R\'enyi entropies and nonlinear diffusion equations
Mathematical Physics
2014-01-20 v1 Information Theory
math.IT
math.MP
Abstract
Since their introduction in the early sixties, the R\'enyi 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 R\'enyi entropies and nonlinear diffusion equations. In particular, it is shown that these relationships allow to prove various functional inequalities in sharp form.
Keywords
Cite
@article{arxiv.1401.4271,
title = {R\'enyi entropies and nonlinear diffusion equations},
author = {Giuseppe Toscani},
journal= {arXiv preprint arXiv:1401.4271},
year = {2014}
}