Can classical thermic agitation modeled using QM?

Question

A number of people has considered probability clouds as the sign there was hidden variables determining actual motion and always definite positions of particles, as a thermal agitation. This question is not about suggesting an interpretation of QM but exactly the opposite: can QM be applied to the random agitation of, for example, molecules of air to model thermal agitation?

Answer 1

My answer deals with the case where you want to model the Brownian motion of an object, i.e. motion of a big object due to the thermal agitation of all the tiny particles surrounding it. If you want to know about modelling the motion of the said tiny particles, then I won't be any help.

To be more precise, the way statistical physics models thermal agitation is by representing all the tiny particles of the system by one random force applied on bigger objects, usually called the Langevin force. This corresponds to adding a random variable to Newton's second law:

$$ m \vec{a} = \sum \vec{F} + \vec{L}$$

with $\vec{L}$ a random vector.

Now a lot of the physics of the resulting motion depends on the properties of this random force. If you want to find the simplest Brownian motion, then $\vec{L}$ isotropic and with always the same norm is enough. But you can also have a probability distribution for the norm and thus have a more detailed description of the motion.

So this is where QM could be applied: use QM description of your tiny particles to get some information about the random force. The next step is, of course, to plug that random force in your model and forget all about the underlying quantum mechanics, but at least they were somewhere in the process.