# B Why is entropy not reversible?

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1. Feb 17, 2016

### entropy1

Is there an easy way to explain in layman terms why entropy in an open system is not reversible?

2. Feb 17, 2016

### mathman

From a statistical point of view, it would be like tossing a coin and getting heads a million times in a row.

3. Feb 18, 2016

### vanhees71

I don't understand the question. What do you mean by "entropy is not reversible"?

Usually something is irreversible for practical reasons. You have a macroscopic system, and it's simply not possible to know all the details of its state and apply a "time-reversal transformation" to this state in all microscopic details, which would be necessary to reverse the process leading to it.

4. Feb 18, 2016

### Demystifier

5. Feb 18, 2016

### entropy1

I remember Brian Greene on Discovery Channel or National Geographic Channel illustrating this with a wine glass breaking on the floor. Halfway the video, it paused, and he walked about the scene reversing all momenta of all particles in the scene (animated). I don't remember whether the message was that we couldn't know all information (momenta), or we could. Would is be in principle possible to time reverse all processes in an open system given a limited amount of time between t0 an t1 (limited size of the light cone)?

6. Feb 18, 2016

### phinds

I think the HUP says we could not know all information with full detail since at the quantum level much of it is indeterminate.

7. Feb 18, 2016

### newjerseyrunner

8. Apr 19, 2016

### memento

I think your question is: is time reversible?
The typical answer is no, because the entropy have to incresase.

I have recently found a proof of this second law of thermodynamics from quantum coherence: http://arxiv.org/pdf/quant-ph/0610005.pdf

9. Apr 22, 2016

### memento

The article is false because the formula of additive entropies is wrong

10. Apr 22, 2016

### phinds

WHAT article? There have been several articles referenced in this thread. You need to let people know what you are talking about.

11. Apr 22, 2016

### Strilanc

Because of Liouville's theorem. Which basically asserts that the math of classical and quantum mechanics is reversible, but in a very strong sense. Not only is it impossible to merge two states into one state (which violates reversibility), it's also impossible to push them closer together or pull them further apart (according to a specific distance function).

Reversing entropy requires squeezing states together, but the math doesn't allow for processes that do that. Anytime we squeeze one part of the state space, another will balloon outwards by an exactly equivalent amount.

http://lesswrong.com/lw/o5/the_second_law_of_thermodynamics_and_engines_of/

12. Apr 22, 2016

### atyy

In principle you can. In practice you cannot. So most people do not believe the second law is a fundamental law. (And yes, I do know what Einstein said about it - curiously his theory of general relativity is not consistent with the second law as a fundamental law. However, the quantum version of general relativity is consistent with the second law (there are good arguments that neither quantum mechanics nor quantum gravity are fundamental), and provides one of the deepest insights into physics beyond the Planck scale.)

13. Apr 22, 2016

### secur

The question has more or less been answered (vanhees71 in particular) but there's some confusion ...

First: it's not entropy which is reversible, it's the system. When you reverse an open system you reduce its entropy, which increased during the process being reversed, back to its original value.

For instance when Brian Greene's wine glass broke its entropy increased. If he could magically reverse everything it would come back together, with its entropy lowered back to its original value. Of course BG's actions required energy, and increased entropy, so the total system's entropy (wine glass + BG) would increase.

Second: the assumption implicit in your question - that open systems are always irreversible - is not true. They certainly can be reversed in many cases. For example, suppose you let some ice melt - entropy increases. Put the water (presumed in a container) in the refrigerator: it goes back to ice, its entropy is lowered (or as you incorrectly say "reversed"). Of course if you include the refrigerator, overall entropy increased.

Chemists reverse open systems like this all the time, using heat, cold, pressure, and more complicated chemical-engineering processes.

Third: note that at least some answers missed the word "open" - their answers apply to closed systems instead, very different question.

So it seems the real issue you wind up with is: "are all open systems reversible - in principle?"

The true answer is, no they're not. For instance a broken egg left to rot for a week is not reversible. A dead person (like Ted Williams, say) cryogenically frozen by Alcor Corp. will remain dead forever no matter what you do. When a wave function is collapsed by observation (or measurement, whatever), and one particular eigenstate selected by a projection operator on the Hilbert Space, the information of the other states vanishes from the universe. It can never be restored, in principle or practice.

However the typical establishment-physics answer is (as far as I can tell): yes they are. Of course not in practice, but in principle. A broken egg can be restored, so can Ted Williams. Collapsed states can be recovered from parallel universes.

If you believe that, I have a guaranteed system for picking winning lottery tickets which I'll sell only to you for a nominal fee, because I feel you deserve to be a billionaire too! PM me.

Last edited: Apr 22, 2016
14. Apr 22, 2016

### DirkMan

I thought that closed systems have "irreversible" (never-decreasing) entropy , not open systems.

15. Apr 23, 2016

### secur

That's right. But the distinction between entropy reduction, and system reversibility, is important.

You can more-or-less always reduce the entropy of an open system. For instance you could just lower its temperature by an appropriate mechanism. The interesting question is whether it's reversible, that is, can it be returned to a previous state. If so its entropy will be reduced back to what it was, but that's not the key point.

A simple closed system can be reversible, thus have constant entropy. For example one water molecule alone in a complete vacuum can oscillate - the H-O-H bond's angle flexing around 105 degrees. When it returns to maximum or minimum angle we can say the system has been "reversed". That motion won't convert to heat, or cause photon emission. At least it can do many cycles (if not "infinitely" many) with no loss of energy or increase of entropy. (As far as I know)

Finally note a closed system can experience statistical fluctuations that, rarely, reduce entropy temporarily, according to statistical mechanics.

16. Apr 23, 2016

### Jilang

So, the challenge is to explain in layman's terms why the entropy of a closed system (statistical fluctuations aside) increases?

17. Apr 23, 2016

### Staff: Mentor

This thread is in the Quantum Mechanics forum, but most of the replies deal with the macro world. I thought that the OP was seeking a QM explanation of the 2nd law.

I always thought that the 3rd postulate of QM must be involved with the 2nd law because you can't un-observe a state. I don't want to push a personal theory, so I'll pose it as a question. "Does the 3rd postulate of QM lead to the 2nd Law of Thermodynamics?"

18. Apr 23, 2016

### Jilang

I suspect quantum mechanically it has more to do with the path integral formulation of QM. The more ways of getting to a final micro state the more chance there is for that happening. And the more permutations of the final micro states that lead the final macro state likewise for the macro state.

For the first part consider getting lost on the London Underground. You may change lines, swap platforms etc. After several weeks you are more likely to find yourself at Oxford Circus than Edgeware.

19. Apr 23, 2016

### secur

That's a big challenge which, despite the best efforts of Roger Penrose and many others, has never been met. There's a very good reason: first it has to be explained in physicist's terms!
Good point
As I said above, you and others are misreading OP. He asked about reversible open systems. Should have done so without even using the word "entropy" - that's what misled people. Second law, of course, is about entropy of closed systems. Since it's such a huge problem in physics - unexplained, unproven - we naturally start talking about it instead.

However since OP has been answered pretty thoroughly I have no objection to moving along to the "fun stuff" - 2nd law.
The "second half of the third posulate" is the collapse of the wave function. Like you (apparently), intuition tells me it's extremely relevant to 2nd law. Information disappears, entropy increases - simple enough, right? This is one reason I distrust non-collapse interpretations.

By the way the paper memento mentions above, "A GENERAL INFORMATION THEORETICAL PROOF FOR THE SECOND LAW OF THERMODYNAMICS" is relevant, but doesn't seem like the right idea.

Unfortunately the concept of quantum entropy (starting with Von Neumann) is shaky and I, for one, don't understand it (same as entropy in general.)

The only time I understood entropy was when first introduced to it, in Chemistry. Highly recommend any physics student to learn about Gibbs free energy and how it's used to judge whether a chemical reaction will take place. Chemists really do understand entropy, but only in their limited domain. They treat physicist's attempt to generalize it (to information, and the universe, for instance) with contempt. I don't agree, but do sympathize with their attitude.

One reason it's been impossible to prove, or even explain, 2nd law is: it may not even be true in such a setting as the universe! This is one of those assumptions stemming from Cosmological Principle which is only an assumption. The sort of vague hand-waving seen in this area is thoroughly typical of semi-science when it "boldly" ventures far beyond the safe harbor of experiment.
That's a connection I hadn't thought of. Doesn't seem related to anorlunda's collapse - 2nd law connection. They both point in the same direction, that QM may be able to explain 2nd law; because these facts of QM are solid - more so than Boltzmann statistical thermodynamics. Although extremely correct in its domain, statistical thermodynamics seems too frail (e.g., those "statistical fluctuations") to support the kind of sweeping 2nd law physicists seek.

Well these are some of my thoughts on the matter - have plenty more but they're random and don't seem to add up. Bottom line, I think entropy is a major unsolved issue in physics; and maybe QM can provide a way out. anorlunda I suspect you have more solid ideas, and knowledge, on the topic, please enlighten us. But remember, no personal theories! If you have such, claim Roger Penrose said it, who's going to know the difference :-)

20. Apr 23, 2016

### stevendaryl

Staff Emeritus
Hmm. It seems to me that there is sometimes a tension between giving a sensible, useful but false answer and a nonsensical, useless but true answer. As far as usefulness, you might as well treat something that happens once in $10^{10^{10}}$ trials as if it were impossible. But it's actually false to call it impossible.

Your claims about rotten eggs and dead people coming back to life seem along those lines. What I think of as the true, but useless answer is: the odds of these things fixing themselves through random fluctuations is very, very, very, very tiny, but nonzero. Your answer, that these things fixing themselves spontaneously is impossible, is the false, but useful answer.