Connecting the microcanonical with the (grand) canonical ensemble

[vanhees71]

I don't know. I'd say, just post such an "intro posting" and see what happens.

 

[Philip Koeck]

I don't know. I'd say, just post such an "intro posting" and see what happens.

It's started.

 

[Demystifier]

Then I'll go a step further and decide that the system should consist of a single atom.

It doesn't matter whether the number of particles is $N=1$ or $N=10^{23}$. One has to distinguish the number of particles in the system (which doesn't need to be large), from the number of systems in the ensemble (which must be large). In the Gibbs theory of ensembles, an ensemble is a fictitious ensemble; it's a thing we imagine to conceptualize the notion of probability. For example, you can say that the probability of a single coin to be in the heads state is 1/2, but to conceptualize this you can imagine that you flipped this single coin a 1000 times.

That being said, once you said that $N$ is fixed ($N=1$ in your case), you can talk about a canonical ensemble, but not about a grand-canonical ensemble.