Entropy production and effective viscosity in heavy-ion collisions

The entropy production and an effective viscosity in central Au+Au collisions are estimated in a wide range of incident energies 3.3 GeV ≤sNN≤\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\le \sqrt{s_{NN}}\le$\end{document} 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 the reproduction of the momentum-integrated elliptic flow of charged particles in the considered energy range. It is found that more than 80% entropy is produced during a short early collision stage which lasts ∼ 1 fm/c at the highest considered energies sNN≳20\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\sqrt{s_{NN}}\gtrsim 20$\end{document} GeV. The estimated values of the viscosity-to-entropy ratio (η\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\eta$\end{document}/s) are approximately the same in all considered scenarios. At the final stages of the system expansion they range from ∼ 0.05 at the highest considered energies to ∼ 0.5 at the lowest ones. It is found that the η\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\eta$\end{document}/s ratio decreases with the temperature (T) rise, approximately as ∼1/T4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\sim 1/T^{4}$\end{document}, and exhibits a rather weak dependence on the net-baryon density.