{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,12]],"date-time":"2026-09-12T20:00:39Z","timestamp":1789243239408,"version":"build-2803163510"},"reference-count":26,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2015,2,9]],"date-time":"2015-02-09T00:00:00Z","timestamp":1423440000000},"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>The non-linear Fokker-Planck equation or Kolmogorov forward equation is currently successfully applied for deep analysis of irreversibility and it gives an excellent approximation near the free energy minimum, just as Boltzmann\u2019s definition of entropy follows from finding the maximum entropy state. A connection to Fokker-Planck dynamics and the free energy functional is presented and discussed\u2014this approach has been particularly successful to deal with metastability. We focus our attention on investigating and discussing the fundamental role of dissipation analysis in metastable systems. The major novelty of our approach is that the obtained results enable us to reveal an appealing, and previously unexplored relationship between Fokker-Planck equation and the associated free energy functional. Namely, we point out that the dynamics may be regarded as a gradient flux, or a steepest descent, for the free energy.<\/jats:p>","DOI":"10.3390\/e17020763","type":"journal-article","created":{"date-parts":[[2015,2,9]],"date-time":"2015-02-09T10:17:04Z","timestamp":1423477024000},"page":"763-771","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Fokker-Planck Equation and Thermodynamic System Analysis"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3123-2133","authenticated-orcid":false,"given":"Umberto","family":"Lucia","sequence":"first","affiliation":[{"name":"Dipartimento Energia, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gianpiero","family":"Gervino","sequence":"additional","affiliation":[{"name":"Dipartimento di Fisica, Universit\u00e0 di Torino, via Giuria 1, 10125 Torino, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2015,2,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1137\/S0036141096303359","article-title":"The Variational Formulation of the Fokker-Planck Equation","volume":"29","author":"Jordan","year":"1998","journal-title":"SIAM J. 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