Subadditivity of The Entropy and its Relation to Brascamp–Lieb Type Inequalities

  title={Subadditivity of The Entropy and its Relation to Brascamp–Lieb Type Inequalities},
  author={Eric A. Carlen and Dario Cordero-Erausquin},
  journal={Geometric and Functional Analysis},
We prove a general duality result showing that a Brascamp–Lieb type inequality is equivalent to an inequality expressing subadditivity of the entropy, with a complete correspondence of best constants and cases of equality. This opens a new approach to the proof of Brascamp–Lieb type inequalities, via subadditivity of the entropy. We illustrate the utility of this approach by proving a general inequality expressing the subadditivity property of the entropy on $${\mathbb {R}^n}$$, and fully… Expand

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