{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:42:30Z","timestamp":1760236950100,"version":"build-2065373602"},"reference-count":44,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,1,31]],"date-time":"2020-01-31T00:00:00Z","timestamp":1580428800000},"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>Nonlinear Fokker\u2013Planck equations (NLFPEs) constitute useful effective descriptions of some interacting many-body systems. Important instances of these nonlinear evolution equations are closely related to the thermostatistics based on the     S q     power-law entropic functionals. Most applications of the connection between the NLFPE and the     S q     entropies have focused on systems interacting through short-range forces. In the present contribution we re-visit the NLFPE approach to interacting systems in order to clarify the role played by the range of the interactions, and to explore the possibility of developing similar treatments for systems with long-range interactions, such as those corresponding to Newtonian gravitation. In particular, we consider a system of particles interacting via forces following the inverse square law and performing overdamped motion, that is described by a density obeying an integro-differential evolution equation that admits exact time-dependent solutions of the q-Gaussian form. These q-Gaussian solutions, which constitute a signature of     S q    -thermostatistics, evolve in a similar but not identical way to the solutions of an appropriate nonlinear, power-law Fokker\u2013Planck equation.<\/jats:p>","DOI":"10.3390\/e22020163","type":"journal-article","created":{"date-parts":[[2020,1,31]],"date-time":"2020-01-31T11:55:56Z","timestamp":1580471756000},"page":"163","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Nonlinear Fokker\u2013Planck Equation Approach to Systems of Interacting Particles: Thermostatistical Features Related to the Range of the Interactions"],"prefix":"10.3390","volume":"22","author":[{"given":"Angel","family":"Plastino","sequence":"first","affiliation":[{"name":"CeBio y Departamento de Ciencias B\u00e1sicas, Universidad Nacional del Noroeste de la Prov\u00edncia de Buenos Aires, UNNOBA, Conicet, Roque Saenz Pe\u00f1a 456, Junin 6000, Argentina"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7532-3881","authenticated-orcid":false,"given":"Roseli","family":"Wedemann","sequence":"additional","affiliation":[{"name":"Instituto de Matem\u00e1tica e Estat\u00edstica, Universidade do Estado do Rio de Janeiro, Rua S\u00e3o Francisco Xavier, 524, Rio de Janeiro 20550-900, RJ, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,1,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1765","DOI":"10.3390\/e13101765","article-title":"The nonadditive entropy Sq and its applications in physics and elsewhere: Some remarks","volume":"13","author":"Tsallis","year":"2011","journal-title":"Entropy"},{"key":"ref_2","unstructured":"Tsallis, C. 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