Dynamics of Dilute Gases at Equilibrium: From the Atomistic Description to Fluctuating Hydrodynamics

We derive linear fluctuating hydrodynamics as the low density limit of a deterministic system of particles at equilibrium. The proof builds upon the results of Bodineau et al. (Long-time correlations for a hard-sphere gas at equilibrium, 2022) where the asymptotics of the covariance of the fluctuation field is obtained, and on the proof of the Wick rule for the fluctuation field in Bodineau et al. (Long-time derivation at equilibrium of the fluctuating Boltzmann equation, 2022).