I\'m preparing my statistical physics course, and while writing the lecture note

Question

I'm preparing my statistical physics course, and while writing the lecture notes it says that a system with non distinguishable particles has much less microstates asociated with a particular macrostate. Hence, a system with distinguishable particles has much more microstates asociated with a particular microstate. Entropy S is related with the number of microstates ? via:

S=kln(?)

where k is Boltzmann's constant. Then my question is

Given the same macrostate for both systems, the entropy of the first is much lower than the entropy of the second?

Thanks for your time.

Explanation / Answer

In the microcanonical ensemble, the probability of each microstate is assumed to be the same. In this case, the Gibbs entropy formula reduces to Boltzmann

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