  We present a theory of molecular motors based on the Ehrenfest dynamics for
the nuclear coordinates and the adiabatic limit of the Kadanoff-Baym equations
for the current-induced forces. Electron-electron interactions can be
systematically included through many-body perturbation theory, making the
nonequilibrium Green's functions formulation suitable for first-principles
treatments of realistic junctions. The method is benchmarked against
simulations via real-time Kadanoff-Baym equations, finding an excellent
agreement. Results on a paradigmatic model of molecular motor show that
correlations can change dramatically the physical scenario by, e.g. introducing
a sizable damping in the self-sustained van der Pol oscillations.
