Comment on "Ratchet universality in the presence of thermal noise"

TL;DR

This paper critically examines claims of a universal optimal force waveform for directed transport in ratchet systems, providing numerical evidence that challenges previous conjectures and supports existing theories within their validity regimes.

Contribution

It offers a detailed numerical analysis demonstrating the non-existence of a universal waveform and clarifies the conditions under which previous theories remain valid.

Findings

No universal optimal force waveform exists.

Previous theories accurately predict the waveform in their validity regime.

The conjecture of universality is shown to be incorrect.

Abstract

A recent paper [Phys. Rev. E 87, 062114 (2013)] presents numerical simulations on a system exhibiting directed ratchet transport of a driven overdamped Brownian particle subjected to a spatially periodic, symmetric potential. The authors claim that their simulations prove the existence of a universal waveform of the external force which optimally enhances directed transport, hence confirming the validity of a previous conjecture put forward by one of them in the limit of vanishing noise intensity. With minor corrections due to noise, the conjecture holds even in the presence of noise, according to the authors. On the basis of their results the authors claim that all previous theories, which predict a different optimal force waveform, are incorrect. In this comment we provide sufficient numerical evidence showing that there is no such universal force waveform and that the evidence obtained by the authors otherwise is due to a fortunate choice of the parameters. Our simulations also suggest that previous theories correctly predict the shape of the optimal waveform within their validity regime, namely when the forcing is weak. On the contrary, the aforementioned conjecture is shown to be wrong.