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Hydrodynamics predicts long-lived sound and shear waves. Thermal fluctuationsin these waves can lead to the diffusion of momentum density, contributing tothe shear viscosity and other transport coefficients. Within viscoushydrodynamics in 3+1 dimensions, this leads to a positive contribution to theshear viscosity, which is finite but inversely proportional to the microscopicshear viscosity. Therefore the effective infrared viscosity is bounded frombelow. The contribution to the second-order transport coefficient $\tau_\pi$ isdivergent, which means that second-order relativistic viscous hydrodynamics isinconsistent below some frequency scale. We estimate the importance of eacheffect for the Quark-Gluon Plasma, finding them to be minor if $\eta/s = 0.16$but important if $\eta/s = 0.08$.

The stickiness of sound: An absolute lower limit on viscosity and the breakdown of second order relativistic hydrodynamics