From the popular summary of my paper with Arshag and Mark, “Thermodynamic constraints on quantum information gain and error correction” just published on PRX Quantum.

It is now widely accepted that Maxwell’s demon does not, in fact, break the second law of thermodynamics, if the energetic cost of resetting its memory is taken into account. This resolution of the paradox is known as Landauer’s principle.

In this work, we delve into the inner workings of Maxwell’s demon by considering how it behaves in the quantum error correction setting. We show that Landauer’s principle is only the limiting case of a more general triple trade-off relation between the thermodynamic, information-theoretic, and logic performances of the demon. For example, we show that for most measurements that the demon can perform, extracting work above the Carnot limit is penalized by a drop in the error correction fidelity. Moreover, when the demon successfully performs perfect error correction, work extraction above the Carnot limit becomes impossible with most quantum measurements. Finally, we realize that the amount of information that the demon can extract about the error type is bounded from above by the dissipated heat during that process. Interestingly, this also gives physical meaning to negative values of this information gain.