In [1], it is claimed that entropy decreases can occur, but that any such decrease necessarily coincides with an erasure of memory. It is argued that this resolves the directionality of the arrow of time, since we can only ever have records of entropy increasing events. Specifically, a memory of an event E is defined [1] as a physical system A that has a nonzero classical mutual information with a system C that bears the consequences of event E.

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Given this setting, the principal claim in [1] is that ‘‘any decrease in entropy of a system that is correlated with an observer entails a memory erasure of said observer’’ (*). In a classical setting, (*) is true by definition of the entropies— classical events involving the reduction of local entropies trivially coincide with a reduction of memory records, since these are defined as the classical correlations between the memory system A and system C. However, the extension of the argument to all quantum mechanical states, where there is a much richer correlation structure, is nontrivial.

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First and foremost, we point out that demanding an entropy-decreasing event E is very different from demanding an event in which all correlations are eliminated. In the central proof of [1], the author mistakenly assumes the elimination of all correlations, when in fact his actual focus is that of entropy decreasing events. Clearly given a complete elimination of correlations, memory erasure occurs by assumption, and so for this highly atypical (measure zero) case, the argument is tautological. For the correct case in question (the set of entropy decreasing events), we can show that the central claim (*) of [1] is false by presenting a simple counterexample.

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In a sense, we see that instead of quantum mechanics resolving the fact that we have no classical memory records of entropy-decreasing events, it actually makes the ssue worse.