  We study transport properties of weakly interacting one-dimensional electron
systems including on an equal footing thermal equilibration due to
three-particle collisions and the effects of large-scale inhomogeneities. We
show that equilibration in an inhomogeneous quantum wire is characterized by
the competition of interaction processes which reduce the electrons total
momentum and such which change the number of right- and left-moving electrons.
We find that the combined effect of interactions and inhomogeneities can
dramatically increase the resistance of the wire. In addition, we find that the
interactions strongly affect the thermoelectric properties of inhomogeneous
wires and calculate their thermal conductance, thermopower, and Peltier
coefficient.
