Stable Equilibrium Based on Lévy Statistics: Stochastic Collision Models Approach

Details Stable Equilibrium Based on Lévy Statistics: Stochastic Collision Models Approach Stable Equilibrium Based on Lévy Statistics: Stochastic Collision Models Approach

2003-10-22

arxiv.org/abs/cond-mat/0310509v1

Phys. Rev. E. Rapid Communication, {\bf 68} 055104(R) (2003)

Physics

Condensed Matter

Statistical Mechanics

PRE Rapid Communication (in press)

Scientific paper

10.1103/PhysRevE.68.055104

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 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.

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