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I Behavior that seems to violate the arrow of time, but...

  1. Dec 1, 2017 #1
    Very simply put, I have an intense desire to understand an experimental result which, on the surface, violates entropy and the arrow of time-- although, since the experimenters predicted exactly that outcome, a deeper analysis must show that it does not actually violate entropy and the arrow of time-- I’d like to have that deeper analysis explained to me. .

    The experiment, which can be found here (https://arxiv.org/abs/1711.03323 ), involved first cooling the Carbon portion of a chloroform molecule and warming the Hydrogen portion, and also establishing a quantum correlation between those two atoms. Then, as the correlation decohered, the experimenters observed-- as predicted-- a flow of heat from the cold Carbon to the warm Hydrogen, contrary to what would have occurred, of course, if the two atoms had not been correlated. I realize that the correlation, when it existed, constituted ‘information’, and so the correlation’s decoherence meant information loss and an entropy increase, which in turn meant the release of heat. My question is: why wasn’t all of the heat produced by the decoherence of the correlation simply lost to the environment--why did some of that heat flow from the cold Carbon to the warm Hydrogen causing an entropy decrease there, and thereby a reduction in the net entropy gain for the system overall (the entropy gain from the correlation’s decoherence was diminished by the entropy loss from the heat flow from the cold Carbon to the warm Hydrogen atom-- strikingly odd behavior for heat that would not have occurred if the two atoms had not been correlated to begin with)? Evidently the initial existence of the correlation dictated that very strange cool-to-warm heat flow behavior, but why?
     
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  3. Dec 1, 2017 #2

    PeterDonis

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    Because the system was very, very carefully isolated from the environment--it had to be in order for the experiment to work.

    Also note that the "temperatures" referred to are "effective spin temperatures"--which basically means extending the statistical notion of temperature, which assumes a large number of particles, to a case where you only have two particles, and the difference in "temperature" is really the difference in the energy levels occupied by the two particles.
     
  4. Dec 1, 2017 #3
    First of all, thank you very much PeterDonis for taking the time and expending the energy to reply to someone like me, as obviously unschooled in the nuances of the quantum world as I am intrigued by those nuances-- those strange, deeply counter-intuitive little details that fascinate everyone aware of them!!

    Your response immediately triggered this follow-up question: all right, the experiment was carefully isolated from the environment but why would the heat that resulted from the dissipation of the correlation-- and let’s say that this correlation-ended heat was equally distributed between the Carbon and Hydrogen atoms-- why would that heat not flow from the even-hotter Hydrogen to the warmer-than-it-was-but-still-cooler Carbon? Even if everything you said is exactly correct, I still don’t understand what is causing this reversal of the normal heat flow.
     
  5. Dec 1, 2017 #4

    PeterDonis

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    Because in this particular setup, that is the direction of increasing entropy. The second law does not say that heat always flows from hot to cold; it only says that entropy always increases. This setup is just a counterintuitive one in which increasing entropy means heat flowing from "cold" to "hot" (and I put those terms in quotes because, as I pointed out in my last post, we are dealing with single qubits, so the concept of "temperature" being used is not the usual one from statistical mechanics in any case, meaning that our intuitions about the normal direction of heat flow are inapplicable).
     
  6. Dec 1, 2017 #5
    Yes, PeterDonis, entropy increased overall, we agree-- but why was this cold to hot (I understand the special way we’re using ‘cold to hot’, as you pointed out) entropy decrease a part of what happened? Why didn’t the correlation-loss heat, equally distributed between the Carbon and Hydrogen atoms, simply flow from the even-hotter Hydrogen to the now-warmer-than-it-was-but-still-cooler-than-the-Hydrogen Carbon? Wouldn't that also have caused an increase in entropy?

    So for someone to say "entropy increased" and to leave it at that does not, it seems to me, fully explain the anomalous details of what happened! Yes, I grant you that entropy increased overall, but why was it apparently necessary for it to decrease in one particular portion in a most peculiar way as part of that overall increase?????!!!
     
  7. Dec 1, 2017 #6

    PeterDonis

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    First of all, you are assuming that this is somehow "anomalous". It's not. As I said, the second law does not say that heat always flows from hot to cold. It does not even say that heat "almost always" flows from hot to cold, and any case where it does the reverse requires special explanation. It just says entropy always increases.

    To understand why the entropy increases for heat flowing from "cold" to "hot" in this particular case, you need to understand what entropy is. Heuristically, entropy is the logarithm of the number of ways the individual particles can be arranged and still have the same macroscopic properties. So the number of ways the particles can be arranged in the final state should be larger than the number of ways they could be arranged in the initial state.

    For an ordinary case of heat flow, where large numbers of particles are involved, heat flows from hot to cold, heuristically, because the increase in the number of ways the particles in the cold object can be arranged as it warms up, more than makes up for the decrease in the number of ways the particles in the hot object can be arranged as it cools down.

    However, for the case in question, as I've said, we aren't dealing with a large number of particles; we're dealing with just two qubits. And the way the energy levels are arranged in the quantum system containing these qubits, the situation is reversed as regards the number of ways (here it's the number of possible quantum states for the two-qubit system, not the number of ways classical particles can be arranged, as in the usual stastistical mechanics case for a large number of particles): the number of possible quantum states for the two-qubit system, under the conditions of the experiment, is larger when the "hot" qubit gets hotter and the "cold" qubit gets colder.

    Obviously not, since that's not what happened.

    Again, this is a situation where your usual intuitions about heat flow simply don't apply. So you can't expect to understand it by asking "why don't my usual intuitions about heat flow work?"--all that does is describe the situation, not explain it. You have to actually look at how the number of ways the system can be arranged (or the number of possible quantum states of the system, which is the same thing for this case) changes as heat flows. A full treatment of that is really an "A" level discussion, not an "I" level discussion (and I am not myself an "A" level expert in this field). I've done the best I can to explain the basic idea at the "I" level.
     
  8. Dec 1, 2017 #7
    Of course, my initial words to you PeterDonis must be a pure and sincere expression of appreciation for your efforts to explain this experiment to me-- my only regret is that I already put a thanks to you in bold face and italics in an earlier post, so what do I do now, when so much more appreciation must be expressed? I guess all that remains is:
    Thank you very much, PeterDonis!!!!

    Now I hope you don’t consider it a mark of ingratitude if I raise a few points about your latest post.

    Here’s how you define entropy: “To understand why the entropy increases for heat flowing from "cold" to "hot" in this particular case, you need to understand what entropy is. Heuristically, entropy is the logarithm of the number of ways the individual particles can be arranged and still have the same macroscopic properties. So the number of ways the particles can be arranged in the final state should be larger than the number of ways they could be arranged in the initial state.”

    Then you apply your definition to the heat flow situation: “For an ordinary case of heat flow, where large numbers of particles are involved, heat flows from hot to cold, heuristically, because the increase in the number of ways the particles in the cold object can be arranged as it warms up, more than makes up for the decrease in the number of ways the particles in the hot object can be arranged as it cools down.”

    Perhaps that’s the best way to visualize it, Peter, but it seems to make more sense to me in understanding heat flow and entropy to consider the hot and cold areas as a single large system, and when one area of the system is hot and the other area cold, it is ‘structured’ or ‘organized’ – and in order to maintain that degree of organization, rapidly moving molecules have to remain in the hot area, and more slowly moving molecules in the colder area, meaning that there’s a major limitation on the number of ways the overall system can be arranged. However, if heat flows from the hot area to the cold area and eventually equalizes the two, there are vastly more ways you can arrange the system (now of uniform temperature) without changing its macroscopic characteristics. So that’s why a single uniform system has higher entropy than a single system with hot and cold areas.

    And explaining heat flow in physical terms: when there are still hot and cold areas, the random motion of molecules in the hot area will send some of those molecules out of the hot area and into the cold area, and similarly random motion in the cold area will do the reverse, causing the hot area to cool down and the cool area to heat up, thus the heat flow from hot to cold. And that’s why, once you have a uniform temperature, almost any motion of the molecules will maintain that uniformity, while it would require a lengthy series of extremely unlikely molecular motions to recreate-- by chance-- even a hint of the original areas of hot and cold.

    Then, in discussing the experiment, you say, “However, for the case in question, as I've said, we aren't dealing with a large number of particles; we're dealing with just two qubits. And the way the energy levels are arranged in the quantum system containing these qubits, the situation is reversed as regards the number of ways (here it's the number of possible quantum states for the two-qubit system, not the number of ways classical particles can be arranged, as in the usual stastistical mechanics case for a large number of particles): the number of possible quantum states for the two-qubit system, under the conditions of the experiment, is larger when the "hot" qubit gets hotter and the "cold" qubit gets colder.”

    But if it’s true that, as you say, the way that the energy levels are arranged in the quantum situation containing these two qubits, the number of possible quantum states for the two-qubit system, under the conditions of the experiment, is larger when the ‘hot’ qubit gets hotter and the ‘cold’ qubit gets colder, then why would it be the case that when the arrangement is the same but the two atoms are not correlated then the heat flow is normal, from hot to cold! Let me quote briefly from the study itself: “We observe the standard arrow of time in the absence of initial correlations, i.e., the hot qubit A cools down, while the cold qubit B heats up.”

    And the experimenters relate the cold to hot heat flow directly to the dissipation of the initial correlation, saying: “The situation changes dramatically in the presence of initial quantum correlations: the arrow of time is here reversed, as heat flows from the cold to the hot spin. This reversal is accompanied by a decrease of mutual information and geometric quantum discord….In this case, quantum correlations are converted into energy and used to switch the direction of the heat flow, in an apparent violation of the second law.”

    So, to the extent that the experimenters ‘explain’ the results (and they really don’t give a reason for why the quantum correlations, when converted into energy, are used to switch the direction of heat flow) they don’t in any way suggest that it’s because the hotter arrangement has higher entropy than the colder arrangement (which is the basis of your explanation, Peter). In fact, if it were the case that the hotter arrangement had higher entropy, then it wouldn’t require the energy of the converted quantum correlations to make it occur, it would happen naturally and spontaneously!
     
  9. Dec 1, 2017 #8

    PeterDonis

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    This is the same thing I was saying, just in different words. If you look at the underlying math it works out the same either way.

    Because whether or not the qubits are correlated makes a difference to what quantum states are accessible to the system. That's what "correlated" means.

    Heuristically, the uncorrelated case works like statistical mechanics with large numbers of classical particles; if you look into the details, you will see that in that ordinary case, it is implicitly assumed that the states of the individual particles are uncorrelated. For that case, your heuristic reasoning about the state with a temperature difference being more organized, and hence lower entropy, applies. To put it another way, there are more states with a smaller temperature difference between particles (or regions of a macroscopic system like a gas).

    The correlated case, however, restricts the quantum states available to the system, and in this restricted state space, greater temperature difference corresponds to higher entropy; i.e., there are more states with a larger temperature difference. The paper doesn't give enough information about the specific systems involved to be able to say in detail what the energy spectrum is; but heuristically, since qubits are fermions, one would expect there to be more states with a larger energy difference between them if they are correlated, by the Pauli exclusion principle.
     
  10. Dec 2, 2017 #9
    But Peter, you didn’t respond to the point of mine that dealt a coup de grace to your assertion that the hotter Hydrogen had higher entropy than the colder Carbon: The experimenters themselves wrote in their paper that “This reversal is accompanied by a decrease of mutual information and geometric quantum discord….In this case, quantum correlations are converted into energy and used to switch the direction of the heat flow, in an apparent violation of the second law.” (Bold face and italics mine)

    If the experimenters-- who ought to know what their own experiment is demonstrating-- say that the quantum correlations (as they decohere) are converted into energy which is used to switch the direction of the heat flow, then it can’t possibly be the case that the hotter Hydrogen has higher entropy than the colder Carbon in this experimental arrangement--as you claim-- because then it wouldn’t require any energy at all to make the heat flow in that direction: it would be the natural way for heat to flow, from lower to higher entropy!!
     
  11. Dec 2, 2017 #10

    PeterDonis

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    No, it doesn't. You are misinterpreting what the paper says and what I am saying.

    That's not what I said. I said that the system has higher entropy when the hot qubit is hotter and the cold qubit is colder.

    The paper does not say that entropy does not increase when heat flows from the cold qubit to the hot qubit. If entropy did not increase when that happened, then it wouldn't happen. The experiment does not violate the second law (note the word "apparent violation"--that means it isn't really a violation, it only appears to be to a person who doesn't understand the actual implications of the second law for this experiment).
     
  12. Dec 2, 2017 #11
    I have to be very brief for now-- sleep beckons!-- but I know that the experiment doesn’t actually violate thermodynamics laws! Give me a wee bit of credit, Peter!

    But you still are disregarding the experimenters’ own partial explanation-- that the energy of the decohering correlations is used to switch the direction of heat flow. If cold to hot were the natural direction in this experimental set-up, then no switch of direction would be necessary and no energy would be expended in switching the direction.

    As for the math of it: all that is necessary to jibe with thermodynamics is that the total, net entropy be higher-- therefore, as long as the gain in entropy from the decohering correlation is greater than the reduction in entropy from heat flow from cold to hot, then everything is fine and dandy re the Laws of T.

    By the way, I had what may be a huge epiphany, Peter: I think I may have the explanation. I can elaborate tomorrow, but for tonight let me simply say that it may just be a case of energy being energy. As you pointed out, the experimental set-up isolates the qubits, so that when the correlation decoheres, there’s very little for the energy to do. So it takes the only ‘job’ available and does the work of changing the direction of heat flow, lowering the entropy by that act, but not as much as the decoherence of the correlation raised it. I’m too groggy (sleep is now not merely beckoning but screaming at the top of its lungs!) to think it through, but it might possibly actually make sense!
     
  13. Dec 2, 2017 #12

    vanhees71

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    Hi haven't studied this interesting paper yet, but I trust @PeterDonis in having it analyzed right. Then it's another example for the tendency to create some sensationalism by misleading titles and abstracts. The thermodynamic/kinetic arrow of time is defined by increasing entropy, and since the total entropy of the system is increasing, there's no arrow of time reversed, but it's as it is expected from standard kinetic theory (i.e., the entropy is increasing). The surprising thing in this case just is that here, due to a special careful preparation the increase in entropy in this case implies energy flow from parts of the system of lower temperature to parts that have higher temperature, which is indeed reversed compared to what's usually the case for macroscopic objects. So the confusion expressed in the OP is due to the authors' misleading title and abstract rather than what really has been observed.

    My suspicion is that the article is submitted to Nature (SCNR) ;-)).
     
  14. Dec 2, 2017 #13

    PeterDonis

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    Once again, you are misunderstanding what the paper is saying. (I think @vanhees71 is correct that the paper's language is not chosen very well, at least not to communicate with non-experts. But the paper is written for an audience of experts, so, as with any such paper, you have to be careful reading it if you're not an expert.)

    Even without that caveat, you should be able to see that your argument is wrong by asking: what is the "natural" direction of heat flow, in any setup? The answer, of course, is whichever direction increases entropy. But only one direction can increase entropy. In an ordinary situation, that direction is hot to cold. In this setup, it is cold to hot.

    You are contradicting that by claiming that hot to cold is the "natural" direction, but somehow "expending energy" switches that. But that can't be right, because the system is isolated. In a case like a refrigerator or an air conditioner, where "expending energy" moves heat in an "unnatural" direction, that happens because the system is not isolated; the refrigerator or air conditioner has to exchange heat with its environment, and entropy increases overall. Here that dodge is not possible: there is no exchange with the environment. So there can be only one "natural" direction of heat flow for this isolated system: the one that happens, cold to hot. "Expending energy" can't change that, because the energy is already there, in the isolated system, and already makes whatever contribution it makes to the "natural" direction of heat flow, whether you use the word "expended" or not.
     
  15. Dec 2, 2017 #14

    PeterDonis

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    You are talking as if these are two different things. They're not, because, as I said in my previous post, this is an isolated system. So you can't separate out the entropy change due to heat flow from the entropy change due to decohering correlation. They're the same process and the same entropy change.
     
  16. Dec 2, 2017 #15

    PeterDonis

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    Please review the PF rules on personal speculation. What you are saying here is headed in that direction.
     
  17. Dec 2, 2017 #16
    Having an explanation to something isn't necessarily personal speculation. I'm pretty sure you have an explanation for why you are here on Earth rather than floating in space, or why (and this seems to be your field) time and lenghts differ for an observer moving relative to an other observer, and that will not be just speculation.
     
  18. Dec 2, 2017 #17
    But it may be if someone who tries to explain something doesn't really understand the thing he's trying to explain.
     
  19. Dec 2, 2017 #18

    PeterDonis

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    Having an explanation that is not based on a valid understanding of the subject is.
     
  20. Dec 3, 2017 #19
    Sometimes, the full truth is right there in front of you, but as many children will be discovering on the morning of the 25th, some assembly is required! Is that the case here? Or is a crucial part of the truth missing from the box, so to speak, and we have to put in a call to relevant parties to obtain it?

    I’m the Original Poster, and I started this thread to have a question answered about an intriguing but puzzling experiment by Serra and Lutz, and the good news is that the question has been answered. The bad news is that it’s been answered twice, and in ways that apparently contradict one another!!

    Yes, as I crawled off to bed on Friday night, I left this site in a state of perplexity, confronted with what appeared to be two starkly different explanations for the cold to hot heat flow in the Serra-Lutz experiment.

    Here’s our boy, Physics Forums’ very own PeterDonis, giving me his explanation, beginning with the case of uncorrelated cold Carbon and hot Hydrogen atoms:”Heuristically, the uncorrelated case works like statistical mechanics with large numbers of classical particles; if you look into the details, you will see that in that ordinary case, it is implicitly assumed that the states of the individual particles are uncorrelated. For that case, your heuristic reasoning about the state with a temperature difference being more organized, and hence lower entropy, applies. To put it another way, there are more states with a smaller temperature difference between particles (or regions of a macroscopic system like a gas). The correlated case, however, restricts the quantum states available to the system, and in this restricted state space, greater temperature difference corresponds to higher entropy; i.e., there are more states with a larger temperature difference. The paper doesn't give enough information about the specific systems involved to be able to say in detail what the energy spectrum is; but heuristically, since qubits are fermions, one would expect there to be more states with a larger energy difference between them if they are correlated, by the Pauli exclusion principle.” (Bold face and italics mine)

    Impressive, Peter!! And Peter delivers his explanation in a very authoritative fashion--not surprising for a Mentor of long-standing, a valued contributor of a remarkable 18,000+ posts and the author of 12 perceptive Insights articles!-- a fashion that strongly suggests that he knows precisely what he’s talking about-- but wait, that’s style, not substance, and so not really relevant. More importantly, his explanation is very plausible, which is much more to the point, scientifically speakingand yet … and yet, Peter doesn’t offer definitive proof of his explanation’s correctness. It’s as if someone said, “Look at these right triangles whose sides I’ve measured in the most exacting way: 3, 4, 5 and 8, 15, 17. And note that 3^2 + 4^2= 5^2, and 8^2 + 15^2 = 17^2! My goodness, it seems that the sum of the squares of the sides equals the square of the hypotenuse!” That would be a plausible hypothesis but of course it’s certainly not definitive proof. Peter presented an argument that made intuitive sense, and would explain things in a simple way using a well-established principle (entropy), but he didn’t actually mathematically prove that in the given experimental set-up, correlated qubits would generate a heat flow from cold to hot because of entropy.

    And, naturally, we have to give due consideration to the apparently starkly different explanation of the big shots—the authors of the study in question, whose lead researchers are Roberto Serra, Associate Professor of Quantum Physics at the Federal University in Brazil, with loads of published papers in quantum physics to his credit, dating back to 1997, and Eric Lutz, with an even bigger pile of co-authorships (77, according to Google Scholar!), and a full Professorship, in Theoretical Physics at a university in Germany-- birthplace of Heisenberg and Schrodinger! Could you have better geographical credentials than Lutz?? I say that jokingly, since of course geographical cred is no more relevant when evaluating the merits of a scientific explanation than Peter’s self-assured manner, but it may exert effects subliminally that we have to be cognizant of so we’re not unduly influenced by those effects!

    Now the researchers’ explanation—is it really an explanation? well, it’s kinda, sorta but not really!-- is confined to one point, actually: That the decoherence of the correlation (what their paper actually calls the ‘consumption’ of the correlation) supplies the energy for the reversal of direction of the heat flow. But let’s hear their actual words:”We observe the standard arrow of time in the absence of initial correlations, i.e., the hot qubit A cools down, while the cold qubit B heats up…The situation changes dramatically in the presence of initial quantum correlations: the arrow of time is here reversed, as heat flows from the cold to the hot spin. This reversal is accompanied by a decrease of mutual information and geometric quantum discord….In this case, quantum correlations are converted into energy and used to switch the direction of the heat flow, in an apparent violation of the second law.” (Bold face and italics mine)

    So the researchers don’t say why the energy released by the dissipation of the quantum correlation was used to switch the direction of the heat flow, just that it was. However, we can conclude that the researchers don’t agree with Peter’s explanation—i.e. that the experimental set-up, with the hot Hydrogen and cold Carbon atoms and the correlation between them that was established as an initial condition led to an unusual entropic situation such that the heat naturally flowed from cold Carbon to hot Hydrogen because that was the direction of higher entropy. Why can we safely infer that the researchers don’t agree with Peter’s explanation? Because entropy springs from the probabilities of different randomnesses, and occurs spontaneously, with nothing but a mathematical impetus. It certainly doesn’t require an injection of energy to make it happen!

    So perhaps we should just conclude that the researchers are mistaken: not about the fact that the quantum correlation decohered, or that it released energy in the process of decoherence, or that the heat flowed from cold to hot during the time span of the quantum decoherence-- their experiment demonstrated all those things—but they were mistaken in attributing the cold to hot heat flow to the energy released by the quantum decoherence when in fact it was unrelated: the ‘strange’ direction of heat flow was simply what entropy dictated under the unusual circumstances of the experimental set-up and quantum correlation, just as Peter claims.

    But there are two things arguing against the conclusion that the experiementers are mistaken and Peter is correct. I took a long train trip yesterday and I had time to do a little research. I couldn’t find anything on the internet that corroborated Peter’s analysis of the entropic situation of a two qubit experimental set-up like Serra-Lutz’s, when the qubits were correlated, but I did find an article in Science News about the Serra-Lutz experiment, and in it they quoted a physicist not connected to the experiment. Here’s the relevant paragraph, “Reversing the arrow of time was possible for the quantum particles because they were correlated — their properties were linked in a way that isn’t possible for larger objects, a relationship akin to quantum entanglement but not as strong. This correlation means that the particles share some information. In thermodynamics, information has physical significance(SN: 5/28/16, p. 10). “There’s order in the form of correlations,” says physicist David Jennings of the University of Oxford, who was not involved with the research. “This order is like fuel” that can be consumed to drive heat to flow in reverse.” (bold face and italics mine)

    Or should we conclude that not just the researchers but David Jennings also is mistaken? You might comment, “Who the heck is he, after all, that we should believe him? He’s just a random physicist!” Well, not quite random. The Oxford website describes him as “Theoretical physicist at Imperial College on a Royal Society University Research Fellowship, with research interests in quantum information, quantum thermodynamics, foundational aspects of quantum theory, and quantum field theory.”

    So evidently he’s quite the expert on all things quantum. “But,” you might say, “do impressive credentials prove that he’s correct in this case?” Well, no. But in the absence of clear, definitive, understandable proof of a more substantial, scientific sort, that’s all we can rely on.

    So that’s where things stand. Peter offers a genuinely plausible explanation that goes to the heart of the strangeness of the heat flow, but doesn’t mention the role played by the energy released by the correlation’s decoherence-- does he feel it’s an irrelevant red herring? He doesn’t say-- while the researchers don’t actually offer a full explanation of why the heat flow reversed its normal direction, they just say it was made to do so by the injection of the energy of the dissipating correlation. That led me to suggest, in the final paragraph of my final post on Friday, that, given the isolation of the qubits from the environment, perhaps it was the only way the energy could act. That comment apparently deeply offended Peter, who rebuked me with the words, “Please review the PF rules on personal speculation. What you are saying here is headed in that direction.” I’ve written thousands of words in this thread as we all search for the truth of a puzzling situation; a dozen or two of those words of mine offered a possible way of understanding the truth. “But how did I dare have the effrontery to do that when I didn’t ‘have a valid understanding of the subject’?” Peter, in effect, says in a thinly veiled threat. Very nice, congenial atmosphere around here!
     
  21. Dec 3, 2017 #20

    PeterDonis

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    No, that's not how it works. You are not talking about physics, you're talking about words. Words aren't physics. Everything you're looking at in this long wall of text post is descriptions of what's going on in ordinary language. Ordinary language is vague.

    The physical question is simple. We have a system consisting of two qubits, a "hot" qubit and a "cold" qubit. This system undergoes a transition in which heat flows from the cold qubit to the hot qubit. (Note that this transition is only temporary--as the experiment continues, the heat flows back the other way.) You are claiming that, if we consider these two qubits in isolation, the entropy after this transition is less than the entropy before; and that there is some additional entropy in the system, due to the "correlations", that is "converted" into something that drives the reversed heat flow, and that when this additional entropy is taken into account, the entropy of the system as a whole increases.

    (Yes, you haven't stated your entire claim explicitly, as I just did above. That's part of the problem; you're throwing around vague ordinary language terms without actually stopping to think about the physics. What I've just stated is a necessary implication of what you are arguing in this thread.)

    My refutation of this claim is simple: there is nothing in the system besides the two qubits (since it is isolated from the environment). So there is no other entropy besides the entropy of the two qubits. The "correlations", or whatever you want to call them, aren't separate things; they're part of the two-qubit system, and the entropy of the two qubits already takes into account whatever "correlations" are present. Since the only entropy present is that of the two qubits, that entropy must increase, or what happens in the experiment would not happen. So all that ordinary language about "correlations" providing "fuel" to drive reversed heat flow is just vague ordinary language that is misleading you. (I don't think it's misleading the physicists who are using it, since presumably they understand the underlying physics and aren't using ordinary language to analyze it; they're just looking for catchy ordinary language to describe what's going on to lay people without trying to actually give them a predictive scientific model.)

    Can I guarantee that my refutation is correct? Of course not. I'm not infallible. I could be wrong. But if you want to show that I'm wrong, you can't do it by quoting vague ordinary language, from physicists or anyone else. You have to show me actual physics: in this case, that would be showing me a valid model that separates the entropy of the two-qubit system in this experiment into two pieces: "entropy of the two qubits", which decreases during the period of reversed heat flow, and some other entropy, which increases by more (so the second law is not violated).

    You haven't done this, and haven't shown any understanding that this is what's required. So at this point I am closing the thread. If you can provide what I've described above, feel free to PM me and I will consider it.
     
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