Quote Originally Posted by OngBonga View Post
Nice correction, I have no idea what you just said! I guess I'm imagining this is a classical sense, like there's lots of tiny little balls flying around, colliding. In this instance, everything would settle to the same speed, as eventually all the balls' speeds would average out as the fast ones continually lose energy to the slow ones. Of course, atoms are not tiny little balls, so it's no real surprise that my analogy is flawed.
I'm fairly certain the Boltzmann distribution is known from classical physics, meaning known prior to quantum mechanics, so it's about tiny balls flying around, not wave functions.

I'm actually having trouble visualizing why it's not a stable equilibrium if everything's moving the same speed, and I'm not sure which of my assumptions is giving me grief.

A) we can't assume perfectly elastic collisions, because in that case, the final speeds are equal to the initial speeds, just swapped, so there is no tendency toward the mean. Like a Newton's cradle desk toy. The falling ball hits the other ball and stops, and another ball swings away. The final picture is just a mirror image of the initial picture.

So what does that mean? Nothing shakes the foundation of Conservation of Momentum, but there's no Conservation of Kinetic Energy, only total energy. Kinetic energy is only conserved in purely elastic collisions.

So where else can the energy go? In a molecule, there are modes of vibration and rotation that express energy, so a collision can result in lower translational kinetic energy, if there is higher vibrational or rotational energy.

But what about single atoms, not in molecules? Like the noble gasses? This is where I get tripped up. They don't have any spacial assymetries to exploit for vibration or rotation, the only have their translational energy. I'm not talking about electrons changing energy levels, that's QM stuff. We're still classical, so forget that.

I'm certain that the velocities tend toward a Boltzmann distribution at thermal equilibrium, but I'm not really sure how they're trading momentum but not energy in the collisions. I.e. I know they can't be perfectly elastic collisions, but I'm not sure what energy transformation is allowing them to fail to conserve kinetic energy.