Comment on "Brownian motion of droplets induced by thermal noise"

We simulate phase separated fluids using the Cahn-Hillard fluctuating hydrodynamic (CH-FHD) model and measure the statistical properties of capillary waves generated by thermal fluctuations. Our measurements are in good agreement with stochastic lubrication theory and molecular dynamics simulations but differ significantly from recent CH-FHD results by Zhang et al. (Phys. Rev. E 109 024208 (2024)). Specifically, we find that capillary wave statistics at thermodynamic equilibrium are independent of transport properties, namely viscosity and species diffusion.