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Does Quantum Mechanics Flout the Laws of Thermodynamics?

The views expressed are those of the author and are not necessarily those of Scientific American.


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Vlatko VedralQuantum mechanics is the most successful description of nature known to humans, yet it has many bizarre implications for our understanding of the world. There are phenomena of superposition (objects being in two places at the same time), entanglement (correlations that exceed any classical correlations) and nonlocality (apparent ability for information to travel instantaneously across vast distances). As my cover story in the June issue of Scientific American discusses, these oddities are not just limited to subatomic realms, but challenge our conception of the everyday world, too. Now, in a paper published in Nature, together with my colleagues from Switzerland and Singapore, I have discovered yet another counterintuitive consequence of quantum physics.

Everyone who has ever worked with a computer knows that they get hotter the more we use them. Physicist Rolf Landauer argued that this needs to be so, elevating the observation to the level of a principle. The principle states that in order to erase one bit of information, we need to increase the entropy of the environment by at least as much. In other words we need to dissipate at least one bit of heat into the environment (which is just equal to the bit of entropy times the temperature of the environment).

Landauer’s erasure principle has been considered controversial in physics ever since he proposed it in the early ’60s. Was it a new law of physics or just a consequence of some already existing laws? Our new paper argues that in quantum physics, you can, in fact, erase information and cool the environment at the same time. For many physicists, this is tantamount to saying that perpetual motion is possible! What makes it possible is entanglement, but let me not get too far ahead of myself. I will first set the scene by giving you a bit more background on Landauer.

Landauer always emphasized that there is no disembodied information. Bits of information need to be encoded into real physical systems and will therefore have to conform to the laws of physics that these systems obey. In the case of Landauer’s erasure, the law we are talking about is the in(famous) second law of thermodynamics. The second law states that the disorder in a closed system mostly increases and at best stays the same. Landauer argued that the link between erasing information and generating heat is a consequence of the second law. That sounds reasonable and, in fact, his colleague Charles Bennett showed in the late ’70s that if you could erase information without generating heat you could construct a perpetual machine of the second kind. Bennett thus showed that negating Landauer’s principle implies negating the second law, which (for those who are familiar with the basic laws of logic) is the same as saying that the second law implies Landauer’s erasure. Bennett and Landauer wrote a classic article for Scientific American on this subject.

So where’s the controversy? It comes from asking whether it also true that Landauer’s principle implies the second law. If this were so, then the two would be equivalent, as each implies the other. Some authors have even talked about the possibility of Landauer’s principle being stronger than the second law.

Now my colleagues and I have discovered an additional twist in the Landauer tale. As I said earlier, in quantum physics, you can erase information, but rather than adding heat to the environment you can actually take it away! This sounds like it contradicts Landauer’s principle. Even more worryingly, since we argued the equivalence with the second law, this would mean that quantum physics contradicts the second law. Quantum physics seems to allow us to have a cake and eat it, in that it allows us to erase information and cool the environment too.

But this, luckily for the second law (though not for would-be inventors of perpetual motion machines), is not the case. Landauer’s insight is still fine, and erasing information adds entropy to the environment. What saves the second law is that, in quantum physics, entropy can actually be negative. Adding negative entropy is the same as taking entropy away. The key phenomenon behind it is the spookiest of all quantum phenomena, entanglement.

To understand the connection between entanglement and negative entropy we have to go back to Schrödinger’s view of entanglement. When two systems are entangled, we have complete information about their joint state, but have no information about their individual states. If we are erasing the state, as a whole we need not generate entropy (since the state has zero entropy), but if we erase subsystems individually, then each will contribute to entropy generation. The difference between the global and local erasing is negative entropy. To rephrase, if we have to erase some information, it helps to know whether this information arises from the entanglement with another system. Then, by invoking the other system in the erasure, we can actually erase and the environment can lose entropy.

Landauer’s erasure therefore acquires a new dimension when entanglement is allowed, but even then it still remains fully compliant with the second law. For better or for worse, the entropy of the whole universe still cannot be decreased even with the full assistance of the quantum magic of entanglement and negative entropies of quantum objects.

If all this seems confusing, it is! This is very subtle physics and few people, even eminent physicists, understand it straight away. If you pose your questions below, I’ll do my best to answer them.

The implications of our result could be important for superfast and superefficient computers. Current computers waste about 10,000 units of heat per computational step. If we can somehow control and manipulate entanglement between the microprocessor and the computer memory, then we could erase computations to make room for new ones, but keep the environment cool—we’d be right at the boundary of what is physically allowed. At present, this is admittedly very difficult to do, but who can foretell the already rapid progress of quantum technologies?

Photo courtesy of Jenny Hogan, Centre for Quantum Technologies






Comments 47 Comments

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  1. 1. zhifeige 1:41 pm 06/1/2011

    I still don’t understand where the negative entropy comes from. Why erasing subsystems individually will contribute to entropy generation larger than the global entropy generation?

    Link to this
  2. 2. wolfkiss 2:11 pm 06/1/2011

    Depending on one’s interpretation of QM, isn’t it reasonable to understand entanglement as a distributed, and therefore open system? This would not only preserve the Second Law, which only applies to closed systems, but also get rid of the problem locality/hidden variables. This is because entangled particles aren’t correlating with each other directly, as we humans have evolved to think of things, but with their common distributed surroundings, i.e. the universe. Is this not possible?

    If this is true, then it is not heat, per se, that is the constraining factor for computation but the "noise" that results from a superimposed de-coherent system – which certainly correlates with heat. In other words, the limiting factor for pure saliency is uncertainty (delt(E) x delt(t) > h). Isn’t this consistent with the second law, which is really about the predictability of the system?

    So, if one grants that entanglement is a distributed phenomenon where any entangled pair is open to other pairs, won’t an entangled computer have problems scaling due to a non-linear increase in de-coherence pressure as the system scales in complexity? I.e. the open nature of entanglement will create superpositions upon superpositions that is proportional, though not linearly so, with the complexity of entanglement.

    In any case, it’s worth a try. But Turing computation, which is based on the discrete (i.e. extremely coherent) states, doesn’t seem especially suited to quantum computation without multiples of resources per bit to render them coherent. These layers of resources to cohere discrete bits requires machines, which require heat dissipation. Right?

    Link to this
  3. 3. jtdwyer 3:03 pm 06/1/2011

    I’m no physicist, but information stored magnetically, on a hard disk drive, for example, can be completely lost by exposing the magnetic substrate to a strong magnetic field – passing a strong bar magnet near the disk drive, for example. In this case, no matter how much information is erased, only a constant amount of energy is expended, correct?

    Whether physically identical disc mediums contains storage capacity for 10 MB of 500 GB makes no difference in the energy expended to realign the polarity of all bits, right?

    The number of electrons used to indicate a bit of information is not independent of storage technology – there is no constant ‘bit’ of energy storage…

    Link to this
  4. 4. desai 3:41 pm 06/1/2011

    "I’m no physicist, but information stored magnetically, on a hard disk drive, for example, can be completely lost by exposing the magnetic substrate to a strong magnetic field – passing a strong bar magnet near the disk drive, for example. In this case, no matter how much information is erased, only a constant amount of energy is expended, correct?"

    I’m also not a physicist but let us take an even simpler example. Let us say that a body/object held above ground (earth) represents a unit of information. Then 2 bodies held above ground would represent 2 units of information and so on. Now if these bodies were let go then they would fall down to earth and the corresponding information would be erased. Would you say that the amount of energy expended was the same irrespective of the number of bodies falling down? The same is true for your case — the energy expended is dependent on the number of re-alignments — 0′s turning to 1′s and 1′s turning to 0′s.

    Link to this
  5. 5. jtdwyer 4:56 pm 06/1/2011

    As I understand, in a 3.5 in hard disk, for example, the number of atoms used to store 10 MB of data may, in another disk drive, be used to store 500 GB of data. The amount of energy needed reverse the polarity of ‘n’ number of atoms in one case may clear 10 MB of data and in another case 500 GB of data.

    The energy used should depend on the number of magnetic reversals, not the number of data bits cleared.

    In your example, perhaps one person represented much more information than the other…

    Link to this
  6. 6. ShakaUVM 8:18 pm 06/1/2011

    "Nonlocality (apparent ability for information to travel instantaneously across vast distances)"

    No.

    And since the author gets this basic fact wrong, I stopped reading right there.

    Link to this
  7. 7. akmangalick 8:27 pm 06/1/2011

    I am also not a physicist (and I don’t play one on TV), but I know that energy and entropy are two different, albeit related, concepts. The 2nd Law of Thermodynamics and Landauer’s principle both refer to *entropy*, not energy. Please don’t look to me for an explanation of the difference, though.

    Link to this
  8. 8. jtdwyer 9:18 pm 06/1/2011

    The article states:
    "Everyone who has ever worked with a computer knows that they get hotter the more we use them. Physicist Rolf Landauer argued that this needs to be so, elevating the observation to the level of a principle. The principle states that in order to erase one bit of information, we need to increase the entropy of the environment by at least as much. In other words we need to dissipate at least one bit of heat into the environment (which is just equal to the bit of entropy times the temperature of the environment)."

    I think what ‘everyone knows’ is that the heat generated by computers increases primarily as a function of how long they’re left on. I suggest that the temperature of a memory chip is not closely related to the number of bits that are ‘on’, or flipped or erased but the chip’s refresh rate and circuit density. There is no equivalent ‘bit’ of heat energy. The principal heat produced by variations in computational activity is not from bit erasures but more likely the mechanical motion of a disk drive’s read/write access arm as different areas of the disk are accessed.

    The principal involved here seems to be that the primary product of physicists dabbling in electronics engineering are miscalculations and misconceptions…

    Link to this
  9. 9. desai 9:55 pm 06/1/2011

    "As I understand, in a 3.5 in hard disk, for example, the number of atoms used to store 10 MB of data may, in another disk drive, be used to store 500 GB of data. The amount of energy needed reverse the polarity of ‘n’ number of atoms in one case may clear 10 MB of data and in another case 500 GB of data."

    Interesting example. But, I think the difference in these 2 cases mentioned lies in "information as interpreted by humans" and "information inherent in a system". The article is about latter, "information inherent in a system".

    (On a related note, as technology progresses it tries to harness every bit of information inherent in the system for representing information for human consumption, which is what your example of essentially the same amount/mass of a hard disk containing much more data — 500GB against 10MB — implies.)

    Link to this
  10. 10. GeneralSpecifics 10:39 pm 06/1/2011

    Seriously…you can flout this entire argument of computers getting hotter and hotter…by simply inventing a better fan!

    Link to this
  11. 11. joset 10:50 pm 06/1/2011

    Vlatko:

    I have three questions based upon (though not directly related to) your interesting piece of info (didn’t had time/knowledge to go through Landauer’s paper nor yours), as follows:

    1. Would "nonlocality", on its own, compel information negentropy, given that (apparently), no ‘bit’ is transmitted between an entangled pair?

    2. Might it be that actual QM knowledge could imply a refinement of the Boltzman constant (on what concerns its established validity), since it relates Energy (at the microscopic level) to Temperature (at the macroscopic one)?

    3. Lastly, could this work of yours (et al) implicate any change in the Bekenstein-Hawking formula, namely, on what concerns Black-Hole evaporation, information and negentropy?

    Disclaimer: Not a Physicist. If you’re going to reply, please (try to) do it in layman’s terms. Thank you.

    José Tavares

    Link to this
  12. 12. jtdwyer 11:09 pm 06/1/2011

    IMO, there is no information without human interpretation – physical systems have no ‘inherent information’, only information imparted by systems designed by humans.

    What is the ‘inherent information’ stored in a piece of paper? I suggest it has none until a pencil is used to apply some representative method of information storage.

    The subject of this article is the purported relationship between fundamental information processes and energy/entropy. I found no relationship established – only invalid inferences.

    Link to this
  13. 13. jacquesaladino 12:27 pm 06/2/2011

    Can this be applied to the natural environment, not just computers. For instance could this of cooled the nuclear reactors in Japan?

    Link to this
  14. 14. DMahalko 5:19 pm 06/2/2011

    This article seems a little too brief to explain this. I know physicists use the word "information" differently than regular people, so the article’s summary is probably skipping over some important details.

    Anyway, as far as I understand, all memory/data systems contain information, even when first built and activated. It’s just that the "information" it contains isn’t the information we consider useful because it is disordered.

    Erasure doesn’t remove information, it actually creates order and organization, turning random bit patterns into an orderly state, ready to accept whatever specific organized pattern we want it to store. This initial erasure requires energy to perform.

    If we did not erase a disordered state before trying to use it, our processing methods might mistake the randomness as potentially containing valid data, and processing the raw invalid state requires time and energy to evaluate as being valid or invalid.

    Link to this
  15. 15. jtdwyer 7:04 pm 06/2/2011

    You’re right, I think that neither physics nor information theory use the term information as most people understand it and in fact I think they use many of the sames terms for cross-purposes. Please see:
    http://en.wikipedia.org/wiki/Information_theory
    "Not to be confused with Information science." and
    http://en.wikipedia.org/wiki/Entropy_(information_theory)
    "This article is about the Shannon entropy in information theory. For other uses, see Entropy (disambiguation)."

    To address some of your other points, I think they are based on technical misunderstandings of actual processes.

    I’ve been retired for a while, but as I recall, whenever a computer system is powered up its memory is set to binary zeros. Nothing happens unless…

    When a system is configured with a bootable peripheral device (typically a disk of some kind) that contains valid a bootstrap program to load preconfigured operating system software it is loaded from disk into memory and begins execution, often loading many other concurrently executable software tasks and systems that access data that was preconfigured and/or previously stored from prior executions.

    You may also be thinking of erasure in terms of stored disk files, which are not actually ‘wiped’ from the disk by replacing its stored data from the disk (with binary zeros), but is disk space is marked as being available for reallocation and reuse. Eventually a deleted file’s data will be overwritten with other files’ data. In the meantime, its previous disk space is not generally accessible and seems to contained disordered data.

    I reject this author and any physicist assertion that information complies with any laws of physics. I think that this idea is based on the misapplication of terms and concepts established in physics and the mathematical theory of information.

    Please see my next comment below…

    Link to this
  16. 16. jtdwyer 7:38 pm 06/2/2011

    As joset asks above, the idea that ‘bits of information’ are exchanged between entangled particles is a misconception. IMO, there is no information shared or exchanged between eventually detected ‘entangled’ particles. In fact, nonlocality and propagation are not particle state properties at all but rather properties of the self-propagating wave state.

    While a singularly conjoined, multiply directed wave front could collapse into two or more particles, it also could synchronously propagate dependent particle spin or charge states to multiple detection locations. It this case there would be no need to explain any independent exchange of deterministic information that must occur outside an otherwise closed transmission system.

    IMO, the idea that some independent information abstraction determines the state of quantum particles is a misconception. The idea that this imaginary ‘information’ must not be destroyed, just as energy cannot be destroyed is, I think, absurd.

    Relating to black holes, consider that a neutron star achieves its extremely high mass density by ejecting its electrons (which occupy atomic space), and converting all of its nuclear protons (with their repellant positive charge) into neutrons, allowing the extremely efficient high energy collapse of mass – producing extreme gravitational effects. What happened to the supposed information required to determine the structure of the original atoms?

    I suggest that the same thing happens to matter ‘ingested’ by a black hole, except in this case matter is completely disintegrated. By completely disintegrated, I mean that all matter is separated from its binding energy. Massless or nearly massless fundamental particles are ejected through the black hole’s semiluminal polar jets while all gravitational mass energy is locally retained, directed to the empty ‘singularity’ which exists only as a focal point for contracted spacetime.

    IMO, there is no information that determined the configuration of matter, only energy and physical forces determines can determine the configuration of matter. Everything originally necessary to construct the disintegrated atoms is retained but only the reoccurrence of the originating conditions could reconstruct those atoms, restoring their prior state.

    Could some magical, ethereal information have allowed the reconstruction of the material disintegrated in the development of either a neutron star or black hole? Not without the reoccurrence of the originating conditions!

    Link to this
  17. 17. Dr. Strangelove 9:20 pm 06/2/2011

    Quantum mechanics flouts the 1st law of thermodynamics by the fact that virtual particles can appear and disappear within a time period allowed by the Uncertainty principle. Virtual particles have energy. Hence energy is constantly being created and destroyed by the mere appearance and disappearance of virtual particles.

    This energy has been measured in the lab and known as the Casimir effect. In essence, the Casimir effect lab apparatus is a perpetual motion machine of the 1st kind. It violated the 1st law of thermodynamics by creating a tiny energy that had been detected in the lab.

    Link to this
  18. 18. Mr. Peabody II 10:49 pm 06/2/2011

    I wish I understood anything at all about QM. I seem to be incapable of doing so. It makes me feel dumb as a post. Anyway, here are my questions/observations, asked from the perspective of a computer/electronics technician with 30 years of experience.

    1.) Bits are not "erased". They are "changed". Whether the bit is 1 or 0, it is still datum. The only way to "erase" a bit is to turn off the power, which creates a "null" state.

    2.) Changing the value of a bit requires execution of many commands — i.e. "work". Work creates heat. Not only is this consistent with thermodynamics, it agrees with my decades of first-hand observation: The more bits that are changed, the more heat is generated by the components. Heat will accumulate until it reaches an equilibrium with the capacity of the cooling components — and hopefully, before any of those components burn up.

    So what am I missing here? Neither Landauer’s nor Vedral’s physics seem to take into account simple principles of electronics….? I’m lost.

    Link to this
  19. 19. akmangalick 1:48 am 06/3/2011

    "any physicist assertion that information complies with any laws of physics…is based on the misapplication of terms and concepts established in physics and the mathematical theory of information."

    Not at all. The concept of information is completely consistent with the concept of entropy. The former is a measure of the number of different states of a system. The latter is in some sense the converse, i.e. a measure of the randomness of a system or the *lack* of different states of a system.

    Again, the research described discussed entropy, not energy. And I believe that "erasure" refers to a reduction in the number of possible states, not a change in state. In other words, a change of value from 101010 to 000000 is not an erasure in the context of information theory, since the number of bits remains the same. The value still contains 6 bits of information. However, a change of bit pattern from ANY value containing 6 bits to ANY value containing 1 to 5 bits is an erasure, i.e. a reduction in information of the system.

    Imagine taking a 100 GB hard drive and breaking off 1% of the platter in such a way as to keep the remaining 99% intact and usable. Yes, I know it’s not possible in practice, but if you use the analogy of mag tape, it is more feasible. The 99% of the platter remaining now can still store 99 GB, while the 1% portion, if one were to grind it into a powder, would no longer be able to store ANY information. The grinding operation would clearly increase the entropy (randomness) of the recording system which is now in two parts.

    The research on this topic attempts to get at the relationship between the amount of information in a system (NOT the value at a particular moment in time) and the amount of entropy in that system.

    Link to this
  20. 20. Mr. Peabody II 11:06 am 06/3/2011

    "…the relationship between the amount of information in a system (NOT the value at a particular moment in time) and the amount of entropy in that system."

    Ok. That helps. Thanks!

    However, that brings up another point of confusion: It seems then, that you are saying that information systems exist outside of the physical constructs that manipulate it. …And that is subject to natural (QM) laws that can be contrary to the physical laws we observe.

    However, both information and information systems are creations of the mind. It would seem then, that QM is either a description of mental systems, or a declaration that the mind itself is separate and independent of the physical systems that control it.

    Link to this
  21. 21. gmusser 11:31 am 06/3/2011

    The idea that virtual particles violate energy conservation is a misconception — one that physicists have unfortunately encouraged. Virtual particles arise in Richard Feynman’s diagrammatic description of particle processes, and at each point within the Feynman diagrams, energy is conserved. What distinguishes virtual particles is not a violation of energy conservation, but a deviation from the classical relationship between energy and momentum.

    Link to this
  22. 22. GoshaJora 5:31 pm 06/3/2011

    The second beginning of thermodynamics was created Clausius Rudolf Julius Emanuel (1822-1888), for the description of processes in convertible processes and machines, provided that in machines as a working body the ideal gas is applied.
    Who does not know it – that did not read the primary sources.
    Is proved, that there are essentially not convertible machines and using them as a component it is possible to build isothermal converters of heat of air in mechanical job.
    The prototype of such converter works for me.

    Link to this
  23. 23. GoshaJora 5:32 pm 06/3/2011

    The second beginning of thermodynamics was created Clausius Rudolf Julius Emanuel (1822-1888), for the description of processes in convertible processes and machines, provided that in machines as a working body the ideal gas is applied.
    Who does not know it – that did not read the primary sources.
    Is proved, that there are essentially not convertible machines and using them as a component it is possible to build isothermal converters of heat of air in mechanical job.
    The prototype of such converter works for me.

    Link to this
  24. 24. GoshaJora 5:38 pm 06/3/2011

    The second beginning of thermodynamics was created Clausius Rudolf Julius Emanuel (1822-1888), for the description of processes in convertible processes and machines, provided that in machines as a working body the ideal gas is applied.
    Who does not know it – that did not read the primary sources.
    Is proved, that there are essentially not convertible machines and using them as a component it is possible to build isothermal converters of heat of air in mechanical job.
    The prototype of such converter works for me.

    Link to this
  25. 25. GoshaJora 5:43 pm 06/3/2011

    The second beginning of thermodynamics was created Clausius Rudolf Julius Emanuel (1822-1888), for the description of processes in convertible processes and machines, provided that in machines as a working body the ideal gas is applied.
    Who does not know it – that did not read the primary sources.
    Is proved, that there are essentially not convertible machines and using them as a component it is possible to build isothermal converters of heat of air in mechanical job.
    The prototype of such converter works for me.

    Link to this
  26. 26. skeilson 7:16 pm 06/3/2011

    response to jtdwyer: you raise a good question. In magnetic storage what is important are the magnetic domains (small blocks of the material) and the number of domains (and domain walls) does govern the density of storage (not individual atoms). In flipping a bit or erasing a bit you are in fact changing the alignment of that group of atoms in that domain and that does take energy and the amount of energy required is per bit. A read/write laser head has to heat up the domain to allow the magnetic spins to be flipped.

    Link to this
  27. 27. bucove 7:36 pm 06/3/2011

    In your conclusion, you state "the entropy of the whole universe still cannot be decreased even with the full assistance of the quantum magic of entanglement and negative entropies"…

    Because I am not really so concerned with the decrease of Cosmic Entropy as I am with it’s failure to increase; your conclusion begs the question: Can we now show it is possible the Universe ‘may’ be flat? Could it be true your wonderful newly discovered ability to freely recycle classical information indicates the possibility of an eternally recycling universe??

    This would truly be a fantastic corollary of your work!

    Link to this
  28. 28. jack.123 8:26 pm 06/3/2011

    Lets lets see here if I got the 2nd law right.You have 2 states of heat and the different between the 2 is what we call work.Why won’t this work with electromagnetism?If you take 2 bar magnets and place 2 ends together N to S they stick together.They are hard to pull apart.Now shift the direction of pull 90 degrees and they slide apart with much less work.Why can’t we use the difference between the 2 and produce work and thus energy.Can someone please explain why this won’t work, if you will pardon the pun?

    Link to this
  29. 29. jtdwyer 12:08 am 06/4/2011

    Thanks for clarifying the technical conditions I was attempting to describe. So the amount of energy required to erase all the data on a disk using a bar magnet should be related to the number of atoms whose polarity is changed, regardless how many bits that might represent, correct? The total number of bits stored on a physical disk can vary simply by changing disk formatting parameters.

    Likewise, the number of atoms whose polarity must be changed to write or erase a bit also varies: the amount of energy required per bit is variable.

    These conditions seem to violate the premise that there is some discrete amount of physical energy associated with a logical bit of ‘information’.

    Link to this
  30. 30. jtdwyer 12:35 am 06/4/2011

    I admit there’s a lot of confusion in these discussions – much of which has been introduced by the author. Again, the article states:
    "Everyone who has ever worked with a computer knows that they get hotter the more we use them. Physicist Rolf Landauer argued that this needs to be so, elevating the observation to the level of a principle. The principle states that in order to erase one bit of information, we need to increase the entropy of the environment by at least as much. In other words we need to dissipate at least one bit of heat into the environment (which is just equal to the bit of entropy times the temperature of the environment)."

    It certainly seems that the phrase "we need to dissipate at least one bit of heat into the environment" certainly seems to indicate that the author equivocates heat energy and entropy to a bit of information. I think this is based on a gross misuse of the concepts described by Shannon, below.

    To quote wikipedia:
    http://en.wikipedia.org/wiki/Entropy_(information_theory)

    "This article is about the Shannon entropy in information theory. For other uses, see Entropy (disambiguation)."

    "In information theory, entropy is a measure of the uncertainty associated with a random variable. In this context, the term usually refers to the Shannon entropy, which quantifies the expected value of the information contained in a message, usually in units such as bits. Equivalently, the Shannon entropy is a measure of the average information content one is missing when one does not know the value of the random variable. The concept was introduced by Claude E. Shannon in his 1948 paper "A Mathematical Theory of Communication"."

    I may be confused in some ways, but I think I have certainly been led to any confusion by the author and, I think, other physicists’ misapplication of information theory.

    BTW – your example of breaking a disk drive is an interesting case, in that all the data on the disk would be rendered (effectively) irreversibly irretrievable. In fact, a good scratch on a disk’s platter will, just like an old audio record, can render an entire disk unusable.

    Link to this
  31. 31. Eugene Sittampalam 2:34 pm 06/4/2011

    “the entropy of the whole universe still cannot be decreased even with the full assistance of the quantum magic of entanglement and negative entropies of quantum objects“
    In fact,if our universe can be taken as a closed system, which seems to be the case with increasing observation, then its entropy will remain conserved – very much compliant with not only to the second law of thermodynamics but slso as the second (conservation) law of nature and of classical mechanics. Moreover, if we view the atom as s vibrant and breathing entity and not as some piece of dead matter, then the quantum mechanical world of the atom simply and solely becomes classical mechanical in scope! Please see http://www.sittampalam.net/Synopsis.html.
    Thank you all

    Link to this
  32. 32. Eugene Sittampalam 2:59 pm 06/4/2011

    “the entropy of the whole universe still cannot be decreased even with the full assistance of the quantum magic of entanglement and negative entropies of quantum objects“
    In fact,if our universe can be taken as a closed system, which seems to be the case with increasing observation, then its entropy will remain conserved – very much compliant with not only to the second law of thermodynamics but slso the second (conservation) law of nature and of classical mechanics. Moreover, if we view the atom as s vibrant and breathing entity and not as some piece of dead matter, then the quantum mechanical world of the atom simply and solely becomes classical mechanical in scope! Please see http://www.sittampalam.net/Synopsis.html.
    Thank you all,
    Eugene <www.sittampalam.net>

    Link to this
  33. 33. DoctorRichard 6:38 pm 06/4/2011

    Im sorry but we didn’t even define what "information" is here. What was said basicaly is that erasing the entangled version of whatever holds the information,either does not affect its local environment, or actually decreases the Entropy….which is impossible. If, according to Claude Shannon, information is the reduction of uncertainty, then this article didnt give me much information at all.

    Link to this
  34. 34. denysYeo 2:37 am 06/5/2011

    What would the implications of this discussion be for a quantum computer?

    Link to this
  35. 35. Gray Lensman 11:26 am 06/6/2011

    Humm, where to start. OK, nonlocality is as the author describes, the apparent instantaneous transference of information between distant points; and has been experimentally established; and is one of the signatures of quantum entanglement; and is one of the major disconnects between general relativity and QM. I believe the 2nd law of TD predates QM which is probably the source of the confusion between the terms energy and entropy. Entropy is a better description of what is really going on. There seems to be some confusion about the term "data". Data in the physical system is not the same as the representational data in a higher level information system. A quantum bit of information is not necessarily the same as a bit on a disk drive which is highly dependent on the technology to read/write said bit. As far as heat loss in memory or from a disk drive due to friction, while completely true is not relevant to the theory behind the article.
    Full disclosure, I am not a physicist nor an electronics engineer.

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  36. 36. bernsten69 7:40 am 06/7/2011

    I completely disagree with a few ‘facts’ you state at the beginning and cannot believe your findings, namely:

    superposition (objects being in two places at the same time) – superposition does NOT relate to objects, but relates to addative wave functions which may be observed to have non-zero values within their bounds. Why do you use the word ‘objects’ when Quantum Mechanics appears to say that there is no such thing. . . this line alone made me question whether you have any real credentials.

    entanglement (correlations that exceed any classical correlations) – this is a rather poor explaination of entanglement, and could basically be read as stating that we don’t really know why entanglement exists (yet we know how to ‘create’ it and how it behaves)

    and nonlocality (apparent ability for information to travel instantaneously across vast distances) – this is patently wrong, and any real quantum physicist worth his salt would tell you so. You confuse entanglement with information transfer. There is NO transfer of information. The state exists. You can’t ‘change’ the state in one location, instantaneously changing the state in the other location – this would in fact destroy the entanglement.

    If we are erasing the state, as a whole we need not generate entropy (since the state has zero entropy), but if we erase subsystems individually, then each will contribute to entropy generation – The first half of this statement does not make sense. Here’s why: Assume two entangled particles with opposite spin. The first half of this sentence would claim that erasing the joint state doesn’t create entropy. How exactly do you ‘erase’ the entangled state without creating entropy? How? Do you intend on destroying both particles simultaneously? Compare that to destroying one of the particles. Which generates more entropy? Closing your eyes and not applying an operator to the joint state does not destroy it. Please explain how you intend to erase a joint state without increasing entropy – this appears impossible to me.

    I would also appreciate if you posted your credentials and had a well known 3rd-party peer review of your findings.

    All too often I see bad articles on Scientific American with meta-science worthy of alien-abduction-level credence. Until this changes, I will continue to urge my friends and colleagues not to read Scientific American.

    - University of Illinois B.Sc. Quantum Physics, 2001.

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  37. 37. bernsten69 9:41 am 06/7/2011

    It appears that there is some confusion in the community between entanglement and information transfer.

    Entanglement refers to a joint state in which two particles have attributes that relate to each other in a fixed manner. An example would be: Particle A and Particle B are entangled in such a manner as to have opposite spins.

    What this means is that when you measure the spin of Particle A, you instantly ‘know’ the spin of Particle B. However, this does not mean that Particle B instantly transfered information to you at Particle A’s position. Here’s why:

    Assume that your wife takes a pregnancy test, but the indicator won’t give a result for say 10 years. You both have space ships that will leave earth heading in opposite directions (traveling at 1/2 the speed of light) soon after she takes the test. (Please ignore the time dilative effects in this example, as this does not concern special relativity)

    You create entangled Particle A and Particle B, such that they have opposite spins. You put Particle B in a box and give it to your wife and put Particle A in a box and take it with you. (Each box has a built in detector that can tell you if your particle is spinning up or down the axis of its rotation). The message you want your wife to send you is an UP spin if she has a 10 year old or a DOWN spin if she wasn’t pregnant.

    Can your wife send you that message after 10 years?

    The Answer is no, regardless of the number of particles that you start out with. When you open your box, you observe either an UP spin or a DOWN spin, and you immediately know what your wife’s box shows (the opposite). However, no information has been transferred. Your wife wants to transfer a single bit of information (UP|DOWN) which could easily be a 0 or a 1. However, she is UNABLE to transfer it to you. At her end, she is unable to ‘force’ her particle to have an UP or DOWN.

    Interestingly, your wife would know if you were mistaken about whether you had a child. However, no information (the up or the down that your wife wants to send) has been transferred from one particle to the other, and thus there has not been any information transfer.

    Interestingly, your wife’s knowledge of your mistake has applications in quantum computing parallel processing.

    Instantaneous information transfer is fiction, and any Quantum Physicist worth his salt should know as such.

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  38. 38. bernsten69 10:06 am 06/7/2011

    One last comment:

    Please see the discussion at:
    http://www.physicsforums.com/showthread.php?t=464703
    (and See S. Weinberg, The Quantum Theory of Fields I, Sec. 3.6, pages 150-151.)

    Also see discussions of a quantum dynamical semigroup for proofs of dS/dt 0.

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  39. 39. bernsten69 10:26 am 06/7/2011

    The above should state dS/dt is greater than or equal to 0. (apparently this site does not accept extended characters).

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  40. 40. Omicron 3:00 pm 06/8/2011

    Geez, very good article if "confusion" of thermodynamic properties vs. energy states are the intent.

    1)Assume that the so called "Laws of Thermodynamics" are very much flawed. Flawed in the sense that these laws are "incomplete" in present time (a limitation) of known science of present day knowledge of mankind.

    A Validity Test = Holding (containing) a single high-energy photon in a motionless isolated state from its test environment. Then imparting that same photon with the same energy state it had before it was held captive and motionless. Hint; The observed motionless state will not "appear energized", but can output more energy as a function of time as held in the motionless state. Note: Don’t try this one at home folks (bad things happen)! Uh…Where is Entropy now?

    2)Try putting Gamma rays into increasinly collimated forms of transit as the environment temperature is decreased to absolute zero. Uh…Where is Entropy now?

    Yes,.. these are "thought experiments".

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  41. 41. harrow 7:57 am 06/16/2011

    Nice article!

    To the nitpicking commenters: he said nonlocality is "apparent" immediate communication, because it’s not actual communication, and he points out that true heat losses are about 10^5 times bigger than k_B T ln(2), so this is not of immediate practical use in today’s computers, but is something fundamental that may later be of technological interest. The author definitely knows what he’s talking about, but writing a popular article requires delicate wording that elides technical details. If you want the details, go to arxiv.org (not Nature).

    As for the "bit of heat", this is because of the relation between entropy and free energy established by Boltzmann’s constant and the temperature. It’s like expressing mass in electron-Volts.

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  42. 42. Mauricio956471 6:00 pm 06/20/2011

    I don’t understand the relationship between entangled systems and negative entropy. Why is there no negative entropy when the system is not entangled with another?

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  43. 43. Mauricio956471 6:00 pm 06/20/2011

    I don’t understand the relationship between entangled systems and negative entropy. Why is there no negative entropy when the system is not entangled with another?

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  44. 44. manishjungthapa 10:19 pm 07/5/2011

    The concept that entropy can be negative is a new one. This certainly did not pop out of a grand mathematical construct but with observation/experiments,contrary to Dirac’s sea of negative energy which serendipitously occurred in his universal yet fundamental equation i. = m that describes electron;it would be long before the equation could be deemed right experimentally.

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  45. 45. kostic 9:56 pm 02/18/2012

    If “modern” Physics violate the Fundamental (phenomenological) Laws of Thermodynamics and Nature, too bad for the Physics, as Einstein had stated. During any process (mass-energy transfer), there will be energy transfer and dissipation, thus entropy generation (see below), even if infinitesimal, at every space and time scales (entropy cannot be destroyed). Thus, there should be entropy generation during data record and entropy generation during data erasure: entanglement (without rigor thermodynamic justification) cannot sub-cool the environment. The energy and entropy “accounting” should be properly done for all involved systems, including boundary systems that are causing the processes (boundary causes are not mathematical constructs but physical systems). Real physical analysis is not always properly done by “specialized” physicists who are “creative” (like financial wizards at the Wall Street) to elaborate different, coherent mathematical constructs, and even more creative to justify (without due rigor) that those constructs obey the fundamental Laws (to avoid rejection). Luckily, the phenomenological (cause-and-effect) laws provide needed check-and-balance.
    I am a classical (engineering), phenomenological Thermodynamicist without knowledge of quantum mechanics. The fundamental Laws are reasoned irrespectfully from material structure or analysis methods (like Carnot did), so I like to comment on the issues. The mathematical constructs, regardless how coherent, may be misleading and erroneous. The thermodynamic entropy [J/K], as integral measure of thermal energy per absolute temperature, is conserved in reversible/elastic processes (without energy dissipation/equipartition – directional randomization). Since any process (mass-energy transfer/conversions) always dissipate energy to some degree as thermal energy generation, which, divided with absolute temperature, gives rise to entropy generation always and everywhere (at every space and time scales), without exception.

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  46. 46. chipfields 5:35 pm 09/6/2012

    Please dumb this answer down for me, and don’t use big scientific words….
    Have the first and second laws of thermodynamics now been proven false, or, in other words, has quantum mechanics proven matter/energy can be created and entropy avoided? Thanks.

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  47. 47. Marcus Morgan 10:14 am 10/17/2012

    It’s simpler to say systems de-concentrate over time (lose photons and export entropy) but in doing so they can also concentrate (build intact systems while losing photons when building, as in supernova synthesis of heavier elements). The system, as the element iron, for example, will then be subject to further loss of photons when it binds with other elements into compounds in more economical orbitals. Heat loss is fundamental, and you are abstracting a way to rationalize systems as something special when in fact they are just little islands in a tide of heat loss.

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