Shear viscosity and out of equilibrium dynamics

Understand

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 $\alpha_s$.