Is the second law of thermodynamics routinely violated?

[Half_Man_Half_Wit]

@Max_S

First I want to point out that the law from the coin example is not valid, was not formulated on a valid basis, and need not even appear to be valid. It is possible to observe greyness decreasing on a macroscopic scale in the previous example. The law was formulated nonetheless.

It’s formulated on exactly the same basis as every other law: by generalization from observational regularities. You do the coin example experiment a couple of hundred times, and you’ll always find the law to hold; absent knowledge of the microscopic dynamics, you have no justification to assume that in some cases, it’ll be violated. So it’s on exactly the same grounds as any other law of physics.

I take issue with step 9. I have no reason to believe the observer will observe a gradual change in color. You say the observer can only see gross color. If before he could distinguish two boxes of different colors, as soon as you remove the walls I take it he can only observe the combined box as a whole. Therefore the instant you remove the wall the observer sees flat grey.

~Max

Huh? How on Earth could that happen? The observer’s powers of observation are equal to the previous experiment; they’re able to perceive (what comes down to) the fraction of black vs. white marbles in a region, but not the actual marbles. This is really the same thing your computer screen does—by mixing three colors in different proportions, because you can’t see the individual pixels, different gross colors emerge, like in this picture. Or take something like this ASCII art: the different grey regions are just different fractions of black, mixed with white. That’s the way the observer sees the system: the individual marbles are too small to be individually resolved, but different mixtures of them realize different levels of grey.

@Max_S

Actually I’m not sure if I agree with step 8 either. You can’t necessarily “go” from any arbitrary configuration of marbles to another, certainly not if you include a succession of three states in order.

~Max

But that’s just counting. If there are more ‘more grey’ states than ‘less grey’ states, then a system in a ‘less grey’ state has more ways of evolving towards a ‘more grey’ state.

So assume some ‘less grey’ state G[sub]<[/sub] can be realized by means of white and black marbles in ten different ways (corresponding to microstates G[sub]<[/sub][sup]1[/sup] through G[sub]<[/sub][sup]10[/sup]). Assume there are more ways to realize the ‘more grey’ state G[sub]>[/sub] than there are ways of realizing the ‘even less grey’ state G[sub]<<[/sub]. Then, more of these ten states will evolve towards the more grey state than will evolve towards the less grey one.

Say there are eight states G[sub]>[/sub][sup]1[/sup] through G[sub]>[/sub][sup]8[/sup], and the states G[sub]<<[/sub][sup]1[/sup] and G[sub]<<[/sub][sup]2[/sup]. These are the states available from either of the states realizing G[sub]<[/sub] on the next time-step. Then, eight out of ten times, if the system is in the state G[sub]<[/sub], we will see it evolve into G[sub]>[/sub]. (Perhaps it helps to recall, here, that a reversible evolution always takes different states to different states, as if it didn’t, i. e. by taking two different states to the same following state, you can’t tell which was the original state from looking at the later one, and thus, can’t reverse the evolution.)

Thus, at each time-step, we’re more likely to observe an increase in grey-ness, simply because there are more ways to get more grey.