I am messing around with classical gasses using a demon algorithm, trying to reproduce the behavior of ideal gasses in various situations. Exitingly, this is working very well. Here are my findings so far: Classical gas, 3D : E=1.497 NkT - the usual 3/2 NkT result Classical gas, 2D : E=0.989 NkT - 2 DoF, so 2/2 NkT Relativistic gas, 3D : E = 2.992 NkT - as expected, can be derived from equipartition Classical gas, uniform gravitational field, 3D : E = 2.486 NkT Now the last one quite surprises me. Why is that he case? Intuitevely I would expect 3 DoF on |p| and 3 DoF on x, so 6*1/2 NkT = 3NkT. Is there a hidden constraint?