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## Main Question or Discussion Point

## Homework Statement

Confused about what a statistical ensemble actually means. Why does the ensemble have to have a uniform probability distribution at equilibrium? [If my definition of an ensemble is correct]

## The Attempt at a Solution

This is what I understand so far: [/B]

- For any given macrostate, there is going to be an associated set of microstates ( a region in phase space)
- If we look at a great number of systems started off with the same macrostate, under the same conditions, then if we looked simultaneously at all of them some time later you would have say, five in microstate 1, 2 in microstate 2 etc. etc.
- So in this way you have a probability distribution for the microstates [as a function of time] - is this what an ensemble is?
- But then why is it
*necessarily*true that at equilibrium the probability distribution must be uniform? I.e the ensemble doesn't change with time? - I can understand the logic for an
*isolated*system - but why does it hold in general?