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Entropy 2015, 17(2), 763-771;

Fokker-Planck Equation and Thermodynamic System Analysis

Dipartimento Energia, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
Dipartimento di Fisica, Università di Torino, via Giuria 1, 10125 Torino, Italy
These authors contributed equally to this work.
Author to whom correspondence should be addressed.
Received: 23 November 2014 / Revised: 12 January 2015 / Accepted: 5 February 2015 / Published: 9 February 2015
(This article belongs to the Special Issue Entropic Aspects in Statistical Physics of Complex Systems)
Full-Text   |   PDF [687 KB, uploaded 24 February 2015]


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’s 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—this 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. View Full-Text
Keywords: entropy generation; Fokker-Planck equation; irreversible systems; non-equilibrium thermodynamics entropy generation; Fokker-Planck equation; irreversible systems; non-equilibrium thermodynamics
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Lucia, U.; Gervino, G. Fokker-Planck Equation and Thermodynamic System Analysis. Entropy 2015, 17, 763-771.

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