How much entropy is produced in strongly coupled quark-gluon plasma (sQGP) by dissipative effects?

We argue that estimates of dissipative effects based on 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 relations in thermal $\mathcal{N}=4$ supersymmetric plasma, we calculate the resummed effect of these high-order terms for Bjorken expansion appropriate to heavy ion collisions such as those performed at the BNL Relativistic Heavy Ion Collider (RHIC) and the CERN Large Hadron Collider (LHC). A reduction of entropy production is found to be substantial, up to an order of magnitude.