  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.
