Temperature dependence of the violation of Purcell's theorem experienced by a folding molecular motor

We investigate the violation of Purcell's scallop theorem experienced by a mono-molecular motor, successively folding and unfolding inside a soft matter environment due to an external stimulus. We find a breakdown of the Purcell theorem due to fluctuations, that permits the molecular motor's efficient motion. The diffusion of the motor, its efficiency and its elementary displacement strongly depend on the characteristic time of the folding, but only slightly on the temperature. The increase of the motor's efficiency when the folding characteristic time τ decreases agrees with the fluctuation theorem expectation as the entropy generated inside the medium increases. The constant efficiency with respect to temperature is more difficult to understand as it suggests a generated entropy independent of temperature. In contrast with these results, the diffusion of the medium induced by the motor's folding strongly depends on the temperature, but doesn't depend on the characteristic time of the folding. That result suggests that the medium's diffusion is not due to the motor's displacement. We find that cooperative motions known as dynamic heterogeneity depend significantly on both temperature and folding time, leading in some conditions to a decoupling between dynamic heterogeneity and the medium's diffusion. Eventually, we find that the cooperative motions induced by the folding are larger when the motor cannot move.