An open source Matlab package for stochastic data analysis in the context of Fokker-Plank Equation and Integral Fluctuation Theorem

We present a user-friendly open-source Matlab package for stochastic data analysis. This package enables to perform a standard analysis of given timeseries like scaling analysis of structure functions and energy spectral density, estimation of correlation functions or investigation of the PDF’s of increments including Castaing fits. Also, this package can be used to extract the stochastic equations describing scale-dependent processes, such as the cascade process in turbulent flows, through Fokker-Planck equations and concepts of non-equilibrium stochastic thermodynamics. This stochastic treatment of scale-dependent processes has the potential for a new way to link to fluctuation theorems of non-equilibrium stochastic thermodynamics and extreme events (small scale intermittency, structures of rogue waves). 

The development of this user-friendly package greatly enhances the practicability and availability of this method, which allows a comprehensive statistical description in terms of the complexity of time series. It can also be used by researchers outside of the field of turbulence for the analysis of data with turbulent like complexity, including ocean gravity waves, stock prices and inertial particles in direct numerical simulations. Support is available: github.com/andre-fuchs-uni-oldenburg/OPEN FPE IFT, where questions can be posted and generally receive quick responses from the authors.

This package was developed by the research group Turbulence, Wind energy and Stochastics (TWiSt) at the Carl von Ossietzky University of Oldenburg. We acknowledge funding by Volkswagen Foundation.