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