here's something that's been bothering me for a while now:

We know the Pauli exclusion principle states that 2 Fermions cannot be in an identical state.

So then we have systems like solids or free electron gases, and we calculate and form Fermi-Surfaces, based on the fact that the electrons are being distributed to different states.

What I don't understand is - what defines a "system" in which this principle holds?

We could have another gas next to our gas, and the electrons would once again take the states from ground state up.

So how does a physical system "know" its a system, such that two electrons in it cannot have the same states? What if I have two "distinct" electron gasses and suddenly i instantaneously mix them? Would then half of the electron take hold of higher energy states in an instant?

I hope the question isn't vague.

Thanks a lot!

Tomer.