature limit, the ratio of the bulk to shear viscosity $\zeta/\eta \rightarrow 5/48$. Our results suggest that the GUP introduces a scale into the system breaking the a priori conformal invariance of a system of massless noninteracting particles.