Sources of exponents

Examples are given of scaling relationships governed by fractional exponents. Additional examples are presented with heavy tail probability distributions governed by a fractional exponent. This includes the analysis of the Boltzmann–Gibbs entropy, subject to an appropriate constraint, to generate lo...

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Bibliographic Details
Published in:Physica. D 2004-06, Vol.193 (1), p.67-72
Main Authors: Bendler, John T., Fontanella, John J., Shlesinger, Michael F.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Fractals
Levy flights
Levy walks
Maximum entropy
Physics
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Summary:Examples are given of scaling relationships governed by fractional exponents. Additional examples are presented with heavy tail probability distributions governed by a fractional exponent. This includes the analysis of the Boltzmann–Gibbs entropy, subject to an appropriate constraint, to generate long-tailed probability distributions. The stretched exponential distribution is employed to derive a time scale for the glass transition that contains an essential singularity at a critical temperature. These examples demonstrate that there are many routes to producing fractional exponents in physical systems.
ISSN:0167-2789
1872-8022
DOI:10.1016/j.physd.2004.01.009