  Using molecular dynamics simulations we compare the motion of a nano-swimmer
based on Purcell suggested motor with a time asymmetrical cycle with the motion
of the same molecular motor with a time symmetrical cycle. We show that Purcell
theorem still holds at the nanoscale, despite the local structure and the
medium fluctuations. Then, with the purpose of both orienting the swimmer
displacement and increasing the breakdown of the theorem, we study the effect
of an electric field on a polarized version of these swimmers. For small and
large fields, the time asymmetrical swimmer is more efficient, as suggested by
Purcell. However we find a field range for which Purcell theorem is broken for
the time symmetric motor. Results suggest that the breakdown of the theorem is
arising from the competition of the orientation field and Brownian forces,
while for larger fields the field destroys the effect of fluctuations restoring
the theorem.
