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 Łoskot-Rudnicki’s inequality that is reminiscent of Jensen’s inequality.
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Acknowledgements
The author is grateful to Benoît Perthame for bringing to his attention the subject of Generalized Relative Entropy inequality and for useful discussions. The author also thanks Pierre Gabriel for useful discussions and Tony Lelièvre for also useful discussions and for having pinpointed [4]. Eventually, he also thanks the anonymous reviewers for their careful reading and their many comments and suggestions, especially pinpointing [8] while recalling the concept of KB-spaces. He also thanks them for suggesting some very useful references. All their advice has greatly helped the author to shorten and improve the manuscript.
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Bernard, É. Łoskot-Rudnicki’s Inequality and General Relative Entropy Inequality for Cauchy Problems Preserving Positivity. Acta Appl Math 180, 13 (2022). https://doi.org/10.1007/s10440-022-00514-w
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DOI: https://doi.org/10.1007/s10440-022-00514-w