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Related papers: Superstatistics for fractional systems

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The invariant distribution, which is characterized by the stationary Fokker-Planck equation, is an important object in the study of randomly perturbed dynamical systems. Traditional numerical methods for computing the invariant distribution…

Computational Physics · Physics 2021-10-25 Bo Lin , Qianxiao Li , Weiqing Ren

Generalized superstatistics, i.e., a "statistics of superstatistics," is proposed. A generalized superstatistical system comprises a set of superstatistical subsystems and represents a generalized hyperensemble. There exists a random…

Statistical Mechanics · Physics 2011-11-30 Denis Nikolaevich Sob'yanin

In this paper, we propose a novel method to approximate the mean field stochastic differential equation by means of approximating the density function via Fokker-Planck equation. We construct a well-posed truncated Fokker-Planck equation…

Numerical Analysis · Mathematics 2025-03-25 Jinhui Zhou , Yongkui Zou , Shimin Chai , Boyu Wang , Ziyi Tan

Nowadays, there is a series of complexities in biophysics that require a suitable approach to determine the measurable quantity. In this way, the superstatistics has been an important tool to investigate dynamic aspects of particles,…

Statistical Mechanics · Physics 2020-02-26 Maike A. F. dos Santos

The Fokker-Planck equations describe time evolution of probability densities of stochastic dynamical systems and are thus widely used to quantify random phenomena such as uncertainty propagation. For dynamical systems driven by non-Gaussian…

Dynamical Systems · Mathematics 2015-06-04 Xu Sun , Jinqiao Duan

A recently introduced nonlinear Fokker-Planck equation, derived directly from a master equation, comes out as a very general tool to describe phenomenologically systems presenting complex behavior, like anomalous diffusion, in the presence…

Statistical Mechanics · Physics 2009-11-13 Veit Schwammle , Evaldo M. F. Curado , Fernando D. Nobre

We propose a systematic method to derive the asymptotic behaviour of the persistence distribution, for a large class of stochastic processes described by a general Fokker-Planck equation in one dimension. Theoretical predictions are…

Statistical Mechanics · Physics 2009-10-31 Jean Farago

A new formalism is presented for finding equilibrium distribution functions for axisymmetric systems. The formalism, obtainded by using the concept of fractional derivatives, generalizes the methods of Fricke (1952), Kalnajs (1972) and…

Astrophysics · Physics 2009-06-14 Juan F. Pedraza , Javier Ramos-Caro , Guillermo A. Gonzalez

Superstatistics is a superposition of two different statistics relevant for driven nonequilibrium systems with a stationary state and intensive parameter fluctuations. It contains Tsallis statistics as a special case. After briefly…

Statistical Mechanics · Physics 2009-11-10 Christian Beck

In the present article the author extends the Fourier transform to a more general class of functions; First to power-law functions with integer and half-integer exponents then to the widely used quantum statistics function (Fermi-Dirac and…

General Mathematics · Mathematics 2019-12-30 Cyril Belardinelli

Fractional Fokker-Planck equation plays an important role in describing anomalous dynamics. To the best of our knowledge, the existing discussions mainly focus on this kind of equation involving one diffusion operator. In this paper, we…

Numerical Analysis · Mathematics 2021-09-08 Jing Sun , Weihua Deng , Daxin Nie

To describe the nonequilibrium states of a system we introduce a new thermodynamic parameter - the lifetime (the first passage time) of a system. The statistical distributions that can be obtained out of the mesoscopic description…

Chemical Physics · Physics 2007-05-23 V. V. Ryazanov

Fractional calculus allows one to generalize the linear, one-dimensional, diffusion equation by replacing either the first time derivative or the second space derivative by a derivative of fractional order. The fundamental solutions of…

Statistical Mechanics · Physics 2007-05-23 Francesco Mainardi , Paolo Paradisi , Rudolf Gorenflo

Dynamics of complex systems is often hierarchically organized on different time scales. To understand the physics of such hierarchy, here Brownian motion of a particle moving through a fluctuating medium with slowly varying temperature is…

Statistical Mechanics · Physics 2014-02-14 Sumiyoshi Abe

A formalism for quantum many-body systems is proposed through a semiclassical treatment in phase space, allowing us to establish a stochastic thermodynamics incorporating quantum statistics. Specifically, we utilize a stochastic…

Statistical Mechanics · Physics 2024-12-23 Zhaoyu Fei

The dynamics of temperature fluctuations of a gas of Brownian particles in local equilibrium with a nonequilibrium heat bath, are described using an approach consistent with Boltzmann-Gibbs statistics (BG). We use mesoscopic nonequilibrium…

Statistical Mechanics · Physics 2009-11-13 R. F. Rodriguez , I. Santamaria-Holek

The focus of our study in this paper is on the active dynamics and a fractional generalized Langevin equation with a memory kernel K(t). The Fokker-Planck equation is obtained by deriving it from a second-order differential equation. The…

Statistical Mechanics · Physics 2024-12-17 Yun Jeong Kang , Kyungsik Kim

We propose a framework for fitting fractional polynomials models as special cases of Bayesian Generalized Nonlinear Models, applying an adapted version of the Genetically Modified Mode Jumping Markov Chain Monte Carlo algorithm. The…

Methodology · Statistics 2023-05-26 Aliaksandr Hubin , Georg Heinze , Riccardo De Bin

We improve the standard theory of collisional stellar systems by considering the presence of a continuous mass distribution. The calculus of the diffusion coefficients is generalized and a new expression of the Fokker-Planck equation is…

Astrophysics of Galaxies · Physics 2022-12-20 Marco Merafina , Matteo Teodori

This contribution presents a derivation of the steady-state distribution of velocities and distances of vehicles in freeway traffic which has been suggested for the evaluation of interaction potentials among vehicles (see preprint…

Statistical Mechanics · Physics 2007-05-23 Dirk Helbing , Martin Treiber