Recently I asked a question about the relationship between Von Neumann entropy and heat transfer. The link is here.
I feel as though the answer is not quite so clear so I will ask a couple of questions that I think may essentially be the same question as this previous one or, if these new questions aren't the same as the old question, your answers will help me clarify some key points.
Original question: Is the change in Von Neumann entropy related to heat transfer? I think I can rephrase and ask if information theory can explain heat transfer in terms of evolving information.
New Question #1:
The Wikipedia page "Maximum entropy thermodynamics" says under "Second Law": (paraphrased) Liouville's equation shows how the phase space evolves from a maximum entropy distribution to one that is not necessarily maximum entropy, yet the thermodynamic entropy is certainly maximized.
Does this mean what I think it does: that the evolution of information entropy and thermodynamic entropy are not the same? When I see people comparing information and thermodynamic entropy they always do it for a single state. But I don't think I've ever seen a discussion of whether, if the state evolves, the two entropies evolve to the same value. The Wiki article suggests to me that they don't. So, if they don't behave exactly the same, aren't they different things?
Here's the link: https://en.wikipedia.org/wiki/Maximum_entropy_thermodynamics
New Question #2:
Another Wiki article "Entropy in thermodynamics" says, under "Criticisms": (paraphrased) information has no concept of temperature or energy so thermodynamic and information entropies are not the same. Does anybody disagree with this?