  We investigate the dependence of the displacements of a molecular motor
embedded inside a glassy material on its folding characteristic time. We
observe two different time regimes. For slow foldings (regime I) the diffusion
evolves very slowly with the folding time, while for rapid foldings (regime II)
the diffusion increases strongly with the folding time suggesting two different
physical mechanisms. We find that in regime I the motor displacement during the
folding process is counteracted by a reverse displacement during the unfolding,
while in regime II this counteraction is much weaker. We notice that regime I
behavior is reminiscent of the scallop theorem that holds for larger motors in
a continuous medium. We find that the difference in the efficiency of the motor
motion explains most of the observed difference between the two regimes. For
fast foldings the motor trajectories differ significantly from the opposite
trajectories induced by the following unfolding process, resulting in a more
efficient global motion than for slow foldings. This result agrees with the
fluctuation theorems expectation for time reversal mechanisms. In agreement
with the fluctuation theorems we find that the motors are unexpectedly more
efficient when they are generating more entropy, a result that can be used to
increase dramatically the motor motion.
