{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T00:54:34Z","timestamp":1778028874321,"version":"3.51.4"},"reference-count":98,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2015,1,14]],"date-time":"2015-01-14T00:00:00Z","timestamp":1421193600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In many situations, in all branches of physics, one encounters the power-like behavior of some variables, which is best described by a Tsallis distribution characterized by a nonextensivity parameter q and scale parameter T. However, there exist experimental results that can be described only by a Tsallis distributions, which are additionally decorated by some log-periodic oscillating factor. We argue that such a factor can originate from allowing for a complex nonextensivity parameter q. The possible information conveyed by such an approach (like the occurrence of complex heat capacity, the notion of complex probability or complex multiplicative noise) will also be discussed.<\/jats:p>","DOI":"10.3390\/e17010384","type":"journal-article","created":{"date-parts":[[2015,1,14]],"date-time":"2015-01-14T10:33:15Z","timestamp":1421231595000},"page":"384-400","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":36,"title":["Tsallis Distribution Decorated with Log-Periodic Oscillation"],"prefix":"10.3390","volume":"17","author":[{"given":"Grzegorz","family":"Wilk","sequence":"first","affiliation":[{"name":"Department of Fundamental Research, National Centre for Nuclear Research, Hoza 69,00-681 Warsaw, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zbigniew","family":"W\u0142odarczyk","sequence":"additional","affiliation":[{"name":"Institute of Physics, Jan Kochanowski University, Swietokrzyska 15, 25-406 Kielce, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,1,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1007\/BF01016429","article-title":"Possible generalization of Boltzmann-Gibbs statistics","volume":"52","author":"Tsallis","year":"1998","journal-title":"J. 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