Granville Sewell Doubles Down

As much as I hate to drive any traffic to Uncommon Descent, Granville Sewell has clarified his misunderstanding of the Second Law there recently.

Of particular note is his response to the argument that “The second law only applies to thermal entropy, and what is happening in this video does not result in a net decrease in thermal entropy, so there’s no conflict with the second law.”

In fact, it is universally recognized that the second law of thermodynamics applies to more than thermal entropy, it applies to other types of entropy, for example, the “X-entropy” associated with any other diffusing component X: as pointed out in my AML paper, these types of entropy are defined by the same equations as thermal entropy, and are equally quantifiable. And it is widely applied in physics texts to less quantifiable types of “entropy.”

I would be interested in references to the physics texts in which his concept of entropy is “widely applied” but he seems to have inadvertently disabled comments on his post. Perhaps it will provoke discussion here instead.

45 thoughts on “Granville Sewell Doubles Down

  1. As has been the case ever since Henry Morris concocted the argument from the second law of thermodynamics, Sewell is plodding along in the fine tradition of ID/creationists who persist in mischaracterizing science despite the input they receive that their conceptual understandings are wrong.

    Sewell says, “So here is a list of the top 5 reasons, taken from my notes of the last 11 years, why a tornado running backward does not violate the second law:”

    Every “reason” is his own flawed understanding mixed with the flawed understandings of some of the novices with whom he has argued on UD.

    None of the reasons addresses why the movie running backwards is recognized by humans as unnatural. A movie of a tornado or of a breaking egg being played backwards is a mischaracterization of how houses, cars, eggs – and whatever else is being torn apart – are assembled. All these assemblies involve the second law of thermodynamics because energy is spread around in the processes of assembly. The processes of assembly are not the same as the processes of ripping apart, but the second law applies in either case.

    When the structures are broken or are torn apart by a tornado, the second law is still in effect; energy is being spread around and is not coming back into the system because there are photons, phonons, and particles that effectively go off to infinity and spread energy around so it can’t come back. These energy carriers get absorbed by other systems or they get further scattered. The more they are absorbed and scattered by subsequent collisions, the less likely they will return to the system whether it is being assembled or broken.

    Spontaneous assemblies of crystals, such as arrays of water molecules condensing onto a cold window and forming pretty frost patterns, requires the second law; energy must be released in the form of photons and phonons. The growth of an egg involves the release of energy. The building of a house releases energy. Ripping these apart also releases energy that will find its way off to infinity and be spread around. The second law is always working whether matter is condensing or being ripped apart.

    Our sense of time is closely related to the spreading around of energy. We would not exist or be conscious if energy wasn’t spread around. Matter couldn’t condense, metabolic processes would not be driven, and memories could not be formed if molecules couldn’t condense or rearrange with a concomitant spreading around of energy.

    We recognize a movie of a tornado or of a breaking egg being run backwards because, even as we watch the movie, our minds and memories continue to “move” in the direction of the future, which is the direction in which energy is spread around. If our minds also ran backwards – and our memories were erased as we watch – we wouldn’t be aware of anything being “wrong.”

    The tornado-in-a-junkyard, or in a housing development, has always been used by ID/creationists to mischaracterize evolution. The forces that assemble atoms and molecules are huge in proportion to the gravitational attractions among atoms and molecules. There are no corresponding charge-to-mass ratios and quantum mechanical rules among macroscopic objects that would lead to the same kind of spontaneous assemblies of boards or egg parts that we see among atoms and molecules.

    As we showed on another thread, scaling up the forces and binding energies of atoms and molecules to macroscopic objects with masses on the order of kilograms and spacing on the order of meters would make binding energies of macroscopic objects on the order of 2 x 1010 megatons of TNT (8 x 1025 joules). There is no tornado that can compete with that.

    Sewell apparently still believes that spatial order and entropy are synonymous. They are not. Energy spreads around whether things fall into crystalline order or get ripped apart. ID/creationists continue to ignore condensed matter and chemistry as well as matters of scale in their phony “analogies.”

  2. sez dr. febble: “…he seems to have inadvertently disabled comments on his post.”
    “inadvertently”.
    You are a far kinder soul than I, Dr. Febble. 

  3. Disabling the comments may have been a mistake, but I have my doubts, given his bold assertion:

    “The Earth is an open system, tornados derive their energy from the sun, and while turning rubble into houses and cars represents a decrease in entropy, the increase in entropy outside the Earth far exceeds the decrease seen in this video.”

    This is the traditional argument used by Asimov, Dawkins and many others, it is the one I have been primarily criticizing, particularly in my AML paper, “A Second Look at the Second Law“. My arguments seem to have been effective, because I rarely hear this silly argument any more, critics seem to have been forced more and more to fall back on secondary objections now.

    That’s quite a claim, and it deserves a hearty rebuke. Is it any wonder then that Sewell has prevented his critics from responding directly to his public challenge?

  4. In the last paragraph, Sewell asks this:

    So, how does the spontaneous rearrangement of matter on a rocky, barren, planet into human brains and spaceships and jet airplanes and nuclear power plants and libraries full of science texts and novels, and supercomputers running partial differential equation solving software , represent a less obvious or less spectacular violation of the second law—or at least of the fundamental natural principle behind this law—than tornados turning rubble into houses and cars? Can anyone even imagine a more spectacular violation?

    Sewell claims he has been pushing this argument for something like 11 years. Most people can learn a lot of thermodynamics and statistical mechanics in just one year; so what’s his problem?

    One has to wonder what Sewell thinks is “the fundamental natural principle behind this law.” It appears to be an escape hatch that he can use to say that he never claimed the second law was violated.

    Sheesh! Eleven years; and in all that time he hasn’t picked up a good textbook on thermodynamics and statistical mechanics. But he has the time to nurse his grudge against Elsevier and the rest of the scientific community. His constant kvetching over on UD suggests he is still feeling the sting of having his paper rejected; yet that sting isn’t prompting him to check his understanding. He just keeps repeating his misconceptions and misrepresentations.

  5. For the record, I know full well that Sewell deliberately disabled comments on his post.  I was being a snarky bastard.  I’m a little flattered that some of you think I’m remotely as nice as Lizzie.
     

  6. I would still like to hear Sewell state unequivocally whether or not he thinks that the application of human intelligence allows the second law to be violated.  This was mentioned in one of the previous discussions of his claims, and while I haven’t seen a clear statement by him, it seems to be an inescapable conclusion of his position.
     

  7. I think that the previous discussion(s?) here on Sewell’s arguments had some terrific contributions from people like olegt, Mike Elizinga, Richard Hoppe, and Doug Theobald (and the rest of you too!).   To the point where it’s hard to add anything new.

    I will add that my own posts on this at Panda’s Thumb have been based, I now see, on a misreading of Sewell’s argument. He really wants all those carbon-entropy arguments to do the job.  He is <i>not</i>, as I had assumed, making the usual creationist mistake of misunderstanding energy flows.  But at least my assertion that he has “proven” that plants can’t grow is still true.

    And there was some wonderful commentary, along the lines of Patrick’s comment above, about the role creationists like Sewell give to intelligence. (Yes, Sewell is a creationist, not a “design theorist”).   They really think that anything intelligent can violate the Second Law.

    It would be nice to get Sewell to turn up here and explain himself.  He seems to think that no one has answered him.   (But then again, he’s the one turning comments off …) 

  8. Patrick on May 26, 2012 at 5:00 pm 

    I would still like to hear Sewell state unequivocally whether or not he thinks that the application of human intelligence allows the second law to be violated.  This was mentioned in one of the previous discussions of his claims, and while I haven’t seen a clear statement by him, it seems to be an inescapable conclusion of his position.

    I think it’s an inescapable premise.

    And while he hasn’t acknowledged it, he also hasn’t denied it.

    I suspect he is aware of a lurking unchallenged assumption, but doesn’t want to risk investigating it.

    But I do think that many ID proponents think of “intelligence” as as some kind of supernatural force (yeah, yeah, oxymoron I know) that moves stuff around without actually violating physical laws.

    They don’t think of it as something that is the property of systems that obey physical laws.

     

  9. I think Sewell is backpedaling a bit here. Notice the disclaimers in bold: 

    If we actually saw a video of a tornado, running backward, it would certainly not occur to us to make any of the above arguments to claim that what we were seeing did not technically violate the second law, as formulated in physics textbooks. We would immediately recognize that what we were seeing violated a fundamental natural principle, one at least very closely related to the second law of thermodynamics. Even if we were told that what actually happened took a long time and the video had been speeded up, we would still not be interested in anyone’s “scientific” explanation for what we were seeing in the video, we would immediately recognize that the video must be running backward, because what we were seeing was completely unnatural.

    It boils down to an argument from incredulity

  10.  They really think that anything intelligent can violate the Second Law.

    They also think intelligence can violate Dembski’s probability bound. I first saw this clearly when gpuccio started talking about the creation of protein domain sequences. He really believes that the Designer can simply poof thes into existence without evolving them.

    So it is magic they are talking about, and not any process employed by human designers or analogous to what is done by human designers. 

  11. Well, Dembski thinks that intelligence can violate his UPB – it’s the reason he infers intelligence when something does.

     

     

  12. I am not so sure about that.  Of course they think that supernatural magic can violate the Second Law, or Dembski’s probability bound.

    But when you argue that a human designer cannot violate natural laws, I think you will find that they think humans can and do violate natural laws such as the Second Law.   When a human takes coins that are randomly scattered about and makes a stack of them, they see this as a violation of the Second Law by human intelligence.   When a human makes a computer that can do the stacking, they see this as a violation of the Second Law by a computer whose design was put into it by human intelligence, and that’s why it can violate the Second Law.

    Those of us who defend evolutionary biology here (basically everyone in the current discussion) would of course not say any of that, but would point to the energy flows through the human or the computer in the process of looking at coins and stacking them, and we would say that the Second Law is not violated.

    But they are not talking about the real Second Law but the Creationist Second Law, the C2LOT.  Which gets violated by human intelligence and by supernatural activity. 

    What I am unsure about is whether they think that nonhuman animals can violate the C2LOT. Do they think that, say, mice hoarding nuts violates it?  Does the intelligence that violates it have to have resulted from some supernatural event?  Or do they think that all animal brains get to violate the C2LOT because all of them started by supernatural zapping?

    It is hard to figure their view out — you certainly can’t use the real 2LOT to do so! 

  13. Part of this i grounded in the belief that human intelligence isn’t physical.

    Of course, from my point of view, it make me wonder why human intelligence can’t produce DNA coding strings with the fluency of speech.  

    I once has an exchange with someone at DU who argued that inventions like the light bulb were not the result of long chains of incremental discovery. 

    Incrementalism is simply outside their scope of understanding. 

  14. Elizabeth: But I do think that many ID proponents think of “intelligence” as as some kind of supernatural force (yeah, yeah, oxymoron I know) that moves stuff around without actually violating physical laws.

    They don’t think of it as something that is the property of systems that obey physical laws.

    That, indeed, does seem to be how they think.  I can understand that way of thinking coming from people on the humanities side of The Two Cultures but Sewell is an applied mathematician, so he ought to know better.  As a mathematician, he ought to be particularly sensitive to the problem of making unstated assumptions.  That’s what makes his arguments seem so bizarre.

  15. Joe Felsenstein: What I am unsure about is whether they think that nonhuman animals can violate the C2LOT.

    I think they do.  They rather like what Shapiro writes about intelligence in the cell, and they seem to think that this indicates something non-physical is involved.

  16. Regardless of what Sapiro personally believes about the origin of life, his take on evolution is entirely physical. 

  17. The mind-body puzzle has a long history, but the ID/creationists have not generally kept up with progress. We now know that living organism do not violate the second law of thermodynamics; in fact it makes no sense for living systems to violate any laws of physics and chemistry.

    As I have mentioned a number of times, there are some important lessons to be learned from the phenomena of hypothermia and hyperthermia. These are not trivial observations because we are observing some extremely tight limits on the energy ranges that permit the flow of electrical signals in the nervous systems of animals, warm-blooded or cold-blooded.

    What is happening is that, within a very narrow energy window, ions can pop back and forth through potential barriers on the order of a few hundredths of an electron volt. Keeping the system within a given temperature range allows this to happen. But if the temperature is lowered too much, the thermal kinetic energies are no longer sufficient to keep the system on the edge of being operational. Kinetic energies drop to far below binding energies or the potential energies of the “gates” through which ions move. If we raise the temperature too much, thermal kinetic energies now dominate the potential energies and the system becomes chaotic. What is this telling us?

    (I would point out here that studying the behaviors of systems while making temperature changes is a very nice way to probe the relative kinetic and binding energies within the system under study. We use such techniques routinely in experimental condensed matter physics.)

    So the phenomena of hypothermia and hyperthermia are telling us that the ion gates in the nervous systems of animals require energies on the order of 0.05 electron volts (action potentials are something like 70 millivolts). The potential gates that ions have to pop through are smaller than those action potentials.

    For the electrical engineers here, it is somewhat analogous to the gate of a field-effect transistor where a small change in the potential on the gate of the transistor allows a large change in the amount of current that can flow through the device.

    One of the experimental procedures in characterizing electronic devices is to measure their characteristics as a function of temperature. One discovers dramatic effects that reflect the competition between carrier mobility and the changes in the number of carriers that become more tightly bound because of the reduced kinetic energies of carriers and lattice vibrations.

    Organic systems – especially soft systems – are studied using many of these techniques. Soft systems are systems in which the average thermal kinetic energies are slightly smaller than binding energies. Using temperature changes allows exquisitely fine adjustments in the relative sizes of the kinetic and binding energies in order to study how these affect system behavior. Small temperature variations have very large effects on the ways these systems behave.

    In living systems, this tells us that much of what goes on within nervous systems is crudely analogous to the control of large flows of energy by very tiny changes in the potentials of ion gates. So a thought actually can control muscle contractions in a way that roughly analogous to how microvolt changes on the gate of Darlington pair of field-effect transistors can control the flow of large amounts of current.

    ID/creationists continue to believe that living systems involve some kind of dualism in which there must be a supernatural connection between a supernatural homunculus and a physical body. By not keeping up with physics and chemistry for the last few hundred years, they are completely unaware of what we already know and what goes on in real physics and chemistry laboratories.

    One wonders if they know anything about the effects of hypothermia and hypothermia on thinking and moving muscles.

  18. Joe wrote

    Those of us who defend evolutionary biology here (basically everyone in the current discussion) would of course not say any of that, but would point to the energy flows through the human or the computer in the process of looking at coins and stacking them, and we would say that the Second Law is not violated.

    But they are not talking about the real Second Law but the Creationist Second Law, the C2LOT.  Which gets violated by human intelligence and by supernatural activity.

    But the C2LOT is not violated by human intelligence or supernatural activity! Here’s Henry Morris’ formulation of C2SLOT:

    The Second Law of Thermodynamics could well be stated as follows: “In any ordered system, open or closed, there exists a tendency for that system to decay to a state of disorder, which tendency can only be suspended or reversed by an external source of ordering energy directed by an informational program and transformed through an ingestion-storage-converter mechanism into the specific work required to build up the complex structure of that system.

    See how easy it is? Just rewrite SLOT, manufacturing C2SLOT, and there’s no violation if all the conditions are met.

    (How come I keep getting trapped in the comment editor? WinXP Pro SP3, Chrome)

  19. I would still like to hear Sewell state unequivocally whether or not he thinks that the application of human intelligence allows the second law to be violated.  This was mentioned in one of the previous discussions of his claims, and while I haven’t seen a clear statement by him, it seems to be an inescapable conclusion of his position.
     

    Sewell did give a definitive statement.  He said:

    “the second law only applies to unintelligent causes.” 

    http://www.uncommondescent.com/intelligent-design/anything-can-happen-in-an-open-system-or-a-closed-universe/#comment-422639 

  20. Fine, but what this leaves uncertain is whether Sewell sees nonhuman animals as “intelligent causes”.  Is a squirrel that makes a pile of nuts violating the “Second Law” (or the C2LOT) in Sewell’s view?    If it is violating it, is that because the squirrel is intelligent?  Or because an Intelligent Designer designed the squirrel?  On the latter case, that leaves as an open question whether say, a carrot plant can violate the C2LOT.

  21. I suspect one will not be able to pin down Sewell on specifics.  That entire thread to which you linked is a classic example of the muddled thinking on the second law that has characterized ID/creationists since the 1970s and probably earlier.  One needs to read that thread against the historical misuse of the second law by ID/creationists.

    I was looking through my files and notes going back into the 1970s and 1980s, and this includes notes I took at some of the debates I watched between ID/creationists and biologists.  The misconceptions and misrepresentations back then have not changed significantly in the writings of people like Sewell.

     

    The only “new” twist that I can see in Sewell’s paper is his use of those integrals and in his introduction of “X-entropy” in order to essentially cook the books using “disorder” as entropy.  He is arguing against the notion of “compensation” without understanding the colloquial way in which physicists sometimes use it.  Hence his cooking of the books to show that “compensation” doesn’t occur.

    If one goes over to the ICR website and does a search on the second law of thermodynamics or on entropy, one can come up with nearly everything Henry Morris has written on the topic.  That raises the question of why ICR still makes this crap available when they have said on several occasions that the second law argument should not be used.

    Thomas Kindell’s 2004 video of the second law argument – I linked to it in another thread – is a pretty complete summary of how ICR taught it; and Kindell manages to put the entire taunting sneer into it that Duane Gish often did.  Besides using it in debates, Gish used it to bully teachers in Kalamazoo, MI.

    I no longer have that Basic Physics text by Kenneth Ford in my library; I culled it out many years ago.  I don’t remember ever using it to teach a course, but I may have received it from a publisher when considering texts for courses for non-majors. 

    However, I do have a couple of other texts for non-majors in which the authors make the blunder of using disorder as a metaphor for entropy; and they are discussing ideal gases when doing so.  I don’t recall what Ford did, but from what Sewell quotes, Ford’s text apparently contributed to the confusion.  That was probably one of the reasons I never used that text or the two that still remain on my shelves.

  22. Entropy is entropy. You can use any number of yardsticks. Thermal and information are convertible units. Information is convertable into energy, matter  or whatever and vice versa. But all within the bounds of entropy.

  23. The big problem of equating “information” – or the lack of “information’ – with entropy is in answering the question, “‘Information’ about what?” Also, what is “interpreting” this “information”?

    The best rule to follow is to leave entropy to mean what it has always meant.  Don’t conflate it with disorder or lack of information; that can only lead to confusion.

    Disorder is fairly easy to define mathematically once order is defined on a set of objects.  However, “information” is in the “eye of the beholder,” where the beholder has to be defined as well.

  24. If you think you can salvage Sewell’s argument, as refuted so effectively in at least two threads on this blog, I would very much like to see your detailed work.  Don’t forget the dimensional analysis!
     

  25. I would like to see disorder defined in a way that could distinguish which of two randomly generated DNA sequences is less disordered than another.

    I could make it easy and stipulate that both are derived from the same starting point — a sequence taken from a living organism and each having the same number of point mutations.

  26. Amusing irrelevance: The title of this thread can be sung to the tune of LONDON BRIDGE IS FALLING DOWN.

  27. Is Sewell marshaling an argument from incredulity, or is he simply asserting the implausibility of a tornado spontaneously assembling a complex object like a 747 or a supercomputer?

    How is Sewell’s verdict of implausibility materially different from what we read, say, in Richard Fitzpatrick’s Thermodynamics & Statistical Mechanics: An intermediate level course , on pages 79-80? (The text is freely available as a PDF here. For those concerned about his credentials, Fitzpatrick’s CV is here.) In the context of a discussion about reversible and irreversible processes and entropy, Fitzpatrick writes:

    There is a famous passage in the novel “Slaughterhouse 5,” by Kurt Vonnegut, in which the hero, Billy Pilgrim, views a propaganda film of an American World War II bombing raid on a German city in reverse.

    What is there about this passage [quoted in the text, but too lengthy to reproduce here] which strikes us as surreal and fantastic? What is there that immediately tells us that the events shown in the film could never happen in reality? It is not so much that the planes appear to fly backwards and the bombs appear to fall upwards. After all, given a little ingenuity and a sufficiently good pilot, it is probably possible to fly a plane backwards. Likewise, if we were to throw a bomb up in the air with just the right velocity we could, in principle, fix it so that the velocity of the bomb matched that of a passing bomber when their paths intersected. Certainly, if you had never seen a plane before it would not be obvious which way around it was supposed to fly. However, certain events are depicted in the film, “miraculous” events in Vonnegut’s words, which would immediately strike us as the wrong way around even if we had never seen them before. For instance, the film might show thousands of white hot bits of shrapnel approach each other from all directions at great velocity, compressing an explosive gas in the process, which slows them down such that when they meet they fit together exactly to form a metal cylinder enclosing the gases and moving upwards at great velocity. What strikes us as completely implausible about this event is the spontaneous transition from the disordered motion of the gases and metal fragments to the ordered upward motion of the bomb.

    Implausibility, not incredulity.

  28. Kent D,

    Is Sewell marshaling an argument from incredulity, or is he simply asserting the implausibility of a tornado spontaneously assembling a complex object like a 747 or a supercomputer?

    He asserts the implausibility of those things, and then erroneously concludes that the assembly of 747s and computers by any means violates the second law of thermodynamics. It’s a wild and reckless extrapolation.

  29. It would appear this “blunder” is being repeated. In the Fitzpatrick text cited in my prior post, I read on page 78:

    One way of thinking of the number of accessible states Ω is that it is a measure of the disorder associated with a macrostate. For a system exhibiting a high degree of order we would expect a strong correlation between the motions of the individual particles. For instance, in a fluid there might be a strong tendency for the particles to move in one particular direction, giving rise to an ordered flow of the system in that direction. On the other hand, for a system exhibiting a low degree of order we expect far less correlation between the motions of individual particles. It follows that, all other things being equal, an ordered system is more constrained than a disordered system, since the former is excluded from microstates in which there is not a strong correlation between individual particle motions, whereas the latter is not. Another way of saying this is that an ordered system has less accessible microstates than a corresponding disordered system. Thus, entropy is effectively a measure of the disorder in a system (the disorder increases with S). With this interpretation, the second law of thermodynamics reduces to the statement that isolated systems tend to become more disordered with time, and can never become more ordered.

    Emphases are Fitzpatrick’s.

  30. Yes, the blunder is being repeated by Fitzpatrick.

    Disorder and entropy are not the same.  Do you know why?

  31. I take it that most participants in the present discussion understand Sewell to be asserting that there are times when the 2LOTD (as opposed to a so-called C2LOTD) actually does not hold. Am I reading you all correctly? Because that’s not what I understand Sewell to be claiming.

    A “violation of the 2nd law” might simply be a phenomena or an event (real or imaginary) that is inexplicable in terms of the 2nd law alone; i.e. that seems to obviously run counter to the 2nd law, and hence “violate” it.

    There is a potential ambiguity here. For a given phenomena, is the law “violated” because the law was actually suspended (not active; non-binding) for a time while the phenomena was produced? Or is the law “violated” in the sense that, the law being fully and continuously in effect, some force or causal explanation other than the 2nd law must be posited to account for the production of the phenomena?

    Which sense (if either) does Sewell have in mind?

  32. Mike E. wrote:

    Disorder and entropy are not the same. Do you know why?

    No, but I’m sure you’ll be willing to enlighten me. 😉

  33. What does disorder have to do with energy and temperature?  What does entropy have to do with energy and temperature?

    If you jumble up the alphabet, how does it affect the temperature of the alphabet? 

    You can arbitrarily define order on a set of colors. What then does rearranging a collection of different colors do to the temperature of the colors?  

  34. The excerpt from Fitzpatrick cited by Kent_D is not a definition of entropy. That passage follows the precise definitions given in Eqs. 5.50 and 5.68 and is intended as a hand-waving, interpretive analogy. Analogies are a great way to convey a difficult concept, but they sometimes fail. This particular analogy fails, too.

    For starters, look at page 74, where Fitzpatrick computes the change of entropy for a gas that is initially confined in one half of a box by a partition. When the partition is removed, the gas expands to fill the entire container. As a result of the expansion, the entropy increases by ln2 per particle. The disorder story makes little sense in this case. The gas does not look any more disordered when it occupies the entire container than it occupies just half of it. On the other hand, the entropy increase follows straightforwardly from the standard entropy definition: in a volume twice as big the gas has more microstates because every molecule can now access twice as many positions as before.

    In some cases, the hand-waving interpretation is plain wrong. Consider this passage:

    Another way of saying this is that an ordered system has less accessible microstates than a corresponding disordered system. Thus, entropy is effectively a measure of the disorder in a system (the disorder increases with S).

    This works most of the time, but sometimes it fails. For example, Lars Onsager showed that an ordered state of liquid crystals (a nematic, in which molecules tend to be parallel) has a higher entropy than a fully disordered state (molecules are randomly oriented). This directly contradicts the above excerpt but not the precise definition of entropy given by Fitzpatrick.

  35. Gravitational systems are another exception.  In such systems, entropy is maximized when the matter clumps together in the smallest possible volume — a highly ordered state.

  36. Gravitational systems are another exception.  In such systems, entropy is maximized when the matter clumps together in the smallest possible volume — a highly ordered state.

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