  A new formalism to describe steady-state electronic and thermal transport in
the framework of density functional theory is presented. A one-to-one
correspondence is proven between the three basic variables of the theory, i.e.,
the density on as well as the electrical and heat currents through the
junction, and the three basic potentials, i.e., the local potential in as well
as the DC bias and thermal gradient across the junction. Consequently, the
Kohn-Sham system of the theory requires three exchange-correlations potentials.
In linear response, the new formalism leads to exact expressions for the
many-body transport coefficients (both electrical and thermal conductances and
Seebeck coefficient) in terms of both the corresponding Kohn-Sham coefficients
and derivatives of the exchange-correlations potentials. The theory is applied
to the Single Impurity Anderson Model, and an accurate analytic parametrization
for these derivatives in the Coulomb blockade regime is constructed through
reverse engineering.
