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

Abstract

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 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, that the initial time ${\tau }_0$ for hydrodynamics is correlated to the viscosity. The conjectured lower bound for $\eta /s$ provides a lower limit for ${\tau }_0$.

10 pages, 10 figures, Text updated, references added, two new figures added, normalization in Fig.1 corrected, final version to be published in PRC

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