Comment on ``Lyapunov Exponent of a Many Body System and Its Transport Coefficients''

TL;DR

This paper critiques a recent theoretical claim that the maximum Lyapunov exponent in a dilute gas is universally proportional to the cube root of the self-diffusion coefficient, showing it does not hold for hard sphere gases.

Contribution

The paper challenges the generality of a recent theoretical result by demonstrating its inapplicability to hard sphere gases in both dilute and dense phases.

Findings

The proposed proportionality does not apply to hard sphere gases.

The result is specific to systems with long-range interactions.

The claim is not universally valid across different gas models.

Abstract

In a recent Letter, Barnett, Tajima, Nishihara, Ueshima and Furukawa obtained a theoretical expression for the maximum Lyapunov exponent $\lambda_1$ of a dilute gas. They conclude that $\lambda_1$ is proportional to the cube root of the self-diffusion coefficient $D$, independent of the range of the interaction potential. They validate their conjecture with numerical data for a dense one-component plasma, a system with long-range forces. We claim that their result is highly non-generic. We show in the following that it does not apply to a gas of hard spheres, neither in the dilute nor in the dense phase.