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Collisional thermalization of a particle ensemble under the energydissipation can be seen in variety of systems, such as heated granular gassesand particles in plasmas. Despite its universal existence, analyticaldescriptions of the steady-state distribution have been missing. Here, we showthat the steady-state energy distribution of the wide class of collisionalenergy cascades can be well approximated by the generalized Mittag-Lefflerdistribution, which is one of stable distributions. This distribution has apower-law tail, as similar to Levy's stable distribution, the index of which isrelated to the energy dissipation rate. We demonstrate its universality bycomparing Mont-Carlo simulations of dissipative gasses as well as thespectroscopic observation of the atom velocity distribution in alow-temperature plasma.

Stable Energy Distribution of Weakly Dissipative Gasses under Collisional Energy Cascades