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Robledo, A (2011)

Laws of Zipf and Benford, intermittency, and critical fluctuations

Chinese Science Bulletin 56(34), pp. 36433648.

ISSN/ISBN: Not available at this time. DOI: 10.1007/s11434-011-4827-y



Abstract: We describe precise equivalences between theoretical descriptions of: (i) size-rank and first-digit laws for numerical data sets, (ii) intermittency at the transition to chaos in nonlinear maps, and (iii) cluster fluctuations at criticality. The equivalences stem from a common statistical-mechanical structure that departs from the usual via a one-parameter deformation of the exponential and logarithmic functions. The generalized structure arises when configurational phase space is incompletely visited such that the accessible fraction has fractal properties. Thermodynamically, the common focal expression is an (incomplete) Legendre transform between two entropy (or Massieu) potentials. The theory is in quantitative agreement with real size-rank data and it naturally includes the bends or tails observed for small and large rank.


Bibtex:
@Article{, author="Robledo, Alberto", title="Laws of Zipf and Benford, intermittency, and critical fluctuations", journal="Chinese Science Bulletin", year="2011", month="Dec", day="01", volume="56", number="34", pages="3643--3648", issn="1861-9541", doi="10.1007/s11434-011-4827-y", url="https://doi.org/10.1007/s11434-011-4827-y" }


Reference Type: Journal Article

Subject Area(s): Probability Theory, Statistics