  We show that the Landauer multi-terminal formula for the conductance of a
nanoscale system is incomplete because it does not take into account many-body
effects which cannot be treated as contributions to the single-particle
transmission probabilities. We show that the physical origin of these effects
is related to the viscous nature of the electron liquid, and develop a
perturbative formalism, based on the time-dependent current-density-functional
theory, for calculating the corrections to the resistance in terms of the
``Kohn-Sham current distribution'' and the exchange-correlation kernel. The
difficulties that still remain in calculating the latter are critically
discussed.
