Stable equilibrium based on Lévy statistics: Stochastic collision models approach.

@article{Barkai2003StableEB,
  title={Stable equilibrium based on L{\'e}vy statistics: Stochastic collision models approach.},
  author={Eli Barkai},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2003},
  volume={68 5 Pt 2},
  pages={
          055104
        }
}
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… CONTINUE READING