Steven S

I think you misunderstand what they are doing. These guys are not crackpots. Yes, they are finding violations of the 2nd law and Evans and collaborators state this very clearly in their papers on the Fluctuation theorem and the Physical Review Letter of Wang et al. In normal thermodynamical systems in which one system, A, is immersed in another system, B, if the change in entropy in A is negative then this corresponds to a positive influx of heat from the bath B it is immersed in. Or you could have a positive change in entropy in A corresponding with to a dissipation of heat into B. From what I understand what they show for small enough systems in a small enough time scale you have a negative change in entropy corresponding to a negative change in energy in A. Apparently this is all based on something called the Fluctuation theorem which is proved in stochastic dynamics and supported by numerical evidence also. But this stuff is beyond my expertise so I can't really say anthing intelligent about the theorem.
Again, this is unsuprising since it is just stuff going back to Boltzmann--that is, you will see fluctuation about the mean that average out as you sample approaches macroscopic size. What is suprising is the length of deviations in the colloidal sample they used. Plus I'm interested in it for another reason, the experimental technique they used, optical tweezing, is something I worked with quite a lot as an undergrad.

Steven S

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Answerer

Well, I think that whether the second law works, is depend highly on the type of system that is used, whether the system is macro or mirco, isolated or not.
Anyway, it seem that most classical laws break down in quantum levels, so this discovery isn't very surprising or shocking at all.

tronvillain

Steven S, see the beginning of Bill's post, which you should have read rather than just "snipping." Anyway, I think it quite likely that they measured an entropy decrease, but it's only interesting as confirmation of what we already knew about entropy.

Afghan

I have a funny little example that I call Afghan's Magic Beans. It is silly and simplistic but it is quite strange. I'm afraid there is a bit of maths involved so I apologise in advance. First off, I am going to use a very a simplistic definition of Entropy and that is the log of the number of configurations possible for a particular state. This is very crudely like Boltzmann's.

The idea is this, there are these magic beans, right, and they are either black or white. Every hour, on the hour, these beans have a 1 in 3 chance of changing color. The rest of the time they stay the same color.

Now if I have 9 beans, say, and they are all white at a particular time, you would expect that after a couple of hours, one or two might be black. We see the expected increase of entropy. But what about backtracking. What color are they likely to have been a couple of hours before that time. It seems to me to be more likely that there would have been one or two black ones then as well. That is, given the low entropy of the system we would actually expect it to have been higher in the past.

I'll leave it as this rather undetailed exposition for now. I can do the maths if people want but I wouldn't wish to bore unnecessary. The point is that for certain sorts of system, we actually expect entropy to be higher in the past as well as the future.

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tronvillain

Yes, that would be another example of a statistically unlikely decrease in entropy. Of course, such a decrease is not that unlikely, with a probability of around 1/512. Now, what if you have a hundred beans? Then the probability of them being all white by chance drops to 7.8E-31, which is laughably small. Obviously, if you should happen upon a hundred of Afghan's magic beans, and discover that they are all white, you will search for an explanation other than chance.

This is why you have to look at small systems and short time scales to see decreases in entropy.

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Steven S

My mistake, I misread his post.
SS

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Afghan

But this is what befuddles me. Low entropy states are intrinsically unlikely but it seems to me that, given a low entropy state, it is more likely that it developed from high entropy state than a low entropy one. Of course, it is not likely to have developed from any state: the probability of a low entropy state existing at any one time is unlikely. This is true for any number of magic beans.

There are so many more high entropy states for it to have developed from that, if you work out your conditional probabilities, then I think you will see that if you have a low entropy state at time, T, then it is likely that the state at time, T-1, was of higher entropy just as the state at time, T+1, is likely to be more entropic. This rather odd reversibility of entropy stems from the fact that low entropy states are inherently unlikely.

tronvillain

No, if you have a low entropy state at time T, then in a system with small fluctuations then it is most likely that the at time T-1 there was an even lower entropy state, though it there are large fluctuations you are correct. Of course, that assumes that there were no inside interactions, which is unlikely. Think about it: If you were to walk into a room and observe that a collection of one hundred of your magic beans was white, would you think that chance was a good explanation? No. An outside interaction is far more likely - perhaps someone simply picked out one hundred whites from a mixture in order to fool you.

Afghan

I am not sure I agree. I am not sure that I disagree either. But look at it like this. The maths work like this for a hundred beans: if we have a hundred white beans at time T, the probability that we had 100 white beans at time T-1 is (2/3)^100. The probability that the current state emerged from a state of 99 white beans at T-1 is 100*(1/3)*(2/3)^99. That is to say, without factoring in even higher entropy states, it is abou 50 times more likely that the current state with entropy 0 developed from a state of entropy log(100) than one of 0.

tronvillain

As I already said, "if there are large fluctuations you are correct." Of course, that assumes that there were no outside interactions, which is unlikely. If you walk into a room and discover one hundred white magic beans, that someone arranged them that way is a much better explanation than them all being white by chance.