Entropy production in high-energy heavy-ion collisions and the correlation of shear viscosity and thermalization time

We study entropy production in the early stage of high-energy heavy-ion collisions due to shear viscosity. We employ the second-order theory of Israel-Stewart with two different stress relaxation times, as appropriate for strong coupling or for a Boltzmann gas, respectively, and compare the hydrodynamic evolution. Based on the present knowledge of initial particle production, we argue that entropy production is tightly constrained. We derive new limits on the shear viscosity to entropy density ratio eta/s, independent from elliptic flow effects, and determine the corresponding Reynolds number. Furthermore, we show that for a given entropy production bound, the initial time tau(0) for hydrodynamics is correlated to the viscosity. The conjectured lower bound for eta/s provides a lower limit for tau(0).