Entropy versions of additive inequalities

Abstract

The connection between inequalities in additive combinatorics and analogous versions in terms of the entropy of random variables has been extensively explored over the past few years. This paper extends a device introduced by Ruzsa in his seminal work introducing this correspondence. This extension provides a toolbox for establishing the equivalence between sumset inequalities and their entropic versions. It supplies simpler proofs of known results and opens a path for obtaining new ones.