Next Article in Journal
Optimization of Curvilinear Tracing Applied to Solar Physics and Biophysics
Next Article in Special Issue
Information Geometry of Complex Hamiltonians and Exceptional Points
Previous Article in Journal
On the Entropy of a Class of Irreversible Processes
Previous Article in Special Issue
Pushing for the Extreme: Estimation of Poisson Distribution from Low Count Unreplicated Data—How Close Can We Get?
Entropy 2013, 15(8), 2989-3006; doi:10.3390/e15082989
Article

Time Evolution of Relative Entropies for Anomalous Diffusion

1
,
1
,
2
 and
1,*
1 Institut für Physik, Technische Universität Chemnitz, D-09107 Chemnitz, Germany 2 Department of Applied Mathematics, The University of Western Ontario, N6A 5B7 London, Canada
* Author to whom correspondence should be addressed.
Received: 26 June 2013 / Revised: 17 July 2013 / Accepted: 18 July 2013 / Published: 26 July 2013
(This article belongs to the Special Issue Distance in Information and Statistical Physics Volume 2)
Download PDF [298 KB, 24 February 2015; original version 24 February 2015]

Abstract

The entropy production paradox for anomalous diffusion processes describes a phenomenon where one-parameter families of dynamical equations, falling between the diffusion and wave equations, have entropy production rates (Shannon, Tsallis or Renyi) that increase toward the wave equation limit unexpectedly. Moreover, also surprisingly, the entropy does not order the bridging regime between diffusion and waves at all. However, it has been found that relative entropies, with an appropriately chosen reference distribution, do. Relative entropies, thus, provide a physically sensible way of setting which process is “nearer” to pure diffusion than another, placing pure wave propagation, desirably, “furthest” from pure diffusion. We examine here the time behavior of the relative entropies under the evolution dynamics of the underlying one-parameter family of dynamical equations based on space-fractional derivatives.
Keywords: space-fractional diffusion equation; stable distribution; Kullback-Leibler entropy; Tsallis relative entropy space-fractional diffusion equation; stable distribution; Kullback-Leibler entropy; Tsallis relative entropy
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.

Share & Cite This Article

Further Mendeley | CiteULike
Export to BibTeX |
EndNote
MDPI and ACS Style

Prehl, J.; Boldt, F.; Essex, C.; Hoffmann, K.H. Time Evolution of Relative Entropies for Anomalous Diffusion. Entropy 2013, 15, 2989-3006.

View more citation formats

Related Articles

Article Metrics

For more information on the journal, click here

Comments

Cited By

[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert