Reply to "Comment on `Directed motion of spheres by unbiased driving forces in viscous fluids beyond the Stokes' law regime' "

TL;DR

This paper defends the authors' previous work on directed motion in viscous fluids, clarifying misunderstandings and invalidating criticisms that misrepresent the formalism and its predictions, reaffirming the validity of their original findings.

Contribution

The authors refute criticisms by clarifying misunderstandings and demonstrating the correctness of their original formalism and results in the context of viscous fluid motion.

Findings

The original paper is free of mistakes.

Criticisms are based on misunderstandings and incorrect equations.

The formalism remains valid despite criticisms.

Abstract

We refute the criticism expressed in a Comment by P. J. Mart\'{\i}nez and R. Chac\'on [arXiv:2105.09308] on our paper Phys. Rev. E \textbf{97}, 032219 (2018). We first show that our paper is free of any mistakes and that the criticism expressed in the Comment is based on a misunderstanding or misrepresentation of what is actually claimed in our paper. We also show that the argument presented against the general formalism mentioned in the Comment is invalid because it is based on a confusion by the authors of the Comment between the general formalism per se and its lowest order approximation. In fact, the arguments contained in the Comment do not show that such a formalism is in general incorrect, as the authors of the Comment suggest, but rather that the supposedly universal predictions of the theory of ratchet universality are in general incorrect. In addition, we show that other arguments presented in Comment are invalid because they are based on incorrect equations.