Steady-state Velocity Distribution of Neutral Atoms with Energy Dissipation

Collisional thermalization of a particle ensemble under energy dissipation can be seen in a variety of systems, such as neutral particles in plasmas and granular particle systems. Despite its universal existence, analytical descriptions of the steady-state distribution have been missing. Here, we show that the steady-state energy distribution of a wide class of nonthermal system with energy dissipation can be well approximated by a generalized Mittag-Leffler distribution, which is a stable distribution. This distribution has a power-law tail, similar to Levy's stable distribution, the index of which is related to the relative significance of the energy dissipation rate against the entropy production by elastic collisions. We demonstrate its universality by comparing with a molecular-dynamics simulations as well as spectroscopic observations of the atom velocity distribution in a low-temperature plasma.