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In classical statistical mechanics, it is often argued that, when computing the partition function, states are overcounted if particles are identical/indistinguishable, thus the result has to be divided by $N!$ to account for the overcounted states. My question is, will this indistingushability affect macroscopic results? Will the equations of states or any macroscopic quantities behave differently if I treat my particles as distinguishable during the calculations?

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    $\begingroup$ You may want to see this beautiful piece by Jaynes: damtp.cam.ac.uk/user/tong/statphys/jaynes.pdf $\endgroup$
    – user207248
    Oct 4, 2019 at 16:36
  • $\begingroup$ it affects hypersonic shock waves on planets that don't have $X_2$ atmospheres, and is rumored to be why our unguided Mars landers went long for while (using Apollo code), but I've never been able to find an open reference. $\endgroup$
    – JEB
    Oct 4, 2019 at 16:43
  • $\begingroup$ Here is a beautiful paper that discusses the Gibbs paradox and related (in)distinguishability issues in the context of experiments with colloids: the latter are "macro"-particles, and thus fundamentally distinguishable. But we might or might not have information that distibguishes between the particles. This existence of lack of information has experimental consequences. arxiv.org/pdf/1507.04030.pdf $\endgroup$
    – Ori
    Nov 14, 2019 at 16:50

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