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Non-Gaussian probability distribution functions from maximum-entropy-principle considerations.

Fabio Sattin1

  • 1Consorzio RFX, Associazione Euratom-ENEA, Corso Stati Uniti 4, 35127 Padova, Italy. fabio.sattin@igi.cnr.it

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 4, 2003
PubMed
Summary

This study introduces superstatistics and uses the maximum-entropy principle to determine system statistics without full microscopic knowledge. This approach refines probability distributions for turbulent fluid velocity fluctuations.

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Area of Science:

  • Statistical physics
  • Fluid dynamics
  • Non-equilibrium systems

Background:

  • Superstatistics offers a framework for systems with fluctuating parameters.
  • Estimating statistics for systems with unknown microscopic dynamics is challenging.
  • Previous work suggested specific distributions for turbulent fluid velocity fluctuations.

Purpose of the Study:

  • To develop and apply the superstatistics concept.
  • To establish a method for determining system statistics using the maximum-entropy principle when microscopic dynamics are unknown.
  • To derive the probability distribution function for velocity fluctuations in turbulent fluids.

Main Methods:

  • Application of the superstatistics framework.
  • Utilization of the maximum-entropy principle for statistical estimation.

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  • Derivation of probability distribution functions.

    • Main Results:

    • A method for estimating system statistics based on limited knowledge was developed.
    • The probability distribution function for velocity fluctuations in turbulent fluids was deduced.
    • The derived distribution differs slightly from previously suggested forms.

    Conclusions:

    • The maximum-entropy principle provides a viable approach to estimate statistics within the superstatistics framework.
    • The study refines understanding of probability distributions in turbulent fluid dynamics.
    • This work contributes to the theoretical foundation of superstatistics.