2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59360We define a free probability analogue of the Wasserstein metric, which extends the classical one. In dimension one, we prove that the square of the Wasserstein distance to the semi-circle distribution is majorized by a modified free entropy quantity.14 pages, Incomplete Preliminary VersionOperator Algebras46L54; 60E99; 94A17text