Landauer conductance without two chemical potentials

We present a theory of the four-terminal conductance for the multichannel tunneling barrier, which is based on the self-consistent solution of Shr\"odinger, Poisson, and continuity equations. We derive results for the case of a barrier embedded in a long wire with and without disorder. We also recover known expressions for the conductance of the barrier placed into a ballistic constriction. Our approach avoids a problematic use of two chemical potentials in the same system.