Shear viscosity and out of equilibrium dynamics

TL;DR

This paper derives a second-order shear viscosity coefficient for out-of-equilibrium gluon matter using Grad's method and compares hydrodynamic and microscopic transport results, revealing the limits of hydrodynamics at different coupling strengths.

Contribution

The paper provides a new calculation of shear viscosity in out-of-equilibrium conditions and compares it with microscopic transport, highlighting the validity range of second-order hydrodynamics.

Findings

Shear viscosity to entropy density ratio $\, ext{η/s} \,$ is about 20% larger than Navier-Stokes at $\, ext{α}_s \,\, ext{~0.3}

At small coupling $\, ext{α}_s \,\, ext{~0.01}$, $\, ext{η/s} \,$ is 2-3 times larger

Hydrodynamics agrees with microscopic results except at very small $\, ext{α}_s \,",

Abstract

Using Grad's method, we calculate the entropy production and derive a formula for the second-order shear viscosity coefficient in a one-dimensionally expanding particle system, which can also be considered out of chemical equilibrium. For a one-dimensional expansion of gluon matter with Bjorken boost invariance, the shear tensor and the shear viscosity to entropy density ratio $\eta/s$ are numerically calculated by an iterative and self-consistent prescription within the second-order Israel-Stewart hydrodynamics and by a microscopic parton cascade transport theory. Compared with $\eta/s$ obtained using the Navier-Stokes approximation, the present result is about 20% larger at a QCD coupling $\alpha_s \sim 0.3$(with $\eta/s\approx 0.18$) and is a factor of 2-3 larger at a small coupling $\alpha_s \sim 0.01$. We demonstrate an agreement between the viscous hydrodynamic calculations and the microscopic transport results on $\eta/s$, except when employing a small $\alpha_s$. On the other hand, we demonstrate that for such small $\alpha_s$, the gluon system is far from kinetic and chemical equilibrium, which indicates the break down of second-order hydrodynamics because of the strong noneqilibrium evolution. In addition, for large $\alpha_s$ ($0.3-0.6$), the Israel-Stewart hydrodynamics formally breaks down at large momentum $p_T\gtrsim 3$ GeV but is still a reasonably good approximation.