Power-law distributions arise in colliding hard-sphere systems from Maxwell-Boltzmann when starting far from equilibrium, with scale-free intermediate dynamics and open scale-free boundaries.
The energy growth is exponential, rather than poly- nomial in time, leading to an exponential self-similarity in the time evolving DF
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On the transformation of the Maxwell-Boltzmann Distribution to a Power-Law
Power-law distributions arise in colliding hard-sphere systems from Maxwell-Boltzmann when starting far from equilibrium, with scale-free intermediate dynamics and open scale-free boundaries.