Important Things to Note:
It is extremely important to be able to tell the difference between the canonical ensemble and the GRANDcanonical ensemble.
In a nutshell:
In the canonical ensemble, we’re looking at a small system in a heat bath. This small system can exchange energy with the outside but it cannot exchange particles with it. In the grand canonical picture we break that and allow exchange of particles with the heatbath. In addition, we say that there’s a chemical potential term in our total energy due to our particles hitting each other.
Even though we came up with the grand canonical ensemble to work with particle exchange, we will very often use it even in situations where there is NO particle exchange with the heat bath because it’s so much easier to work with.
Understand EVERY WORD of these:
Grandcanonical Ensemble Notes from Professor Mona Berciu at University of British Columbia
(Try not to be discouraged. The grand canonical ensemble is probably the most difficult to understand, but it’s used for bose gases, photons, and fermions.)
Most important Problems & Solutions:
(Strangely there’s not a lot of Grandcanonical problems on the internet..This is the only one I can really find.)