Time Evolution of Relative Entropies for Anomalous Diffusion
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 unexpe...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2013-07-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/15/8/2989 |
| _version_ | 1811297909565554688 |
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| author | Karl Heinz Hoffmann Christopher Essex Frank Boldt Janett Prehl |
| author_facet | Karl Heinz Hoffmann Christopher Essex Frank Boldt Janett Prehl |
| author_sort | Karl Heinz Hoffmann |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-13T06:12:07Z |
| format | Article |
| id | doaj.art-e4cd46db148a4187bbb63cf4afd1f08c |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-13T06:12:07Z |
| publishDate | 2013-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-e4cd46db148a4187bbb63cf4afd1f08c2022-12-22T02:59:02ZengMDPI AGEntropy1099-43002013-07-011582989300610.3390/e15082989Time Evolution of Relative Entropies for Anomalous DiffusionKarl Heinz HoffmannChristopher EssexFrank BoldtJanett PrehlThe 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.http://www.mdpi.com/1099-4300/15/8/2989space-fractional diffusion equationstable distributionKullback-Leibler entropyTsallis relative entropy |
| spellingShingle | Karl Heinz Hoffmann Christopher Essex Frank Boldt Janett Prehl Time Evolution of Relative Entropies for Anomalous Diffusion Entropy space-fractional diffusion equation stable distribution Kullback-Leibler entropy Tsallis relative entropy |
| title | Time Evolution of Relative Entropies for Anomalous Diffusion |
| title_full | Time Evolution of Relative Entropies for Anomalous Diffusion |
| title_fullStr | Time Evolution of Relative Entropies for Anomalous Diffusion |
| title_full_unstemmed | Time Evolution of Relative Entropies for Anomalous Diffusion |
| title_short | Time Evolution of Relative Entropies for Anomalous Diffusion |
| title_sort | time evolution of relative entropies for anomalous diffusion |
| topic | space-fractional diffusion equation stable distribution Kullback-Leibler entropy Tsallis relative entropy |
| url | http://www.mdpi.com/1099-4300/15/8/2989 |
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