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The Generalized Relative Entropy inequality is a ubiquitous property inmathematical models applied in physics or biology. In spite of its importance,it is currently proved on a case-by-case basis in the literature. Here, we showthat GRE is actually a generic consequence of Loskot-Rudnicki's inequality thatis reminiscent of Jensen's inequality.

Loskot-Rudnicki's inequality and General Relative Entropy inequality for Cauchy problems preserving positivity