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We know that we can quantify the degree of irreversibility of a quantum process using the entropy production rate of the same process. But sometimes it seems that the very fact that information has been lost in an irreversible way might be advantageous.

For instance we know that there is a way in which coherence plays a role in the entropy production, which in itself is a quantity measuring the degree of irreversibility.

Also, we know that some quantum information processing tasks (CHSH game) may depend on the degree of irreversibility in a crucial way.

With all this in mind I wonder if the following exists:

Question: Is there some resource theory of irreversibility? In particular could be one that strictly mentions entropy production in quantum thermodynamics. Or for instance one that uses the erasure of (quantum) bits of information.

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