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In the framework of density functional theory a formalism to describeelectronic transport in the steady state is proposed which uses the density onthe junction and the {\em steady current} as basic variables. We prove that, ina finite window around zero bias, there is a one-to-one map between the basicvariables and both local potential on as well as bias across the junction. Theresulting Kohn-Sham system features two exchange-correlation (xc) potentials, alocal xc potential and an xc contribution to the bias. For weakly coupledjunctions the xc potentials exhibit steps in the density-current plane whichare shown to be crucial to describe the Coulomb blockade diamonds. At smallcurrents these steps emerge as the equilibrium xc discontinuity bifurcates. Theformalism is applied to a model benzene junction, finding perfect agreementwith the orthodox theory of Coulomb blockade.

Steady-State Density Functional Theory for Finite Bias Conductances