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I don't know, it looks like the conservation of mutual information is like the fact that entropy always remains constant or increases. This is true for the overall universe, but not true for individuals.

A human isn't some magical entropy reducer -- we reduce entropy in ourselves by increasing it elsewhere. I suspect mutual information works the same way.

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That is a good insight. The law does seem similar to the 2nd law of thermodynamics. The form of the free energy formula looks a lot like mutual information.

So, this could go two ways. Either humans are not net entropy reducers, and also not information creators. Or, they are information creators, and thus are net entropy reducers. Not sure there is evidence the latter is false.

A broader point is that regardless of whether the human mind is an entropy reducer, something in existence is an information creator/entropy reducer, otherwise we wouldn't have information/low entropy to begin with.

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