  We present a combined treatment of the non-equilibrium dynamics and transport
of electrons and phonons by carrying out \textit{ab initio} calculations of the
fully coupled electron and phonon Boltzmann transport equations. We find that
the presence of mutual drag between the two carriers causes the thermopower to
be enhanced and dominated by the transport of phonons, rather than electrons as
in the traditional semiconductor picture. Drag also strongly boosts the
intrinsic electron mobility, thermal conductivity and the Lorenz number.
Impurity scattering is seen to suppress the drag-enhancement of the thermal and
electrical conductivities, while having weak effects on the enhancement of the
Lorenz number and thermopower. We demonstrate these effects in \textit{n}-doped
3C-SiC at room temperature, and explain their origins. This work establishes
the roles of microscopic scattering mechanisms in the emergence of strong drag
effects in the transport of the interacting electron-phonon gas.
