As it happens, if you want to draw the boundary to exclude me, then the two-gas-system-without-pump also happens to be entropy increasing...
This is what I'm disputing you can get if you treat entropy as subjective uncertainty, while also assuming that the only way to update subjective uncertainty is Bayesian conditionalization. Perhaps you can explain how the two-gas system turns out to be entropy increasing on that viewpoint if you draw the boundary to exclude the observer. How does the entropy of the probability distribution describing the system increase?
"The entropy of the probability distribution describing the system" only has meaning if there is an observer to actually hold that probability distribution. Since probability is in the mind, there is no fixed external thing that just "is" the probability distribution of the system.
There are two distinct things; one is "the system" and the other is "the probability distribution over states of the system." If you make an idealization and do math just on "the system" then the distributions in those idealizatio...
Link to the Question
I haven't gotten an answer on this yet and I set up a bounty; I figured I'd link it here too in case any stats/physics people care to take a crack at it.