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The local-equilibrium approach to transport processes is related to theapproach based on time-dependent correlation functions and their associatedspectral functions characterizing the equilibrium fluctuations of particle,momentum and other densities. On the one hand, the transport coefficients arecalculated with the Einstein-Helfand formulas derived in the local-equilibriumapproach. On the other hand, the poles of the spectral functions at complexfrequencies give the damping rates of the hydrodynamic modes. Since these ratesalso depend on the transport coefficients, their values can be compared to thepredictions of the local-equilibrium approach. This comparison issystematically carried out for the hard-sphere fluid by computing numericallythe transport coefficients, the spectral functions, and their poles as afunction of the wave number in the hydrodynamic limit. The study shows theconsistency between the two approaches for the determination of the transportproperties.

Poles of hydrodynamic spectral functions and Einstein-Helfand formulas for transport coefficients