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Entropy 2015, 17(9), 6056-6071; doi:10.3390/e17096056

Self-Similar Solutions of Rényi’s Entropy and the Concavity of Its Entropy Power

1
Department of Mathematics, School of Sciences, University of Aegean, Karlovasi, Samos 83200, Greece
2
School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, UK 
Academic Editor: Demosthenes Ellinas
Received: 8 July 2015 / Revised: 26 August 2015 / Accepted: 27 August 2015 / Published: 31 August 2015
(This article belongs to the Special Issue Quantum Computation and Information: Multi-Particle Aspects)
View Full-Text   |   Download PDF [313 KB, uploaded 31 August 2015]   |  

Abstract

We study the class of self-similar probability density functions with finite mean and variance, which maximize Rényi’s entropy. The investigation is restricted in the Schwartz space S(Rd) and in the space of l-differentiable compactly supported functions Clc (Rd). Interestingly, the solutions of this optimization problem do not coincide with the solutions of the usual porous medium equation with a Dirac point source, as occurs in the optimization of Shannon’s entropy. We also study the concavity of the entropy power in Rd with respect to time using two different methods. The first one takes advantage of the solutions determined earlier, while the second one is based on a setting that could be used for Riemannian manifolds. View Full-Text
Keywords: maximum Rényi entropy; entropy power; Fisher information; nonlinear diffusion equation maximum Rényi entropy; entropy power; Fisher information; nonlinear diffusion equation
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Hatzinikitas, A.N. Self-Similar Solutions of Rényi’s Entropy and the Concavity of Its Entropy Power. Entropy 2015, 17, 6056-6071.

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