We investigate the dependence of the displacements of a molecular motor embedded inside a glassy material on its folding characteristic time τ f . We observe two different time regimes. For slow foldings (regime I) the diffusion evolves very slowly with τ f , while for rapid foldings (regime II) the diffusion increases strongly with τ f ( D ≈ τ −2 f ) suggesting two different physical mechanisms. We find that in regime I the motor's 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's 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's motion.

Using molecular dynamics simulations we investigate the finite size dependence of the dynamical properties of a diatomic supercooled liquid. The simplicity of the molecule permits us to access the microsecond time scale. We find that the relaxation time decreases simultaneously with the strength of cooperative motions when the size of the system decreases. While the decrease of the cooperative motions is in agreement with previous studies, the decrease of the relaxation time opposes what has been reported to date in monatomic glass-formers and in silica. This result suggests the presence of different competing physical mechanisms in the relaxation process. For very small box sizes the relaxation times behavior reverses itself and increases strongly when the box size decreases, thus leading to a non-monotonic behavior. This result is in qualitative agreement with defect and facilitation theories.

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