  Entropies of mixing can be derived directly from the parent distributions of
extreme value theory. They correspond to pseudo-additive entropies in the case
of Pareto and power function distributions, while to the Shannon entropy in the
case of the exponential distribution.The former tend to the latter when their
shape parameters tend to infinity and zero, respectively. Hence processes whose
entropies of mixing are pseudo-additive entropies majorize, in the Lorenz order
sense, those whose entropy is the Shannon entropy. In the case of the arcsine
distribution, maximal properties of regular polygons correspond to maximum
entropy of mixing.
