Ruzsa's equivalence theorem provided a framework for converting certain families of inequalities in additive combinatorics to entropic inequalities (which sometimes did not possess stand-alone entropic proofs). In this work, we first establish formal equivalences between some families (different from Ruzsa) of inequalities in additive combinatorics and entropic ones. As a first step to further these equivalences, we establish an information-theoretic characterization of the magnification ratio that could also be of independent interest.

翻译：Ruzsa等价定理提供了一个框架，可将加性组合中的某些不等式族转化为熵不等式（其中部分不等式此前并无独立的熵证明）。本研究首先建立了加性组合与熵不等式之间不同于Ruzsa框架的若干不等式族的形式等价关系。作为深化这些等价关系的初步步骤，我们给出了放大比率的信息论表征，该结果或具有独立学术价值。