Non-Gaussian PDFs from Maximum-Entropy-principle considerations

TL;DR

This paper applies the Maximum Entropy Principle to superstatistics, deriving non-Gaussian probability distributions for turbulent fluid velocity fluctuations, providing a method to estimate system statistics with limited microscopic information.

Contribution

It introduces a maximum entropy-based approach to determine non-Gaussian PDFs in superstatistics, refining previous models for turbulent systems.

Findings

Derived a new form of velocity fluctuation distribution for turbulence.

Demonstrated the method's ability to estimate system statistics without detailed microscopic data.

Compared the new distribution with previous models, showing slight differences.

Abstract

In this work we develop on the recently suggested concept of superstatistics [C. Beck and E.G.D. Cohen, Physica A {\bf 322}, 267 (2003)], face the problem of devising a viable way for estimating the correct statistics for a system in absence of sufficient knowledge of its microscopical dynamics, and suggest to solve it through the Maximum Entropy Principle. As an example, we deduce the Probability Distribution Function for velocity fluctuations in turbulent fluids, which is slightly different from the form suggested in [C. Beck, Phys. Rev. Lett. {\bf 87}, 180601 (2001)].