Skewed superstatistical distributions from a Langevin and Fokker-Planck approach

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.

arXiv comment7 pages, 6 figures

References in corpus (22)

• Dynamical foundations of nonextensive statistical mechanics
• From time series to superstatistics
• Constructing a statistical mechanics for Beck-Cohen superstatistics
• Pathway Model, Superstatistics, Tsallis Statistics, and a Generalized Measure of Entropy
• Superstatistics, thermodynamics, and fluctuations
• Asymptotics of superstatistics
• Statistics of 3-dimensional Lagrangian turbulence
• Intensity Thresholds and the Statistics of the Temporal Occurrence of Solar Flares
• Coarse-grained distributions and superstatistics
• Unified Multifractal Description of Velocity Increments Statistics in Turbulence: Intermittency and Skewness
• Superstatistical fluctuations in time series: Applications to share-price dynamics and turbulence
• Beyond Boltzmann-Gibbs statistics: Maximum entropy hyperensembles out-of-equilibrium
• Superstatistical generalization of the work fluctuation theorem
• Superstatistical distributions from a maximum entropy principle
• The statistics of particle velocities in dense granular flows
• Superpositions of Probability Distributions
• Spectral fluctuations of billiards with mixed dynamics: from time series to superstatistics
• Superstatistics in random matrix theory
• Environmental Atmospheric Turbulence at Florence Airport
• Non-extensive statistics in stringy space-time foam models and entangled meson states
• Generalised thermostatistics using hyperensembles
• Bistable stochastic processes in the q-exponential family