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

The stable equilibrium properties based on Lévy statistics for the devising of stochastic collision models were investigated. The two stochastic collision models were the Rayleigh particle and the driven Maxwell gas models. The velocity distribution for both the models was a Lévy distribution, with the the Maxwell distribution being a special case. The relation of these models with fractional kinetic equations was explored. The study demonstrated a stable power-law equilibrium as a natural generalization of Maxwell's velocity distribution.