Graduate Volume constraint in micro-canonical derivation of statistical physics

[Philip Koeck]

Another question about the use of the micro-canonical ensemble in deriving distributions.

On the Wikipedia-page the authors mention that the total volume of the system has to be constant.
See: https://en.wikipedia.org/wiki/Bose–Einstein_statistics#Derivation_from_the_microcanonical_ensemble

On the other hand this statement is not used as a constraint or in any other way that I can see.

In a way it would however make sense to introduce a volume constraint in order to make sure the system is closed.
If V is not constant (meaning W is not zero), but U is constant, then Q is not zero and the system is not closed (at least for an ideal gas).

Does anybody know about volume constraints in the microcanonical picture?

 

[Lord Jestocost]

In E = ∑n_iε_i one has generally E = ∑n_iε_i(N,V). Each ε_i changes in a continuous manner if V is vhanged infinetely slowly.

 

[Philip Koeck]

In E = ∑n_iε_i one has generally E = ∑n_iε_i(N,V). Each ε_i changes in a continuous manner if V is vhanged infinetely slowly.

So the volume constraint is not used explicitly, but if the energy levels e_i depend on the volume then the assumption of fixed energy levels implies a constant volume.
Is that correct?

 

[Lord Jestocost]

One can see it in this way.