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

TL;DR

This paper demonstrates that the Generalized Relative Entropy inequality, crucial in physics and biology models, can be derived from Loskot-Rudnicki's inequality, providing a unifying theoretical foundation.

Contribution

It establishes that GRE is a generic consequence of Loskot-Rudnicki's inequality, simplifying proofs and understanding of entropy inequalities.

Findings

GRE follows from Loskot-Rudnicki's inequality

Provides a unified theoretical framework for entropy inequalities

Simplifies proofs in mathematical physics and biology

Abstract

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.