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.
Fokker-Planck Equation and Thermodynamic System Analysis / Lucia, Umberto; Gianpiero, Gervino. - In: ENTROPY. - ISSN 1099-4300. - STAMPA. - 17:2(2015), pp. 763-771. [10.3390/e17020763]
Fokker-Planck Equation and Thermodynamic System Analysis
LUCIA, UMBERTO;
2015
Abstract
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.File | Dimensione | Formato | |
---|---|---|---|
entropy-17-00763.pdf
accesso aperto
Tipologia:
2a Post-print versione editoriale / Version of Record
Licenza:
Creative commons
Dimensione
687.07 kB
Formato
Adobe PDF
|
687.07 kB | Adobe PDF | Visualizza/Apri |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
https://hdl.handle.net/11583/2588596
Attenzione
Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo