Stable equilibrium based on Lévy statistics: Stochastic collision models approach

2003/10/22 by Eli Barkai · 5 citations
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Fractional Differential Equations Solutions #Statistical Mechanics and Entropy #cond-mat.stat-mech

paper · pdf · doi:10.1103/physreve.68.055104

published as Phys. Rev. E. Rapid Communication, {\bf 68} 055104(R) (2003) · PRE Rapid Communication (in press)

arxiv created 2003/10/22 · openalex publication_date 2003/11/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate equilibrium properties of two very different stochastic collision models: (i) the Rayleigh particle and (ii) the driven Maxwell gas. For both models the equilibrium velocity distribution is a Lévy distribution, the Maxwell distribution being a special case. We show how these models are related to fractional kinetic equations. Our work demonstrates that a stable power-law equilibrium, which is independent of details of the underlying models, is a natural generalization of Maxwell's velocity distribution.

Citations

• The random walk's guide to anomalous diffusion: a fractional dynamics approach

Cited by

• On the higher order corrections to the Fokker–Planck equation
• Inelastically scattering particles and wealth distribution in an open economy
• A theory of non-local linear drift wave transport
• On anomalous diffusion in a plasma in velocity space
• Anomalous diffusion in systems driven by the stable Lévy noise with a finite noise relaxation time and inertia