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I understand from the formula of Clausius idea of Entropy that the change in entropy in an adiabatic quasi-static process is zero. I do not understand, how we can explain the same idea from the Boltzman idea of entropy?

In an adiabatic quasi-static process, why the number of microstates does not change that the change the entropy is zero? And, why does the number of microstates change in an adiabatic free expansion that entropy in such a process changes?

How do we understand this phenomenon on the basis of Boltzman's Idea of Entropy i.e. "Number of Microstates"?

Kindly help.

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