Features of constrained entropic functional variational problems

We describe in great generality features concerning constrained entropic, functional variational problems that allow for a broad range of applications. Our discussion encompasses not only entropies but, potentially, any functional of the probability distribution, like Fisher-information or relative entropies, etc. In particular, in dealing with generalized statistics in straightforward fashion one may sometimes find that the celebrated relation between entropic small changes and mean energy ones, dS dβ = βd(U) dβ, does not seems respected. We show here that, on the contrary, it is indeed obeyed by any system subject to a Legendre extremization process, i.e. in all constrained entropic variational problems.Fil: Plastino, Ángel Ricardo. Univ. Nac. del Noroeste de la Prov. de Bs. As.; ArgentinaFil: Plastino, Ángel Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina. Facultad de Ciencias Exactas, Universidad Nacional de la Plata; ArgentinaFil: Rocca, Mario Carlos. Facultad de Ciencias Exactas, Universidad Nacional de la Plata; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentin