Stable Equilibrium Based on L\'evy Statistics: Stochastic Collision Models Approach
Statistical Mechanics
2009-11-10 v1
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 L\'evy 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.
Keywords
Cite
@article{arxiv.cond-mat/0310509,
title = {Stable Equilibrium Based on L\'evy Statistics: Stochastic Collision Models Approach},
author = {Eli Barkai},
journal= {arXiv preprint arXiv:cond-mat/0310509},
year = {2009}
}
Comments
PRE Rapid Communication (in press)