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

A recent paper [P. J. Martínez and R. Chacón, 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 that optimally enhances directed transport, hence confirming the validity of a previous conjecture put forth 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 their particular choice of 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 does not hold.