Rényi entropy is subadditive on the majorization lattice for every α ∈ [0,∞] and supermodular for α ∈ {0} ∪ [1,∞]; Tsallis entropy is subadditive and supermodular for all α ∈ [0,∞).
Minimum-entropy coupling approximation guarantees beyond the majorization barrier
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Geometry of R\'enyi Entropy on the Majorization Lattice
Rényi entropy is subadditive on the majorization lattice for every α ∈ [0,∞] and supermodular for α ∈ {0} ∪ [1,∞]; Tsallis entropy is subadditive and supermodular for all α ∈ [0,∞).