The Sharma-Mittal Entropy is Subadditive and Supermodular on the Majorization Lattice
arXiv:2605.1860010.2
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Provides a unified theoretical result for entropy measures, but is incremental as it extends known properties to a more general family.
The authors prove that Sharma-Mittal entropy is subadditive and supermodular on the majorization lattice, unifying and extending similar results for Shannon, Tsallis, and Rényi entropies.
We prove that Sharma-Mittal entropy is a subadditive and supermodular function on the lattice of all $n$-dimensional probability distributions, ordered according to the partial order relation defined by majorization among vectors. Our result unifies and extends analogous results presented in the literature for the Shannon entropy, the Tsallis entropy, and the Rényi entropy.