Wave mechanics vs Statistical Mechanics

[Jimster41]

Is it accurate to say that interference cannot happen in Statistical Mechanics? I know it is considered a wave mechanics phenomenon but aren't waves just highly statistical ensembles, like anything else?

I always thought that Fourier says periodic spectra could be summed to create any signal. As such any distribution is a sum of "waves", and vice versus.

 

[BvU]

Interference doesn't play a role in Statistical Mechanics (at least as far as I remember, but if it does, it's not as central as in wave mechanics). To say it cannot happen is weird. Where does this question come from ?

And yes, Fourier decomposition is a change of basis that goes from one basis to describe a function to another. Both bases are complete and orthogonal.

 

[Jimster41]

Thanks. I don't think it is central to the thread below at all. It did confuse me though. I think I lean pretty heavily on the picture I have of the series-to-frequency dual, especially when trying to follow conversations about QM. I can picture a set of composite "waves" that are randomly different from each other except for one frequency component. I had this cartoon of the Rogue Wave phenomenon. It seemed totally legitimate to me to picture them as a set of statistical ensembles that "interfere" specifically. But maybe that is not a good way to remember it.

https://www.physicsforums.com/threads/basic-questions-about-decoherence.827771/#post-5200884

 

[BvU]

I see where it comes from. Ask Bhobba, he seems to be a lot better equipped than I am (did QM and Stat Mech but never had to worry about interference in the latter).