TITLE: Entropy increase vs Conservation of information (QM)
QUESTION [19 upvotes]: Unitarity of quantum mechanics prohibits information destruction. On the other hand, the second law of thermodynamics claims entropy to be increasing. If entropy is to be thought of as a measure of information content, how can these two principles be compatible?

REPLY [0 votes]: I wrote an article exactly on that question ! https://aurelien-pelissier.medium.com/on-the-conservation-of-information-and-the-second-law-of-thermodynamics-f22c0645d8ec
To make it short, the entropy (or information) constrained by Liouville’s theorem is not the same as the entropy that the Second Law is talking about. The latter is talking about the amount of hidden information (information that is inaccessible to macroscopic measurements), while the former is the total information content of a system. Or in other words, the irreversibility of thermodynamics is a statistical effect and does not conflict the reversibility of classical /quantum mechanics.
To go a bit further, these have to do with the differences between the fine-grained and the coarse-grained entropy of the system. Von Neuman entropy is typically fine grained, so it stays constant in a closed system. On the other hand, the second law states that the coarse grained entropy of a closed system increases.
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