  We theoretically investigate how one can achieve a preferred rotational
direction for the case of a simple electrostatic motor. The motor is composed
by a rotor and two electronic reservoirs. Electronic islands on the rotor can
exchange electrons with the reservoirs. An electrostatic field exerts a force
on the occupied islands. The charge dynamics and the electrostatic field drive
rotations of the rotor. Coupling to an environment lead to damping on the
rotational degree of freedom. We use two different approaches to the charge
dynamics in the electronic islands: hopping process and mean-field. The hopping
process approach takes into account charge fluctuations, which can appear along
Coulomb blockade effects in nanoscale systems. The mean-field approach neglects
the charge fluctuations on the islands, which is typically suitable for larger
systems. We show that for a system described by the mean-field equations one
can in principle prepare initial conditions to obtain a desired rotational
direction. In contrast, this is not possible in the stochastic description.
However, for both cases one can achieve rotational directionality by changing
the geometry of the rotor. By scanning the space formed by the relevant
geometric parameters we find optimal geometries, while fixing the dissipation
and driving parameters. Remarkably, in the hopping process approach perfect
rotational directionality is possible for a large range of geometries.
