Comment on "Two definitions of the hopping time in a confined fluid of finite particles" [J. Chem. Phys. 129, 154117 (2008)].

To resolve the disagreement between two calculations for the hopping time divergence exponent of two diffusing hard disks in a narrow channel, Kalinay and Percus propose that the definitions of the hopping time used in the two calculations are not equivalent, which resulted in different exponents. The first is the mean first passage time (MFPT) and is related to the survival probability function S(t) at long time. Bowles, Mon, and Percus solve an approximate Fick-Jacobs equation to produce a MFPT exponent of -3∕2. The second is defined by Kalinay and Percus in terms of the short time relaxation of S(t). Kalinay and Percus claim that Mon and Percus used the short time relaxation of the survival function to obtain an exponent of -2 in the numerical solution of the diffusion equation. This is not an accurate description of the Mon and Percus method. To the contrary, the method of Mon and Percus is designed to extract the longest relaxation time constant. In this comment, I discuss this misunderstanding of Kalinay and Percus and show that the explanation for the disagreement with the approximate Fick-Jacob equation predictions is not in the difference of the definitions for the hopping time.