The preprint An elementary approach to Wehrl-type entropy bounds in quantitative form by Fabio Nicola, Federico Riccardi and Paolo Tilli is now available on arXiv (arXiv:2512.04245).
We consider the problem of the stability (with sharp exponent) of the Lieb-Solovej inequality for symmetric \(SU(N)\) coherent states, which was obtained only recently by the authors. Here, we propose an elementary proof of this result, based on reformulating the Wehrl-type entropy as a function defined on the unit sphere in \(\mathbb{C}^d\), for some suitable \(d\), and on some explicit (and somewhat surprising) computations.