DocumentCode
15636
Title
The Concavity of Rényi Entropy Power
Author
Savare, Giuseppe ; Toscani, Giuseppe
Author_Institution
Dept. of Math., Univ. of Pavia, Pavia, Italy
Volume
60
Issue
5
fYear
2014
fDate
May-14
Firstpage
2687
Lastpage
2693
Abstract
We associate to the pth Rényi entropy a definition of entropy power, which is the natural extension of Shannon´s entropy power and exhibits a nice behavior along solutions to the p-nonlinear heat equation in Rn. We show that the Rényi entropy power of general probability densities solving such equations is always a concave function of time, whereas it has a linear behavior in correspondence to the Barenblatt source-type solutions. This result extends Costa´s concavity inequality for Shannon´s entropy power to Rényi entropies.
Keywords
entropy; probability; Barenblatt source-type solutions; Costa concavity inequality; Rényi entropy power; Shannon entropy power; concave function; p-nonlinear heat equation; probability densities; Entropy; Equations; Indexes; Mathematical model; Plasmas; Space heating; Entropy; R??nyi entropy; information measure; information theory; nonlinear heat equation;
fLanguage
English
Journal_Title
Information Theory, IEEE Transactions on
Publisher
ieee
ISSN
0018-9448
Type
jour
DOI
10.1109/TIT.2014.2309341
Filename
6754151
Link To Document