It is often said that the paradox of “Maxwell’s demon” is resolved by including the thermodynamic costs of measurement and memory erasure. The common claim is that these costs offset the demon’s apparent violation of the second law of thermodynamics, thereby restoring its validity. The truth, however, is quite the opposite: the fact that the costs of measurement and erasure offset the demon’s violation is a consequence of assuming that the second law is valid in the first place. In other words, it is the assumption of the validity of the second law that forces this equilibrium, not the other way around!

This realization, which echoes the thesis of Earman and Norton, came while studying some not-so-recent-anymore but still quite influential papers on quantum feedback protocols in quantum thermodynamics. While the narrative there adhered to the usual folklore on the subject (i.e., that quantum feedback protocols obey the second law whenever the thermodynamic costs of measurement and erasure are properly accounted for), what we found instead was quite different: quantum theory is in fact completely independent of the second law of thermodynamics! And it couldn’t be otherwise, simply because quantum theory has no built-in thermodynamics. There is no “quantum bullet” to exorcise Maxwell’s demon. In fact, in our work we explicitly constructed a model of a measurement and feedback process that violates the bounds required by the second law, even after including all costs (i.e., measurement and erasure costs) in the thermodynamic balance.

However, we also found that although quantum theory can violate the second law, it does not need to: any quantum process can be realized in a way that does not violate the second law of thermodynamics, simply by adding more systems (bath, battery, and so on) until the thermodynamic balance is restored.

There are two main takeaways from this story. First, even in quantum theory, it is the second law that guarantees the balance between gains and costs in feedback protocols, not the other way around. Second, although quantum theory and the second law of thermodynamics are logically independent, they can peacefully coexist. The second law of thermodynamics does not impose any hard constraints on what can be achieved in quantum theory: there is always a way to ensure compliance with the second law.

In conclusion, by no means can we claim that quantum theory is “demon-proof” by design. However, we now have a much clearer understanding of how quantum feedback protocols work, what they can and cannot do. The paper appeared today on npj Quantum Information but I like the look of the arXiv version better.