  Despite the viscosity of a fluid ranges over several orders of magnitudes and
is extremely sensitive to microscopic structure and molecular interactions, it
has been conjectured that its (opportunely normalized) minimum displays a
universal value which is experimentally approached in strongly coupled fluids
such as the quark-gluon plasma. At the same time, recent findings suggest that
hydrodynamics could serve as a universal attractor even when the deformation
gradients are large and that dissipative transport coefficients, such as
viscosity, could still display a universal behavior far-from-equilibrium.
Motivated by these observations, we consider the real-time dissipative dynamics
of several holographic models under large shear deformations. In all the cases
considered, we observe that at late time both the viscosity-entropy density
ratio and the dimensionless ratio between energy density and entropy density
approach a constant value. Whenever the shear rate in units of the energy
density is small at late time, these values coincide with the expectations from
near equilibrium hydrodynamics. Surprisingly, even when this is not the case,
and the system at late time is far from equilibrium, the viscosity-to-entropy
ratio approaches a constant which decreases monotonically with the
dimensionless shear rate and can be parametrically smaller than the
hydrodynamic result.
