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

We confirm and expand on work by Chafin and Schaefer 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. Re-analyzing 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> 0.3 from Chafin and Schaefer and the quantum Monte Carlo results \eta/n<0.2$ from Wlazlowski et al. near the critical temperature