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If you are not careful, answers you get for statistical physics entropy disagree with the thermodynamic result (the classic example is removing the partition between two identical boxes of gas). The resolution is usually to claim that this is evidence for QM: in QM, identical particles are indistinguishable, and this changes the multiplicity by a factor $1/N!$.  Do we believe this invocation of QM into a classical theory? Where It seems very {\it ad hoc}.Where  else does it appear? What about phase-space quantisation, where a factor of $1/\hbar^3$ accompanies the integrals over phase space? What happens for smaller $N$ when Stirling's approximation is not applicable?