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We show that the Landauer multi-terminal formula for the conductance of ananoscale system is incomplete because it does not take into account many-bodyeffects which cannot be treated as contributions to the single-particletransmission probabilities. We show that the physical origin of these effectsis related to the viscous nature of the electron liquid, and develop aperturbative formalism, based on the time-dependent current-density-functionaltheory, for calculating the corrections to the resistance in terms of the``Kohn-Sham current distribution'' and the exchange-correlation kernel. Thedifficulties that still remain in calculating the latter are criticallydiscussed.

Incompleteness of the Landauer Formula for Electronic Transport