We bring attention to the fact that Maxwell's mean free path for a dilute hard-sphere gas in thermal equilibrium, $(2\sigma n)\u22121$, which is ordinarily obtained by multiplying the average speed by the average time between collisions, is also the statistical mean of the distribution of free path lengths in such a gas.

## REFERENCES

*t*is discretized into

*N*equal intervals

*dt*. Then the probability to not undergo a collision in

*N*steps is $p(t|v)=[1\u2212r(v)dt]N=[1\u2212r(v)t/N]N$. In the limit that

*N*→ ∞, $p(t|v)$ becomes exponential.

*n*. Therefore, the probable excluded volume on any molecule scales as

*n*, and there are order

*N*molecules. Thus, the overlap correction to the naive inhabitable volume estimate appears at

*O*(

*n*

^{2}) in the factor χ.

*g*(

*r*) is the radial distribution function for the hard-sphere gas. Expanding in the density,

*g*(

*r*) = 1 +

*O*(

*n*), so the lowest order term, 1, is sufficient to calculate χ to

*O*(

*n*) accuracy.

*r*(

*v*

_{1}) that is more general than the one given in this article. Reif's expression involves an additional integration over all solid angle of a differential scattering cross section that can be computed for an arbitrary interaction potential between molecules.

*x*the main contribution to the integral comes from an environment of

*v*wherein the function $\u2212(2\pi )\u22121/2v\u22122\psi (v)$, which multiplies the factor

*x*in the exponent of the integrand, goes through a maximum; this happens as

*v*→∞. Therefore, the dominant asymptotic behavior of the integral is of the form $exp(bx)$, where $b=limv\u2192\u221e\u2212(2\pi )\u22121/2v\u22122\psi (v)=\u22121/2$.

In Ref. 6, the authors actually formulate the scaled free-path-length distribution without the additional factor of *r*(*v*)/ω, because they incorrectly assumed that the probability to find a molecule with a given speed in a collision was given by the Maxwell speed distribution. In our notation they found $Fincorrect(x)=(22/\pi )\u222b0\u221edv\u2009\psi (v)exp[\u2212v2\u2212(1/2\pi )v\u22122\psi (v)x]$. Somewhat fortuitously, the error incurred by using the wrong distribution makes a very small adjustment to the shape of the scaling function. The absolute value of the difference between *F* and *F*_{incorrect} is no greater than about 0.07 and this occurs for small values of the argument. This discrepancy is noticeable in Fig. 1 of Ref. 18. Note that the correct scaling function predicts *F*(0) ≈ 1.0921, which matches the data better at very small free path length than is reported in that letter.

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