{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T12:02:08Z","timestamp":1772020928564,"version":"3.50.1"},"reference-count":197,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2026,2,12]],"date-time":"2026-02-12T00:00:00Z","timestamp":1770854400000},"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>Recently introduced, power Brownian motion and power Levy motion are versatile and practical anomalous-diffusion models. On the one hand, the power motions are easily constructed and are easily tracked. On the other hand, the power motions display an assortment of anomalous behaviors including: sub-diffusion and super-diffusion; aging and anti-aging; and persistence and anti-persistence. This paper investigates the power motions from a socioeconomic-inequality perspective. Using this perspective, key statistical and temporal behaviors of the power motions are interpreted and scored. In particular, the paper provides simple and explicit quantitative answers\u2013which are based on socioeconomic inequality indices\u2013to the following question: what is the \u2018degree of anomaly\u2019 of each of the power-motions\u2019 anomalous behaviors? The socioeconomic approach presented in this paper may be applied (in future research) to additional anomalous-diffusion models.<\/jats:p>","DOI":"10.3390\/e28020216","type":"journal-article","created":{"date-parts":[[2026,2,12]],"date-time":"2026-02-12T14:06:16Z","timestamp":1770905176000},"page":"216","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Socioeconomic Gauging of Brown and Levy Power Motions"],"prefix":"10.3390","volume":"28","author":[{"given":"Iddo","family":"Eliazar","sequence":"first","affiliation":[{"name":"School of Chemistry, Tel Aviv University, Tel Aviv 6997801, Israel"}]}],"member":"1968","published-online":{"date-parts":[[2026,2,12]]},"reference":[{"key":"ref_1","unstructured":"Mandelbrot, B.B. (1982). The Fractal Geometry of Nature, Freeman."},{"key":"ref_2","unstructured":"Feder, J. (2013). Fractals, Springer Science & Business Media."},{"key":"ref_3","unstructured":"Barnsley, M.F. 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