Non-Gaussian PDFs from Maximum-Entropy-principle considerations

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)].

v2: final accepted version: one statement corrected, other minor changes. To appear in Phys. Rev. E

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