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Probabilistic evolution of black hole thermodynamic states via Fokker–Planck equation.

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Title: Probabilistic evolution of black hole thermodynamic states via Fokker–Planck equation.
Authors: Wang, Chao1 (AUTHOR), Ma, Chen2 (AUTHOR), He, Meng-Ci1 (AUTHOR), Wu, Bin2,3,4,5 (AUTHOR) binwu@nwu.edu.cn
Source: European Physical Journal C -- Particles & Fields. Jun2026, Vol. 86 Issue 6, p1-11. 11p.
Subjects: Fokker-Planck equation, Phase transitions, Black holes, Energy dissipation, Entropy, Nonequilibrium thermodynamics, Gibbs' energy diagram
Abstract: Employing the generalized free energy landscape and solving the associated Fokker–Planck equation, we obtain the time-dependent probability evolution of the order parameter for the RN-AdS black hole phase transitions. Our analysis reveals two distinct kinetic regimes, namely relaxation dynamics initialized at the unstable maximum and phase transition from the metastable state. Furthermore, we characterize the non-equilibrium irreversibility and macroscopic uncertainty using the entropy production rate and the Shannon entropy. The results demonstrate that the phase transition synchronizes exactly with a prominent peak in the entropy production rate, identifying the barrier crossing event as a process fundamentally driven by maximum thermodynamic dissipation. [ABSTRACT FROM AUTHOR]
Copyright of European Physical Journal C -- Particles & Fields is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Probabilistic evolution of black hole thermodynamic states via Fokker–Planck equation.
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  Data: <searchLink fieldCode="JN" term="%22European+Physical+Journal+C+--+Particles+%26+Fields%22">European Physical Journal C -- Particles & Fields</searchLink>. Jun2026, Vol. 86 Issue 6, p1-11. 11p.
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  Data: <searchLink fieldCode="DE" term="%22Fokker-Planck+equation%22">Fokker-Planck equation</searchLink><br /><searchLink fieldCode="DE" term="%22Phase+transitions%22">Phase transitions</searchLink><br /><searchLink fieldCode="DE" term="%22Black+holes%22">Black holes</searchLink><br /><searchLink fieldCode="DE" term="%22Energy+dissipation%22">Energy dissipation</searchLink><br /><searchLink fieldCode="DE" term="%22Entropy%22">Entropy</searchLink><br /><searchLink fieldCode="DE" term="%22Nonequilibrium+thermodynamics%22">Nonequilibrium thermodynamics</searchLink><br /><searchLink fieldCode="DE" term="%22Gibbs'+energy+diagram%22">Gibbs' energy diagram</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Employing the generalized free energy landscape and solving the associated Fokker–Planck equation, we obtain the time-dependent probability evolution of the order parameter for the RN-AdS black hole phase transitions. Our analysis reveals two distinct kinetic regimes, namely relaxation dynamics initialized at the unstable maximum and phase transition from the metastable state. Furthermore, we characterize the non-equilibrium irreversibility and macroscopic uncertainty using the entropy production rate and the Shannon entropy. The results demonstrate that the phase transition synchronizes exactly with a prominent peak in the entropy production rate, identifying the barrier crossing event as a process fundamentally driven by maximum thermodynamic dissipation. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of European Physical Journal C -- Particles & Fields is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.1140/epjc/s10052-026-15855-1
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      – Code: eng
        Text: English
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        PageCount: 11
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      – SubjectFull: Fokker-Planck equation
        Type: general
      – SubjectFull: Phase transitions
        Type: general
      – SubjectFull: Black holes
        Type: general
      – SubjectFull: Energy dissipation
        Type: general
      – SubjectFull: Entropy
        Type: general
      – SubjectFull: Nonequilibrium thermodynamics
        Type: general
      – SubjectFull: Gibbs' energy diagram
        Type: general
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      – TitleFull: Probabilistic evolution of black hole thermodynamic states via Fokker–Planck equation.
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            NameFull: Wang, Chao
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            NameFull: Ma, Chen
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            NameFull: He, Meng-Ci
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            NameFull: Wu, Bin
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            – D: 01
              M: 06
              Text: Jun2026
              Type: published
              Y: 2026
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            – TitleFull: European Physical Journal C -- Particles & Fields
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