2-dimensional Lennard-Jones gas:

N interacting particles in a periodic box

N=2: Velocity space is 4-dimensional, with a 3-dimensional energy "surface".

N>2: Velocity space has 2N dimensions. The statistical distributions evidently approach the large-N limits.
In particular, the velocity density p(vx) already resembles a Gaussian. Note that the 2D Maxwell distribution starts out linearly (not parabolically as in 3D).

[Code: LJones, still under construction]