Entropy Production and Effective Viscosity in Heavy-Ion Collisions

Entropy production and an effective viscosity in central Au+Au collisions are estimated in a wide range of incident energies 3.3 GeV $\le \sqrt{s_{NN}}\le$ 39 GeV. The simulations are performed within a three-fluid model employing three different equations of state with and without deconfinement transition, which are equally good in reproduction of the momentum-integrated elliptic flow of charged particles in the considered energy range. It is found that more that 80\% entropy is prodused during a short early collision stage which lasts $\sim$1 fm/c at highest considered energies $\sqrt{s_{NN}}\ge$ 20 GeV. The estimated values of the viscosity-to-entropy ratio ($\eta/s$) are approximately the same in all considered scenarios. At final stages of the system expansion they range from $\sim$0.05 at highest considered energies to $\sim$0.5 lowest ones. It is found that the $\eta/s$ ratio decreases with the temperature ($T$) rise approximately as $\sim 1/T^4$ and exhibits a rather weak dependence on the net-baryon density.