We study thermoelectric transport through a coherent molecular conductor connected to two electron and two phonon baths using the nonequilibrium Greens function method. We focus on the mutual drag between electron and phonon transport as a result of `momentum transfer, which happens only when there are at least two phonon degrees of freedom. After deriving expressions for the linear drag coefficients, obeying the Onsager relation, we further investigate their effect on nonequilibrium transport. We show that the drag effect is closely related to two other phenomena: (1) adiabatic charge pumping through a coherent conductor; (2) the current-induced nonconservative and effective magnetic forces on phonons.
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