Rényi entropies and nonlinear diffusion equations

2014/01/17 by Giuseppe Toscani, Toscani, Giuseppe
Mathematics · Physics and Astronomy · #FOS: Computer and information sciences #FOS: Physical sciences #Fractional Differential Equations Solutions #Information Theory (cs.IT) #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1401.4271

openalex publication_date 2014/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Since their introduction in the early sixties, the Rényi entropies have been used in many contexts, ranging from information theory to astrophysics, turbulence phenomena and others. In this note, we enlighten the main connections between Rényi entropies and nonlinear diffusion equations. In particular, it is shown that these relationships allow to prove various functional inequalities in sharp form.

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