  We argue that the ratio between the shear viscosity and the shear relaxation
time, $\eta/\tau_\pi$, should be defined as a thermodynamic quantity obtained
from the equal-time symmetric correlator of the shear-stress tensor. In kinetic
theory, we show that this ratio does not depend on the type of interaction.
Similarly, an exact expression for this ratio is obtained for holographic gauge
theories. We also determine how stochastic fluctuations change $\eta/\tau_\pi$
in transient relativistic hydrodynamics and show that thermal fluctuations do
not spoil causality and stability.
