From theory, we know that Boltzmann entropy for a given distribution, defined through a set of occupancy numbers {ni}, of the macrostate M, is given by:(adsbygoogle = window.adsbygoogle || []).push({});

S=k log(Ω{ni})

where omega is the number of microstates for the previously given set of occupancy number, {ni} . Assuming that the system is in equilibrium, we get omega to be predominantly the number of microstates which fill up the entire 6ND gamma space.

Using counting principles in the 6 dimensional mu space we get omega to be equal to product(1/[factorial(ni)]).

My question is would interchanging particle labels (such that {ni} does not change) result in a new microstate? If yes, it means that particles are no longer indistinguishable. If no, then entropy becomes zero since there is just 1 microstate for the given {ni} in gamma space.

I would appreciate if anyone clears this doubt.

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# Boltzmann Entropy for micro state or macro state?

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