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

Étienne Bernard (1, 2)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
2 ENPC - École des Ponts ParisTech

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.

Mots clés: Generalized Relative Entropy; Riesz space; function space; Jensen inequality; Loskot-Rudnicki's inequality

Domaines: Mathématiques [math]

Étienne Bernard. Loskot-Rudnicki's inequality and General Relative Entropy inequality for Cauchy problems preserving positivity. 2022. ⟨hal-03560418v2⟩