Implications of hydrodynamic fluctuations for the minimum shear viscosity of the dilute Fermi gas at unitarity

We confirm and expand on work by Chafin and Schafer [Phys. Rev. A 87, 023629 (2013)] on hydrodynamic fluctuations in the unitary Fermi gas. Using the result for the equation of state from a recent MIT experiment, we derive lower bounds for eta/n and eta/s as a function of temperature. Reanalyzing recent quantum Monte Carlo data for the shear-viscosity spectral function, we point out a possible resolution for the tension between the viscosity bound eta/n greater than or similar to 0.3 from Chafin and Schafer and the quantum Monte Carlo results eta/n less than or similar to 0.2 from Wlazlowski, Magierski, and Drut [Phys. Rev. Lett. 109, 020406 (2012)] near the critical temperature.