Deriving the Fermi Distribution: Fixed Particle Canonical Ensemble

[aaaa202]

All derivations of the Fermidistribution uses a canonical ensemble with a chemical potential, which is the same as to say that the ensemble can exchange particles with a resevoir. But are the derivations still valid for the canonical ensemble with a fixed number of particles and why isn't this just used?

 

[DrDu]

The calculation of the grand-canonical partition function is much easier than calculation of the canonical one.
There is a folk theorem that all ensembles are equal in the large N limit, although there are counter-examples.
However, I strongly doubt that "All" derivations of the Fermi distribution use a grand-canonical ensemble.
E.g. I think Thirrings book "Quantum Mathematical Physics: Atoms, Molecules and Large Systems" contains a derivation using the canonical ensemble.