Many text books claim that particles that obey Boltzmann statistics have to be indistinguishable in order to ensure an extensive expression for entropy. However a first principle derivation using combinatorics gives the Boltzmann only for distinguishable and the Bose Einstein distribution for indistinguishable particles (see Beiser, Atkins or my own text on Research Gate). Is there any direct evidence that indistinguishable particles can obey Boltzmann statistics?
Usually, division by N!, where N is the number of particles, is used as a correction factor to account for the number of configurations for indistinguishable particles obeying Boltzmann statistics. If the correction factor of N! is not used, the number of configurations would be too large by a factor of N! and the entropy too large by ln N! (= N ln N - N for large N). But this would not affect calculations of CHANGES in entropy of the N particles, since the same overestimate of the number of configurations too large by a factor of N! and of the entropy by ln N! (= N ln N - N for large N) would obtain for both the initial and final states.
Entropy: A concept that is not a physical quantity
https://www.researchgate.net/publication/230554936_Entropy_A_concept_that_is_not_a_physical_quantity
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