{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T14:06:29Z","timestamp":1772805989219,"version":"3.50.1"},"reference-count":87,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2018,8,31]],"date-time":"2018-08-31T00:00:00Z","timestamp":1535673600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Entropy Editorial Office Voucher","award":["70f88db7c22fe75e"],"award-info":[{"award-number":["70f88db7c22fe75e"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Scale free L\u00e9vy motion is a generalized analogue of the Wiener process. Its time derivative extends the notion of \u201cwhite noise\u201d to non-Gaussian noise sources, and as such, it has been widely used to model natural signal variations described by an overdamped Langevin stochastic differential equation. Here, we consider the dynamics of an archetypal model: a Brownian-like particle is driven by external forces, and noise is represented by uncorrelated L\u00e9vy fluctuations. An unperturbed system of that form eventually attains a steady state which is uniquely determined by the set of parameter values. We show that the analyzed Markov process with the stability index \u03b1 &lt; 2 violates the detailed balance, i.e., its stationary state is quantified by a stationary probability density and nonvanishing current. We discuss consequences of the non-Gibbsian character of the stationary state of the system and its impact on the general form of the fluctuation\u2013dissipation theorem derived for weak external forcing.<\/jats:p>","DOI":"10.3390\/e20090658","type":"journal-article","created":{"date-parts":[[2018,8,31]],"date-time":"2018-08-31T10:57:52Z","timestamp":1535713072000},"page":"658","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Thermodynamics of Superdiffusion Generated by L\u00e9vy\u2013Wiener Fluctuating Forces"],"prefix":"10.3390","volume":"20","author":[{"given":"\u0141ukasz","family":"Ku\u015bmierz","sequence":"first","affiliation":[{"name":"Laboratory for Neural Computation and Adaptation, RIKEN Center for Brain Science, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan"}]},{"given":"Bart\u0142omiej","family":"Dybiec","sequence":"additional","affiliation":[{"name":"Marian Smoluchowski Institute of Physics and Mark Kac Complex Systems Research Center, Jagiellonian University, ul. S. \u0141ojasiewicza 11, 30-348 Krak\u00f3w, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5604-094X","authenticated-orcid":false,"given":"Ewa","family":"Gudowska-Nowak","sequence":"additional","affiliation":[{"name":"Marian Smoluchowski Institute of Physics and Mark Kac Complex Systems Research Center, Jagiellonian University, ul. S. \u0141ojasiewicza 11, 30-348 Krak\u00f3w, Poland"}]}],"member":"1968","published-online":{"date-parts":[[2018,8,31]]},"reference":[{"key":"ref_1","unstructured":"Samorodnitsky, G., and Taqqu, M.S. (1994). Stable Non-Gaussian Processes: Stochastic Models with Infinite Variance, Chapman and Hall."},{"key":"ref_2","unstructured":"Meerschaert, M.M., and Scheffler, H.P. (2001). Limit Distributions for Sums of Independent Random Vectors: Heavy Tails in Theory and Practice, John Wiley & Sons."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Klages, R., Radons, G., and Sokolov, I.M. (2008). Anomalous Transport. 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