Skewed superstatistical distributions from a Langevin and Fokker-Planck approach

TL;DR

This paper derives superstatistical distributions from wind speed data using Langevin and Fokker-Planck models with position-dependent parameters, linking inhomogeneous fluctuations to superstatistics.

Contribution

It introduces a method to extract superstatistical distributions directly from data and connects Langevin/Fokker-Planck models with superstatistics in the overdamped limit.

Findings

Extracted superstatistical distribution from wind data

Constructed Langevin and Fokker-Planck models with position-dependent $eta$

Models reduce to standard superstatistics in overdamped limit

Abstract

The superstatistics concept is a useful statistical method to describe inhomogeneous complex systems for which a system parameter $\beta$ fluctuates on a large spatio-temporal scale. In this paper we analyze a measured time series of wind speed fluctuations and extract the superstatistical distribution function $f(\beta)$ directly from the data. We construct suitable Langevin and Fokker-Planck models with a position dependent $\beta$-field and show that they reduce to standard type of superstatistics in the overdamped limit.