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Comment on "Fluctuation theorem for hidden entropy production"

Recently, Kawaguchi and Nakayama (KN) [Phys. Rev. E {\bf 88}, 022147 (2013)] showed that the hidden entropy production associated with a coarse-graining procedure obeys the integral fluctuation theorem (IFT) if the original process does not involve any odd-parity variable that changes its sign under time reversal. This was interpreted as the evidence that odd-parity variables play an important role in the derivation of irreversible stochastic dynamics from time-reversible deterministic dynamics. In this Comment, we show that KN's approach is inadequate for describing the origin of irreversible stochastic dynamics, which calls into question whether odd-parity variables are required for the emergence of macroscopic irreversibility.