2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/150928To calculate the entropy of a subalgebra or of a channel with respect to a state, one has to solve an intriguing optimalization problem. The latter is also the key part in the entanglement of formation concept, in which case the subalgebra is a subfactor. I consider some general properties, valid for these definitions in finite dimensions, and apply them to a maximal commutative subalgebra of a full matrix algebra. The main method is an interplay between convexity and symmetry. A collection of helpful tools from convex analysis for the problems in question is collected in an appendix.20 pages, latex, no figures. Some calculations and reasonings are done in more detail. I have to thank an unknown referee for asking me to do so. Misprints, if detected, are corrected. To be published in: Open Systems & Information DynamicsQuantum Physicstext