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It is shown that the hydrodynamic modes of a dilute granular gas of inelastichard spheres can be identified, and calculated in the long wavelength limit.Assuming they dominate at long times, formal expressions for the Navier-Stokestransport coefficients are derived. They can be expressed in a form thatgeneralizes the Green-Kubo relations for molecular systems, and it is shownthat they can also be evaluated by means of $N$-particle simulation methods.The form of the hydrodynamic modes to zeroth order in the gradients is used todetect the presence of inherent velocity correlations in the homogeneouscooling state, even in the low density limit. They manifest themselves in thefluctuations of the total energy of the system. The theoretical predictions areshown to be in agreement with molecular dynamics simulations. Relevant relatedquestions deserving further attention are pointed out

Hydrodynamic modes, Green–Kubo relations, and velocity correlations in dilute granular gases