Connection With Liouville's Theorem
We have
(the curly bracket is Poisson bracket) since is a function of H. Therefore, according to Liouville's theorem (Hamiltonian) we get
In particular, is time-invariant, that is, the ensemble is a stationary one.
Alternatively, one can say that since the Liouville measure is invariant under the Hamiltonian flow, so is the measure .
Physically speaking, this means the local density of a region of representative points in phase space is invariant, as viewed by an observer moving along with the systems.
Read more about this topic: Microcanonical Ensemble
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