Diffusion Entropy and Waiting Time Statistics of Hard-X-Ray Solar Flares

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Article on diffusion entropy and waiting time statistics of hard-x-ray solar flares.

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13 p.

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Grigolini, Paolo; Leddon, Deborah & Scafetta, Nicola March 25, 2002.


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Article on diffusion entropy and waiting time statistics of hard-x-ray solar flares.

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13 p.


Copyright 2002 American Physical Society. The following article appeared in Physical Review E, 65:4; http://pre.aps.org/abstract/PRE/v65/i4/e046203

Abstract: We show at work a technique of scaling detection based on evaluating the Shannon entropy of the diffusion process obtained by converting the time series under study into trajectories. This method, called diffusion entropy, affords information that cannot be derived from the direct evaluation of waiting times. We apply this method to the analysis of the distribution of time distance τ between two nearest-neighbor solar flares. This traditional part of the analysis is based on the direct evaluation of the distribution function ψ(τ), or of the probability ψ(τ), that no time distance smaller than a given τ is found. We adopt the paradigm of the inverse power-law behavior, and the authors focus on the determination of the inverse power index μ, without ruling out different asymptotic properties that might be revealed, at larger scales, with the help of richer statistics. We then use the DE method, with three different walking rules, and the authors focus on the regime of transition to scaling. This regime of transition and the value of the scaling parameter itself, δ, depends on the walking rule adopted, a property of interest to shed light on the slow process of transition from dynamics to thermodynamics often occurring under anomalous statistical conditions. With the first two rules the transition regime occurs through-out a large time interval, and the information contained in the time series is transmitted, to a great extent, to it, as well as to the scaling regime. By using the third rule, on the contrary, the same information is essentially conveyed to the scaling regime, which, in fact, emerges very quickly after a fast transition process. We show that the DE method not only causes to emerge the long-range correlation with a given μ<3, and so a basin of attraction different from the ordinary Gaussian one, but it also reveals the presence of memory effects induced by the time dependence of the solar flare rate. When this memory is annihilated by shuffling, the scaling parameter δ is shown to fit the theoretically expected function of μ. All this leads us to the compelling conclusion that μ=2.138±0.01.


  • Physical Review E, 2002, College Park: American Physical Society


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  • Publication Title: Physical Review E
  • Volume: 65
  • Issue: 4
  • Peer Reviewed: Yes


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The Scholarly Works Collection is home to materials from the University of North Texas community's research, creative, and scholarly activities and serves as UNT's Open Access Repository. It brings together articles, papers, artwork, music, research data, reports, presentations, and other scholarly and creative products representing the expertise in our university community. Access to some items in this collection may be restricted.

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  • March 25, 2002

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  • Nov. 24, 2011, 12:20 a.m.

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  • May 13, 2014, 4:11 p.m.

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Grigolini, Paolo; Leddon, Deborah & Scafetta, Nicola. Diffusion Entropy and Waiting Time Statistics of Hard-X-Ray Solar Flares, article, March 25, 2002; [College Park, Maryland]. (digital.library.unt.edu/ark:/67531/metadc67629/: accessed May 28, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT College of Arts and Sciences.