variance of Maxwell Boltzmann energy distribution?

Answer 1

Sure, under non-equilibrium conditions. Remember the Maxwell-Bolzmann energy distribution is only fixed at equilibrium...and thus the concept of "temperature" is only valid under equilibrium conditions.

However, under pseudo-equilibrium conditions you can see a variance. You may get one "temperature" for translational energy, and different (higher) "temperatures" for rotational and vibrational energies.

You can see this in supersonic expansions of gases into a vacuum. The collision rate drops so rapidly that the higher "temperatures" of the rotational and vibrational energies are frozen in...no collisions are available to establish a true equilibrium w/ the translational energies.