  In a recent Note (Am. J. Phys. 92:397, 2024; arXiv:2309.10826), Vallejo and
Bove provide a physical argument based nominally on the second law of
thermodynamics as a way of resolving the mathematical question appearing in the
title. A remarkable aspect of their argument is that it does not depend on the
numerical value of $\pi$, because $e^{x} \ge x^{e}$ for all positive $x$, with
equality occurring only when $x = e$. Moreover, their argument does not depend
on the validity of the second law but is rather a limited proof of it for this
particular case.
