[mannykannot]

> If that doesn't, I'm not sure what would.

It is not clear to me in which direction you think the question would be resolved, given a situation in which it would be possible to empirically demonstrate that the proponent of the lower figure (for S) was wrong. Maybe that is because I do not see the connection between your thought experiment and this issue: neither of the candidate values for S entail a particular distribution of states, let alone a particular sequence of future times when a molecule will approach the gate in a particular direction.

As I see it, your experiment is a difficult-to-perform way to demonstrate that, due to the inherent randomness of thermal processes, the entropy of a closed system may decrease when the conditions are right. This is explicitly covered in the article (see also "Monkeys typing Hamlet.")

Furthermore, in the case where the microstates of the system are measured in detail and the arrival times and velocities of the molecules at the gate are computed, one must add in the change in entropy resulting from those measurements and calculations. I am pretty sure this has been done, and is in accordance with the 2nd. law.

Your definition of 'subjective' in your penultimate paragraph is contrary to both common usage and what is being discussed in this thicket of threads, and appears to be closer to 'stochastic'. The outcome of the spin of a roulette wheel does not become subjective when different gamblers place different bets on it, or even when someone who has recorded statistics for its outcomes is able to place better-than-random bets.