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Are power-law distributions an equilibrium distribution or a stationary nonequilibrium distribution?

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  • Guo, Ran
  • Du, Jiulin

Abstract

We examine whether the principle of detailed balance holds for the power-law distributions that are generated from the well-known two-variable Langevin equation and the associated Fokker–Planck equations. With the detailed balance and the generalized fluctuation–dissipation relation, we derive analytically the stationary power-law distribution from the Ito’s, Stratonovich’s and Zwanzig’s Fokker–Planck equations, and conclude that the power-law distributions can either be a stationary nonequilibrium distribution or an equilibrium distribution, which depend on information about the form of the diffusion coefficient function and the existence and uniqueness of an equilibrium state.

Suggested Citation

  • Guo, Ran & Du, Jiulin, 2014. "Are power-law distributions an equilibrium distribution or a stationary nonequilibrium distribution?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 406(C), pages 281-286.
    • Handle: RePEc:eee:phsmap:v:406:y:2014:i:c:p:281-286
    DOI: 10.1016/j.physa.2014.03.056
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    Cited by:

    1. Tawfik, Ashraf M. & Elkamash, I.S., 2022. "On the correlation between Kappa and Lévy stable distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 601(C).

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