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How much effort do we have to put into measuring properties to distinguish it from something similar? How does this balance with the extractable work?  \subsection{Counting microstates: thermodynamic entropy thermodynamics  versus statistical physics entropy} physics}  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 $1/N!$.