Why is entropy not reversible?

[entropy1]

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

 

[mathman]

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

 

[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.

 

[Demystifier]

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

See e.g. the explanation by Penrose
https://books.google.hr/books?id=0mVEBJ34v9EC&pg=PA407&lpg=PA407&dq=The+second+law+of+thermodynamics+in+action:+as+time+evolves,+the+phase-space+point+enters+compartments+of+larger+and+larger+volume.+Consequently+the+entropy+continually+increases.&source=bl&ots=fvQFrZlMKP&sig=nbEk8mwRAn-sdQ6UinrCdGFtoik&hl=hr&sa=X&ved=0ahUKEwixxaqdkYHLAhUEuBQKHcizAM4Q6AEIHDAA#v=onepage&q=The second law of thermodynamics in action: as time evolves, the phase-space point enters compartments of larger and larger volume. Consequently the entropy continually increases.&f=false

Or even better, read the book
https://www.amazon.com/dp/9812832254/?tag=pfamazon01-20

 

[entropy1]

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.

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)?

 

[phinds]

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)?

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

 

[newjerseyrunner]

"There is insufficient data for a meaningful answer." - http://multivax.com/last_question.html

 

[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

 

[memento]

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

 

[phinds]

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

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

 

[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/

 

[atyy]

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)?

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.)

 

[secur]

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

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.

 

[DirkMan]

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

 

[secur]

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

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.

 

[Jilang]

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

 

[anorlunda]

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?"

An important second half of the third postulate is that, after measurement of ##\psi## yields some eigenvalue ##a_i## the wavefunction immediately ``collapses'' into the corresponding eigenstate ##\psi_i## . Thus, measurement affects the state of the system.

 

[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.

 

[secur]

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

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!

This thread is in the Quantum Mechanics forum, but most of the replies deal with the macro world.

Good point

I thought that the OP was seeking a QM explanation of the 2nd law.

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.

"Does the 3rd postulate of QM lead to the 2nd Law of Thermodynamics?"

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.

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.

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 :-)

 

[stevendaryl]

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.

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 [itex]10^{10^{10}}[/itex] 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.

 

[Nugatory]

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.

That's probably what OP was after, but as the thread develops it's becoming clear that we have to nail down the classical understanding of entropy before we can start considering the quantum-mechanical complications. This thread has been moved to the Classical Physics section.

 

[secur]

Thanks for response, stevendaryl,

As I mentioned elsewhere, the pedagogical imperative is: first get the idea in the student's mind, even if it requires - not false; rather inexact, or over-simplified - statements. Later on you can smooth off the rough spots. But this is not one of those cases.

As I mentioned elsewhere, experiment is the sine qua non of science. (By the way I still owe you an answer in that thread). Observation can be a poor substitute where necessary. But math and theory are legitimate only to fill in holes in the test space, not to extend it. Experiments, or tests as we say in engineering, cover only a discrete subset of the test space, not even dense. Theory necessarily fills in those holes. It's also vital for understanding, and suggesting experiments to extend the test space, but can't do that extension by itself.

A rotten corpse coming to life is far beyond any experiment. Ok, in a very broad sense anything's possible. Lazarus may walk again, or water may turn into wine, because someone appeals to his Father. Or the appeal and Lazarus' resurrection may be coincidence. Who knows? But science - and I - can't indulge in such fantasies. Must rely on experiment, observation, results. Until I see experimental proof that's at least in the ballpark I'm comfortable saying, simply, that I don't believe in miracles. Theory - whether semi-science or theology - is not enough.

In the present case, you're going by the math of QM and statistical thermodynamics. (Of course, you're faithfully representing the physics establishment's position, so my disagreement is with them not you personally.)

It's been said many times, by professors trying to inject some life into the discussion, that you may find yourself on Alpha Centauri in the next moment (or perhaps it's supposed to take a little over 4 years), because your wave function extends throughout the universe and may suddenly "collapse" over there. It's not good enough to admit the chance is very small: 10^10^10^... The closest-to-true statement is no, it can't happen.

How far has a fermionic wave function's extension been checked by experiment? Well we can tunnel through barriers, and "teleport", tiny distances. I think they're too small to be seen by the naked eye. The special case of entanglement has been demonstrated over meters, but that's rather different. Super-conduction experiments are also relevant. I'm willing to extend it to maybe a few miles, maybe a few thousand - for a few fermions, perhaps even an ensemble of randomly-related ones, or Cooper pairs. But a live body? Light-years? Forget it. Perhaps there are astronomical observations to support such distances? If so, please tell me what they are. (Remember we're talking fermions not photons.)

Similarly it's often said that all the air in the room could suddenly collect itself in one corner, by a statistical fluctuation. Again, it's not good enough to admit the chance is very small. How far does experiment support this assertion? I'm not sure, but it's about the same ratio as in the above example: millimeters, or miles, compared to light-years.

Pure mathematicians justifiably put limits of integration at +- infinity. Applied mathematicians follow this habit, but it's justified only by convenience. The real limits are the boundaries of your experimental setup (multiplied by a reasonable factor).

Physicists think they're intellectually sophisticated, taking infinity seriously; I see it as intellectual naivete.

I'm very happy to defer to your (and other PF'ers) superior knowledge of real physics! I know you can show how physics "proves" a rotten body can be resurrected; if you get into details, it might take me a week's study to understand it. But I can just glance and see the illegal use of infinity! And I can examine experimental results to see how far they actually go. Resurrection is not a "statistical fluctuation".

The question, whether you (physicists in general, that is) are justified in extending the experimental results as far as you do, is NOT a physics question. It's philosophy - or simply common sense. And in that area I defer to no one.

So, although a physics non-entity, I disagree with you on the grounds that the question is not about physics. If you admit it's philosophy - i.e., opinion - we're on equal ground; can agree to disagree and leave it at that.

What do you say? Are you really going to claim modern physics - statistical thermodynamics, QM, whatever - proves rotten bodies can resurrect? If so, I'll drop the discussion - not convinced, but overruled.

 

[memento]

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

MY article

 

[stevendaryl]

What do you say? Are you really going to claim modern physics - statistical thermodynamics, QM, whatever - proves rotten bodies can resurrect? If so, I'll drop the discussion - not convinced, but overruled.

I guess it just depends on whether you consider there to be an important difference between "X is impossible" and "X has a tiny probability, so tiny that it will likely never happen in the lifetime of the universe". There is no practical difference. We can't experimentally distinguish between those two cases. So I don't care much about the difference, for practical purposes. For mathematical purposes, it seems to me to be inconsistent to say that the probability of flipping a coin and getting heads 10 times in a row is small, but nonzero, but then act as if getting heads a million times in a row is flat-out impossible. So for mathematical calculations, I go with the "small, but nonzero", and for practical purposes, I go with "impossible".

 

[secur]

Thanks stevendaryl

I'm sure no one wants to waste time on philosophy of physics. Although it really needs to be fixed, this is not the time nor place to do it. That's why I'm glad we agree on this point.

You're right: for mathematical calculations it's sensible, and convenient, to include vanishingly small probabilities. It would be a waste of effort to carefully exclude them when they're negligible anyway.

But for practical purposes, meaning applied math such as theoretical (and a fortiori experimental) physics, they must be considered, actually, impossible when inconceivably beyond the range of experiment.

So we agree: mathematically, include experimentally unverifiable tiny possibilities; but for practical purposes (physics), don't.

This may be the first philosophical discussion on PF which actually got resolved! We deserve some trophy points.