  The local-equilibrium approach to transport processes is related to the
approach based on time-dependent correlation functions and their associated
spectral functions characterizing the equilibrium fluctuations of particle,
momentum and other densities. On the one hand, the transport coefficients are
calculated with the Einstein-Helfand formulas derived in the local-equilibrium
approach. On the other hand, the poles of the spectral functions at complex
frequencies give the damping rates of the hydrodynamic modes. Since these rates
also depend on the transport coefficients, their values can be compared to the
predictions of the local-equilibrium approach. This comparison is
systematically carried out for the hard-sphere fluid by computing numerically
the transport coefficients, the spectral functions, and their poles as a
function of the wave number in the hydrodynamic limit. The study shows the
consistency between the two approaches for the determination of the transport
properties.
