  For any convex body $K \subseteq \mathbb R^n$, S. Bubeck and R. Eldan
introduced the entropic barrier on $K$ and showed that it is a $(1+o(1)) \,
n$-self-concordant barrier. In this note, we observe that the optimal bound of
$n$ on the self-concordance parameter holds as a consequence of the dimensional
Brascamp-Lieb inequality.
