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

The Generalized Relative Entropy inequality is a ubiquitous property in mathematical 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 show that GRE is actually a generic consequence of Loskot-Rudnicki’s inequality that is reminiscent of Jensen’s inequality.