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Boltzmann Entropy for micro state or macro state?

by bikashkanungo
Tags: boltzmann, entropy, macro, micro, state
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Dec21-12, 08:36 AM
P: 9
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:
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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Dec21-12, 09:08 AM
P: 789
I think energy does not completely define a microstate. Momentum does. So each energy state has a number of momentum states and these particles are distinguishable by their momentum (but again, not by any "identity"). You have to take this degeneracy into account.

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