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In a recent paper [1], Sasa, Hiura, Nakagawa, and Yoshida showed that anatural extension of the minimum work principle to small systems uniquelydetermines the factor $N!$ that arrises in relations connecting statisticalmechanical functions (such as the partition function) and thermodynamicfunctions (such as the free energy). We believe that this provides us with theclearest answer to the "puzzle" in classical statistical mechanics that goesback to Gibbs.  Here we attempt at explaining the theory of Sasa, Hiura, Nakagawa, andYoshida [1] by using a process discussed by Horowitz and Parrondo [2] in adifferent context. Although the content of the present note should be obviousto anybody familiar with both [1] and [2], we believe it is useful to have acommentary that presents the same theory from a slightly different perspective.  The present note is written in a self-contained manner. We only assume basicknowledge of classical statistical mechanics and thermodynamics. Wenevertheless invite the reader to refer to the original paper [2] forbackground, references, and related discussions, as well as the originalthoughts.

The best answer to the puzzle of Gibbs about $N!$!: A note on the paper by Sasa, Hiura, Nakagawa, and Yoshida