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This paper proposes a unifying variational approach for proving and extendingsome fundamental information theoretic inequalities. Fundamental informationtheory results such as maximization of differential entropy, minimization ofFisher information (Cram\'er-Rao inequality), worst additive noise lemma,entropy power inequality (EPI), and extremal entropy inequality (EEI) areinterpreted as functional problems and proved within the framework of calculusof variations. Several applications and possible extensions of the proposedresults are briefly mentioned.

A Unifying Variational Perspective on Some Fundamental Information Theoretic Inequalities