Is the second law of thermodynamics routinely violated?

[Max_S]

@Half_Man_Half_Wit

Huh? Sure it is! If the initial state can be either A or B with 50% probability (equiprobability of initial states, remember!), A always yields heads, and B always yields tails, then each throw yields heads with 50% probability.
Again, that’s just going from what you said: initial states can be chosen equiprobably.

If you want to consider the first throw part of the initial state, that’s fine by me. But I still don’t understand how it follows that the second throw has 50% probability. I assume the deterministic process that decides whether to throw A or B, the process we don’t know about, depends on the currently showing side of the coin. Otherwise this whole example of throwing a single coin has no relevance to the point you were trying to make - proving a law that says “the [theoretical] system will always become more grey over time”.

@Half_Man_Half_Wit

Theories are build on observation, so of course, the latter must be what we start with.

Very well.

@Half_Man_Half_Wit

I’m really having trouble believing you’re sincere here. I am not restricting the observer’s vision, or anything. Rather, that he only sees shades of grey, so to speak, is for the same reason as that you only see shades of grey in pictures like the ones here. If the density of black and white pixels were slightly different (say, a black pixel added here and there), you would not observe any difference. If there are some regions with higher density of black pixels, the gray there is darker, if there are regions with whiter pixels, they are brighter.

That’s what our experimenter sees: exactly what you would see.

But we don’t know that downward fluctuations in entropy are small and fast. They could just as well be large and slow. And besides, I can observe the flickering of an LCD display with any number of optical devices. On older monitors I can pick up the flickering with the naked eye. I have at my disposal a number of tools which can distinguish very slight differences between colors in photographs.

@Half_Man_Half_Wit

Of course. The number of possible states to evolve into determines the number of possible evolutions.

Let’s take the smallest possible change of something like the coin system. Take one pixel, and flip its color. Suppose you start with an all-black state. Then, flipping one pixel’s color will make the system more grey with certainty: every other possible state is one with higher ‘greyness’.

Then, take the resulting state, and again, flip one pixel: if you flip any pixel other than the one you’ve flipped before, you will again move towards a state of higher greyness. And so on: there will be more states of higher greyness to flip to, until you’ve reached a 50/50 distribution of black vs. white pixels. If you flip a pixel there, you will get to a state that’s ever so slightly (but undetectably) less grey. The next flip will return you to the equilibrium with a probability of 50% (actually, very slightly more than that, since there is now either one more black or white pixel).

Now, the important thing to realize is that this doesn’t depend on the microdynamics; in particular, it doesn’t assume that this dynamics is random. Rather, this is a conclusion that applies to generic deterministic and reversible dynamics.

This absolutely depends on microdynamics. Is picking “any pixel other than the one you’ve flipped before” “until you’ve reached a 50/50 distribution of black vs. white pixels” a rule? How do you determine which “other” pixel to flip, is it actually random? After you reached 50/50 distribution, how do you determine which pixel to flip then? Are you implying the flips after that are picked at random? If not, how can you assign a 50% probability of evolving towards equilibrium?

@Half_Man_Half_Wit

Think again back to the original, all-black system: any possible microscopic evolution will lead to a more grey state. After that initial chance, still almost every possible evolution will lead to a more grey state. And so on, up until you reach equilibrium. There, half of all evolution laws will lead to a less grey state; but, even for that half that lead away from equilibrium, most will return quickly to it, with some holding out longer, and only one making it all the way to the all-white state, before going back.

In conclusion, as long as you don’t take care to set up a very special evolution of the system (a point I had stressed from the beginning, you will recall), any generic microdynamics will, at any point in the evolution of the system, tend to increase the overall greyness with overwhelming probability.

It does not follow that the system will evolve towards a more grey state simply because there are more ways to do so than to do otherwise. There could be 999 ways to evolve to a more grey state and one way to do otherwise, but it does not follow that the system will do so or is even likely to do so. You are missing a premise.

~Max