I think you're getting several things wrong here.
because the classic result assumes zero correlation between where any two molecules are, and once any kind of significant density difference exists between the two sides of the volume this will break.
The assumption of zero correlation is valid for ideal gases. It will not break if there is a density difference. We're talking about statistical correlation here.
Entropy is as real as energy whether it feels that way or not, and that is why machines work even when left unattended by consciousnesses to perceive their entropy and its flows.
"Entropy is in the mind" doesn't mean that you need consciousness for entropy to exist. All you need is a model of the world. Part of Jaynes' argument is that even though probabilities are subjective, entropy emerges as an objective value for a system (provided the model is given), since any rational Bayesian intelligence will arrive at the same value, given the same physical model and same information about the system.
because the classic result assumes zero correlation between where any two molecules are, and once any kind of significant density difference exists between the two sides of the volume this will break.
The assumption of zero correlation is valid for ideal gases. It will not break if there is a density difference. We're talking about statistical correlation here.
Statistical independence means the chance that a molecule is at a particular spot depends not at all on where the other molecules are. Certainly if the molecules never hit each other, they only...
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
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