Comment on "Influence of Noise on Force Measurement" [arXiv:1004.0874]

TL;DR

This paper critiques a recent experiment on force measurement near a wall, highlighting issues with the application of certain equations and interpretations of stochastic calculus in the presence of space-dependent diffusion.

Contribution

It clarifies the limitations of the original experimental analysis, emphasizing the need for corrections and careful interpretation of forces in stochastic systems.

Findings

Equation (1) does not hold for space-dependent diffusion

Discrepancy between drift-derived and distribution-derived forces is not necessarily indicative of stochastic calculus

Corrections are needed for accurate force measurement in such systems

Abstract

In a recent Letter [arXiv:1004.0874], Volpe et al. describe experiments on a colloidal particle near a wall in the presence of a gravitational field for which they study the influence of noise on the measurement of force. Their central result is a striking discrepancy between the forces derived from experimental drift measurements via their Eq. (1), and from the equilibrium distribution. From this discrepancy they infer the stochastic calculus realised in the system. We comment, however: (a) that Eq. (1) does not hold for space-dependent diffusion, and corrections should be introduced; and (b) that the "force" derived from the drift need not coincide with the "force" obtained from the equilibrium distribution.