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We introduce a notion of majorization flow, and demonstrate it to be apowerful tool for deriving simple and universal proofs of continuity bounds forentropic functions relevant in information theory. In particular, for the caseof the alpha-R\'enyi entropy, whose connections to thermodynamics are discussedin this article, majorization flow yields a Lipschitz continuity bound for thecase alpha > 1, thus resolving an open problem and providing a substantialimprovement over previously known bounds.

Universal proofs of entropic continuity bounds via majorization flow