# Can I usefully interpret a non-unital completely positive (CP) map as a cooling process?

Non-unital completely positive (CP) maps take a maximally mixed quantum state (aka a normalized identity matrix aka an infinite temperature state) and map it to something else. This necessarily decreases its von Neumann entropy and, depending on how you define it, reduces its temperature.

Can a stronger connection be made between thermodynamics and CP maps? To what extent do non-unital CP maps reliably cool states that aren't infinite temperature?

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