Question about applying the Pauli Exclusion Principle

[henryc09]

The principle states that no two identical fermions in a system can be in the same quantum state, but what I don't fully understand is how you define a "system". For example when you apply statistical thermodynamics to a gas of non-interacting fermions you say that a maximum of one can occupy each single particle state. Maybe I'm confused or forgetting something important but I don't see why you couldn't consider all fermions of a particular kind in the universe as a system of non-interacting particles in the same way and conclude that none of them can share a single particle state.

 

[xts]

Of course, you may consider a whole Universe as a system. Pauli's 'system' was introduced just to abstract of spatial relations. Or to reduce those spatial relations to something feasible for calculations (like atomic orbitals)

 

[tom.stoer]

In the abstract Dirac notation no spatial relations are required. Writing down a fermionic quantum state satisfies the Pauli principle by construction (or by the formalism). And of course it applies to the universe as a whole.