The Von Neumann entropy of a QM system, as far as I understand it, is a measure of the information a particular observer has about that system. Is this definition of entropy directly related to heat transfer in a sense analogous to the classical viewpoint where $\Delta S\geq\frac{Q}{T}$ ?
Note that I'm not asking about the equivalence of the mathematical form. My question is whether the amount of information one has affects the evolution of the system i.e., would the physics between two truly identical states (assuming that's even possible) be different if the level of knowledge of its starting conditions was different between the two?
In the classical sense, information is an accounting tool and it doesn't affect how the state evolves over time. Also in the classical sense, entropy may be discussed among physicists and amateurs like me as akin to the amount of knowledge one has of the state but, as I just mentioned, physics doesn't care about how much information there is. Information is not a physical quantity, but entropy clearly is.
This Nature News article suggests there isn't an academic consensus answering the question I posed. I want to see what this community has to say.
http://www.nature.com/news/battle-between-quantum-and-thermodynamic-laws-heats-up-1.21720
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