[amluto]

Since you bring up physics, this has a name: the Maxwell-Boltzmann distribution. You might have trouble getting physicists to describe particles as “gravitating” to it, though — the particles are doing their own thing, and this is the resulting probability distribution.

But this is only for distinguishable particles. If you have a bunch of indistinguishable particles, you get the Fermi-Dirac distribution or the Bose-Einstein distribution, depending on whether they are fermions or bosons.

You can find all of these distributions on Wikipedia.