Dynamical Foundations of Nonextensive Statistical Mechanics

By Christian Beck. 2001

435 citations recorded by the source corpus.

We construct classes of stochastic differential equations with fluctuating friction forces that generate a dynamics correctly described by Tsallis statistics and nonextensive statistical mechanics. These systems generalize the way in which ordinary Langevin equations underly ordinary statistical mechanics to the more general nonextensive case. As a main example, we construct a dynamical model of velocity fluctuations in a turbulent flow, which generates probability densities that very well fit experimentally measured probability densities in Eulerian and Lagrangian turbulence. Our approach provides a dynamical reason why many physical systems with fluctuations in temperature or energy dissipation rate are correctly described by Tsallis statistics.

Subfields: Condensed Matter Physics, Economics and Econometrics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/b931a9a6ebb79f72225d20e3b55efc52447eee00

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Condensed Matter Physics

In Economics and Econometrics

In Statistical and Nonlinear Physics

Citations in the corpus

Brownian yet non-Gaussian diffusion: from superstatistics to subordination of diffusing diffusivities (2016, background): “This approach corresponds to the idea of superstatistics [36]: Accordingly, the overall distribution function Pðx; tÞ of a system of tracer particles, individually moving in sufficiently large, disjunct patches with local diffusivityD, becomes the weighted average, where pDðDÞ is the stationary-stat”
Measurement of particle accelerations in fully developed turbulence (2001, methodology): “Acceleration flatness Even though the convergence of the fourth moment is unclear (§ 4.1, Beck 2001b), it is interesting to quantify the degree of intermittency of the acceleration by calculating the acceleration flatness (〈a4i 〉/〈a2i 〉2) as a function of Reynolds number.”
Generalised information and entropy measures in physics (2009, neutral): “superstatistical systems [12,39,40].”
Experimental Lagrangian acceleration probability density function measurement (2003, methodology): “Among the large class of superstatistics [14], four specific examples have been proposed to model the observed acceleration PDF.”