{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,4]],"date-time":"2026-08-04T20:49:32Z","timestamp":1785876572056,"version":"3.56.0"},"reference-count":46,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2013,7,26]],"date-time":"2013-07-26T00:00:00Z","timestamp":1374796800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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 \u201cnearer\u201d to pure diffusion than another, placing pure wave propagation, desirably, \u201cfurthest\u201d 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.<\/jats:p>","DOI":"10.3390\/e15082989","type":"journal-article","created":{"date-parts":[[2013,7,26]],"date-time":"2013-07-26T22:13:15Z","timestamp":1374876795000},"page":"2989-3006","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Time Evolution of Relative Entropies for Anomalous Diffusion"],"prefix":"10.3390","volume":"15","author":[{"given":"Janett","family":"Prehl","sequence":"first","affiliation":[{"name":"Institut f\u00fcr Physik, Technische Universit\u00e4t Chemnitz, D-09107 Chemnitz, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Frank","family":"Boldt","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Physik, Technische Universit\u00e4t Chemnitz, D-09107 Chemnitz, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Christopher","family":"Essex","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, The University of Western Ontario, N6A 5B7 London, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Karl","family":"Hoffmann","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Physik, Technische Universit\u00e4t Chemnitz, D-09107 Chemnitz, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2013,7,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1214\/aoms\/1177729694","article-title":"On information and sufficiency","volume":"22","author":"Kullback","year":"1951","journal-title":"Ann. 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