# How to understand particle decoupling in the early universe?

We often say that when the rate of some interactions, say the beta decay and electron capture, are slower that the rate of universe's expansion, then the corresponding particles, say neutrinos, decouple.

I just want to know whether such statement based on some concrete mathematics, for instance, QFT in curved spacetime? If the interactions are just classical diffusion, such statement is easy to understand, but for the quantum fields, what's the picture?