How much entropy is produced in strongly coupled Quark-Gluon Plasma (sQGP) by dissipative effects?

Abstract

We argue that estimates of dissipative effects based on the first-order hydrodynamics with shear viscosity are potentially misleading because higher order terms in the gradient expansion of the dissipative part of the stress tensor tend to reduce them. Using recently obtained sound dispersion relation in thermal $\cal N$=4 supersymmetric plasma, we calculate the $resummed$ effect of these high order terms for Bjorken expansion appropriate to RHIC/LHC collisions. A reduction of entropy production is found to be substantial, up to an order of magnitude.

Figures (3)

• Figure 1: Sound dispersion (real and imaginary parts) obtained from the analysis of quasinormal modes in the AdS black hole background. The result and figure are taken from Ref.KS.
• Figure 2: Entropy production as a function of proper time for initial time $\tau_0=0.2\,{\rm fm}$ (left) and $\tau_0=0.5\,{\rm fm}$ (right). The initial temperature $T_0=300\,{\rm MeV}$. The dashed (blue) curves correspond to the first order (shear) viscosity approximation Eq.(\ref{['s']}). The solid curve (red) is the all order dissipative resummation Eq.(\ref{['s1']}).
• Figure 3: Fraction of entropy produced during the hydro phase as a function of initial proper time. The initial temperature $T_0=300\,{\rm MeV}$. The left (blue) points correspond to the first order (shear) viscosity approximation. The right (red) points are for the all order resummation.