Is the second law of thermodynamics routinely violated?

[Max_S]

@Half_Man_Half_Wit

Yes, this is basically right. And for a large enough number of marbles, what’ll happen is that the observer will observe a transition to uniform grey in every case they do the experiment, since the likelihood of the colors separating will decrease with the number of marbles. Thus, at some point, if they do the experiment 10, or a hundred, or a 1000, or a billion times, they won’t observe a violation of the law ‘the system tends to greyness’ with any appreciable probability. Agreed?

If by ‘the system tends to greyness’ you mean “black and white, if brought into contact, eventually even out to a uniform gray”, I disagree, the probability of a violation is exactly 100%. The colors of the two boxes never “eventually even out to a uniform gray”, and our observer will notice a violation if he is allowed to observe the full period of the system. In the likely case that at least one marble from either box moves into the other box, one or both boxes will always be changing color. There can never be equilibrium at any particular shade of grey. If you assume equal aggregate velocities of marbles in each box, the system should cumulatively spend half of its period widening the color gap and half of its period shrinking the color gap between its two halves.

If by ‘the system tends to greyness’ you mean the disparity in color between the left and right boxes will always decrease over time, again this is disproven with 100% probability so long as the observer has enough time to watch the system.

If by ‘the system tends to greyness’ you mean ‘after removing the wall, each box will usually be some shade of grey as opposed to absolute black or white’, I have no qualms. But that is not a law.

@Half_Man_Half_Wit

This is in contradiction to the system as I set it up. The position at every time step is not random; rather, it is determined (exactly and absolutely) by the microstate corresponding to the position of the previous time step.

You assume that entropy gain and loss are equally likely. You get out that entropy gain and loss are equally likely. This isn’t surprising.

You did not prove to my satisfaction that, in any random configuration of marbles moving around in a box, entropy is more likely to increase than decrease over time. Without considering the effects of our assumptions about entropy gain and loss, mine is on equal footing with yours.

~Max