Natural Sciences

Understanding Natural Phenomena 6: How can Order Emerge out of Disorder Spontaneously?

Editor’s Note: This article is a part of the series Understanding Natural Phenomena.

As explained in Part 5, the second law of thermodynamics says that, for an isolated system, the state of maximum disorder is the most likely thing to happen, given enough time. All gradients tend to be obliterated, and ultimately a zero-gradient or equilibrium state is attained if there is no input/output of energy or mass.

The important thing to understand is that the above statement of the second law is for an ISOLATED system; i.e. a system which cannot exchange energy or matter with the surroundings. By contrast, an OPEN system is one which can exchange energy and matter with the surroundings. Your own body is an example. You are alive because you are exchanging energy and matter with the surroundings. Any living organism, if kept fully isolated from everything, would die eventually. It would be reduced to a final state of total equilibrium and stability, with no gradients of any kind. EQUILIBRIUM IS DEATH.

For open systems there is still a second law of thermodynamics, but it has to be so formulated that it includes the possibility of input/output of energy and/or matter.

Any gradient implies that the system is away from a state of equilibrium. Such a system is therefore unstable, and the spontaneous dissipation of the gradient demanded by the second law amounts to a move towards STABILITY. There is a hint here about how to generalize the second law so that it is applicable to open systems also. We have to incorporate two things: The tendency towards disorder; and the tendency to achieve stability by exchanging energy and/or matter with the surroundings (an option not available for isolated systems). We quantify the first part by introducing a parameter called ENTROPY (denoted by S). And the parameter relevant for the second part is INTERNAL ENERGY (denoted by U).

Entropy, or rather change of entropy, is defined as follows. Suppose we have a system at a temperature T, and we add a small amount dQ of heat to it. Then dQ/T is defined as the change of its entropy, and denoted by dS.

Consider a system as having two parts, one at temperature T1, and the other at a slightly higher temperature T2. When heat dQ flows from the second part to the first, the net change of entropy is dS = –dQ/T2 + dQ/T1 . Since T2 > T1, we must have dS > 0 always. Entropy does not decrease.

With the passage of time, T2T1, and therefore dS → 0. Finally, when T1 = T2, we have dS = 0, and equilibrium is said to have been reached. If a system is in equilibrium, it is implied that its entropy has reached the maximum possible value under the circumstances, and stopped changing any further.

So much for the entropy contribution to stability. Let us consider the energy part next. An example will help. Water changes to ice when cooled below 0oC at atmospheric pressure.

A crystal of ice has a highly ordered arranged of water molecules, arranged nicely on a lattice. This is clearly a case of order emerging out of disorder, so why does it happen? Why does an ordered structure emerge out of the highly disordered or chaotic motion of molecules in liquid water? This happens because the watchword is STABILITY, and not just order vs. disorder. For an open system, since energy and mass can be exchanged with the surroundings, the possibility is available that a higher-stability state may be attained (for example by a stronger bonding among the molecules) even at the cost of a little lowering of entropy locally. In the water vs. ice situation, whereas at high temperatures the average speed of the molecules is so high that they just collide with one another and go their separate ways again, for temperatures below 0oC the motion is sluggish enough that the molecules are able to stick together and form chemical bonds. The process of chemical binding releases some heat energy, which is transmitted to the surroundings. This loss of energy is possible here because it is an OPEN system. The bonded or crystalline configuration is a more stable situation at the prevailing temperature: Crystalline water, i.e. ice, has a lower internal energy (U) compared to liquid water.

Thus the overall stability is decided by a tradeoff between two energy terms: U and TS. We define a new thermodynamic parameter F as (U – TS). This parameter (called FREE ENERGY) decreases as the entropy S increases (because of the –ve sign in front of the entropy term TS). And it also decreases when U decreases; i.e. when the systems acquires a more stable configuration.

So, for open systems, the second law of thermodynamics has to be stated as follows:

IN ANY PROCESS OR PHENOMENON, THE OVERALL FREE ENERGY CAN NEVER INCREASE; IT EITHER DECREASES OR REMAINS THE SAME.

The tendency towards greater disorder is present in open systems as well, but the overriding requirement in both isolated and open systems is always that of maximum stability. We see so much order and self-organization around us because what we have are systems which are able to exchange energy and matter with the surroundings for achieving maximum-stability configurations. Nature does abhor gradients, but even the abhorrence of gradients is nothing but a tendency towards greater stability: Zero gradient means equilibrium, and therefore stability.

There is so much self-organization occurring in Nature all the time, but there is no violation of the second law of thermodynamics ever.

‘If someone points out to you that your pet theory of the Universe is contradicted by experiment, well, these experimentalists do bungle things sometimes. But if your theory is found to be against the Second Law, I can give you no hope; there is nothing for it but to collapse in deepest humiliation’ (Arthur Eddington, 1944).

About the author

Vinod Wadhawan

Dr. Vinod Wadhawan is a scientist, rationalist, author, and blogger. He has written books on ferroic materials, smart structures, complexity science, and symmetry. More information about him is available at his website. Since October 2011 he has been writing at The Vinod Wadhawan Blog, which celebrates the spirit of science and the scientific method.

21 Comments

  • Do you mean universe is open system? If so something must exist before bigbang or there is something beyond universe which is non accountable. So ultimately will these theories solve the problem of ‘openness’ of universe?

    Will be grateful to know if I missed anything basic here.

      • Thank you, Arvind, for your comment.

        Ramesh, I shall answer your question at two levels: terrestrial and cosmic. At the terrestrial level our ecosphere is an open system, receiving energy from the Sun, using a small part of it, and sending the rest back to outer space. So it is an open system.

        The cosmic question is difficult at present. There are several unknowns. An example is the value of Einstein’s cosmological constant. The experts are not yet agreed on whether the universe will go on expanding forever, or perhaps it will bounce back in the distant future. In any case, so far as humans are concerned, till all life on Earth is snuffed out when our Sun is about to die, there would be a continuous creation of gradients of various types and, as my article says, the tendency of Nature to annul gradients will create ordered structures locally.

        Future articles in this series will touch on some cosmic aspects. Meanwhile please see:
        http://vinodwadhawan.blogspot.in/2012/02/15-dark-matter-and-dark-energy.html

        • Dear Vinod,

          I understood how ordered structure emerges for closed systems which can be ‘opened’ with the system called universe and that is how all the observed natural phenomena are explained. This is terrestrial and has been the area of scientific work and achievement.

          At the cosmic level may I understand that we cannot explain at all at present as to how the ordered structure emerged out for the very closed system called universe in respect of which there isn’t any open system? Can science reach the area for which it is not at all defined?

          If so then it has been the very eternal problem or riddle for the mankind!

          The moot point would be whether this can be ever solved?

          @Arvind,

          I abhor any sort of idea like creator. That has been our position since the beginning. WHETHER or NOT something can ever emerge out of nothing has not been the problem with us so far. Problem has been WHY AT ALL something emerges from nothing! Nothingness (not vacuum) has no properties to cause something to appear whatsoever. See if you have got my point. Happy to know if I miss anything subtle.

          • Not quite like that. Gradients are being created because the universe is expanding. But it is not as if the universe is expanding into spacetime which was not a part of it earlier. Some earlier research work of Stephen Hawking had established that when we add the effects of quantum theory to the general theory of relativity, in extreme cases warpage can occur to such an extent that time behaves like another dimension of space. Thus in the early universe, when it was small enough to be governed by both general relativity and quantum mechanics, there were effectively four dimensions of space and none for time. Time as we know it did not exist when we extrapolate backwards in time towards the very early universe. So how did time begin? I quote from the book ‘The Grand Design’, mentioned by Arvind:

            ‘Suppose the beginning of the universe was like the South Pole of the Earth, with degrees of latitude playing the role of time. As one moves north, the circles of constant latitude, representing the size of the universe, would expand. The universe would start at a point at the South Pole, but the South Pole is much like any other point. To ask what happened before the beginning of the universe would become a meaningless question, because there is nothing south of the South Pole. In this picture spacetime has no boundary – the same laws of nature hold at the South Pole as in other places. In an analogous manner, when one combines the general theory of relativity with quantum theory, the question of what happened before the beginning of the universe is rendered meaningless.’

            The term ‘no-boundary condition’ is used for the idea that the histories of the universe are closed surfaces without a boundary (in an appropriate hyperspace).

            Thus, we can certainly explain how cosmic structure emerged spontaneously after the Big Bang. It all happened, and is still happening, because gradients were and are being created by the expansion and cooling of the universe.

          • Something emerged from nothing because this ‘something’ was more stable that nothing. This is explained in Lawrence Krauss’s recent book. The quantum-mechanical nothing is not at all stable. It undergoes quantum fluctuations all the time. One such fluctuation at the Big Bang got yanked apart during the ‘inflation’ episode. Please watch this space for more! Or read my post at http://vinodwadhawan.blogspot.in/2012/03/17-all-important-cosmic-inflation.html

          • Dear Vinod Wadhawan,

            //Something emerged from nothing because this ‘something’ was more stable that nothing.//

            Reference from ‘Universe from nothing'((http://www.nobeliefs.com/Krauss.htm))

            //”Why is there something rather than nothing?” must be understood in the context of a cosmos where the meaning of these words is not what it once was, and the very distinction between something and nothing has begun to disappear, where transitions between the two in different contexts are not only common, but required. //

            1. Thus something can hardly be different from nothing. i.e. there can be only energy and no emptiness. This nothing compares to the moment just before the Big bang(Please correct if wrong). Thus there was always something (i.e. quantum nothing)

            2. In a flat universe, and only in a flat universe, the total average Newtonian gravitational energy of each object moving with the expansion is precisely zero! (from the same reference). This zero cannot be quantum nothing from the way it is defined here (i.e. sum zero)

            Thus stating on one hand that there can always be energy and and stating on the other hand that net energy is zero seems to be contradictory.

            Pardon my poor understanding of science quantum mechanism) and pray clarify the things, if possible.

        • I think the main problem relates to entropy. As you have pointed out yourself, physical systems must follow the second law. In that case, all explanations must start with how the universe came to a low entropy state at the instant of big bang. If the universe was the system, what was its surroundings which absorbed massive entropy increases so that the universe could maximize Gibb’s energy. All talk of subsequent patterns, low entropy pockets etc is irrelevant unless science can provide satisfactory solutions to this fundamental problem. As of today, scientific speculations are no more valid than a theory that the universe was created ( the details of which differ as per the differing metaphysics of different religions).

          • Some of my future posts here will explain some more the meaning of entropy, including the idea of NEGATIVE ENTROPY (or NEGENTROPY) introduced by Schrodinger. Apart from the idea of entropy of open systems, another concept poorly understood by many people is that of spacetime, as also the meaning of expansion of the universe. There was no space, time, and entropy before the Big Bang. More and more spacetime gets created as the universe expands. It is silly to ask what does the universe expand into, as there is nothing ‘outside’ it (as explained, for example, by Hawking & Mlodinow).

            As the universe expands and cools, gradients are being created all the time, which is equivalent to the creation of an enormous amount of negative entropy, which must be included in all the book-keeping you do about the change of entropy. If there is a problem here, I fail to see it.

  • I wonder how the above article can have any relevance to the larger cosmological questions. Yes, it is well known that low entropy pockets can arise spontaneously as long as the total entropy of a system + surroundings increases. In such a case, it does not matter if the entropy of the system has decreased since the entropy of the universe has , in any case, gone up. The pertinent question is how, at the time of the big bang (provided the big bang is assumed to have taken place), the entropy of the system was at a minimum. As per the 2nd law, this minimum entropy must have been accompanied by a great increase in entropy elsewhere. Now, what is this elsewhere? And what acted on in that a low entropy pocket was formed? I dont think this article, or science for that matter, has even any remote suggestion in this regard.

    • Some of my future posts here will explain some more the meaning of entropy, including the idea of NEGATIVE ENTROPY (or NEGENTROPY) introduced by Schrodinger. Apart from the idea of entropy of open systems, another concept poorly understood by many people is that of spacetime, as also the meaning of expansion of the universe. There was no space, time, and entropy before the Big Bang. More and more spacetime gets created as the universe expands. It is silly to ask what does the universe expand into, as there is nothing ‘outside’ it (as explained, for example, by Hawking & Mlodinow).

      As the universe expands and cools, gradients are being created all the time, which is equivalent to the creation of an enormous amount of negative entropy, which must be included in all the book-keeping you do about the change of entropy. If there is a problem here, I fail to see it.

      • Yes there is a problem, and I am surprised that you fail to see it. Maybe I have not been too clear in my first post. So i will try to restate it. I am not concerned with the entropy changes which take place after big bang as they are simply secondary phenomena involving rearrangement of thermodynamic sub-systems – so that entropy decrease in one sub-system is compensated by increase elsewhere. Nothing unusual in this and this happens in nature all the time. What I am getting at is that at the instant of the Big Bang, the compressed universe had very low entropy and very high Gibb’s energy. Are you OK with this assertion or do you dispute it? So the fundamental problem is how this low entropy state came into being, and this of course is inextricably linked with how matter-energy came into being in the first place. What happened subsequently is simply a matter of details, and while being interesting, cannot overcome the ignorance about the initial state. I know that science has many theories in this regard – in fact, too many which again indicates that most scientists are simply taking out of their hats. But to be convincing, a theory must provide reasonable explanations for the coming in existence of matter-energy out of nothing. And Krauss’s book notwithstanding, it is clear that science does not have the faintest idea in this regard. In fact, Krauss has been forced to admit that his “nothing” consists of quantum fluctuations and not really nothing in the real sense of the word. This is only pushing the problem one step back as admittedly quantum fluctuations can arise only if there is something for them to arise out of. This being the case, the idealist view of the Upanishads, or even the creationist’s views should be considered as equally valid and legitimate as the wild mumbo jumbo explanations which are being touted as scientific theories of the origin of universe.

        • Just because we can ask questions like what happened “before” the big bang, it does not mean that any fancy nonsense becomes valid. Because here validity is determined by explanatory power. Fancy nonsense has zero explanatory power other than to give an illusion of an answer.

          • Why this aggression my friend? Aggression and name calling only suggest that your position is weak. Is my question not relevant? I asked this question only because science makes a claim that it is the only valid knowledge system and that its methods provide explanatory power for all kinds of phenomena. However, when its comes to larger cosmological issues, there is nothing on offer apart from a menu of wild conjectures. In fact, if you read Mr Wadhawan’s article above, or even the latest in String Theory, it presents more as a story, a kind of broad narrative – even a metaphorical construct – rather than a cogent theory based on accepted laws. This is not the method of science.If stories are what we want to hear, I am sure that the narratives of the Puranas are far more interesting, and I would even claim that they are far more internally consistent. In fact, the entire Hindu metaphysics is remarkably coherent and internally consistent. If science has come up against a wall at the instant of the Big Bang, it cannot be the real McCoy notwithstanding the fact that it has been able to create useful models for common phenomena.

          • Spare me the tone trolling. There is a great deal of evidence for calling something as nonsense and as fancy. That has been elucidated in a number of articles on this site.

            All knowledge is probabilistic. It just happens that science has consistently shown that it can provide valid knowledge. It is that high prior probability which lends credence to cosmological theories based on science. As more observations come in, the probability will be lowered or increased. That is how science works, as opposed to fancy nonsense where probabilities stay constant.

            Another important factor which you conveniently ignored to mention is that any cosmology has to play well with other branches of science like physics or biology. Fancy nonsense cannot do that. For example you can’t construct a phylogenetic tree using Hindu metaphysics. The Harry Potter series too is extremely coherent and consistent. But it would be delusional to think that Harry Potter canon has any validity as a knowledge base for cosmology.

          • You claim that any cosmology should play well with other branches of science. Why should it be so. You are again making an unstated assumption that the methods of science – empiricism, experimental verification and falsification must be the gold standard for all knowledge systems. But why should it be so. Yours is simply a metaphysical assertion which you have no real way of proving. Because science makes certain assumptions, it’s methodology and conclusions must necessarily be limited;but can it then say that this is the only methodology. Suppose I decide that red colored objects are the only real objects and I construct my knowledge system accordingly, cam my method be ever falsified internally. And what if I make the ultimate idealist claim – that the universe is simply the impression produced in my mind due to various inputs from the senses. Can you ever refute this? But you are forcing me to digress . My original response was related to the need for explaining the original low entropy state of the universe -or whatever existed at the instant of big bang. It is a perfectly valid query based on everyday laws of physics.

          • Why should it be so? To meet the standards that you have set – coherency and consistency. I find it hypocritical of you when you critique scientific cosmology using those assumptions and when I pointed out the obvious outcome of such assumptions, you weasel out by asking Why should it be so?.

            As to methods of science, yes they are the best ways we have to understand natural phenomena. They are the methods which help us in understanding what will happen if you jump off a building. You can play the stupid game of science cannot answer what was there “before” big bang and perform the intellectually dishonest feat of equating science with fancy nonsense. Playing that game, when you jump off a building, if you have a broom in your hand, you can fly off on that broom instead of falling down. If such profound knowledge systems make perfect sense to you, good. They don’t for me.

            Science is built on some assumptions. If you think you have found some failing of science by “discovering” those assumptions, well, the joke is on you. These assumptions are known to anyone who understands science. I admit that some questions we construct do not have answers, and may not for forever. But that doesn’t mean we need to resort to fancy nonsense to pretend that the unknown is knowable or can be made sense of. So stop wasting our time and play your pointless games elsewhere.

          • So it is as I suspected. This is an advocacy site rather than a forum for honest discussion – a sort of mutual admiration society. I realize that you have internalized the dogma of scientism to such an extent that it is impossible for you to appreciate that it’s foundations are arbitrary. And this is precisely what religion has been accused of. Read Karl Pooper to understand how the metaphysical foundations of science are themselves completely arbitrary, and may even be irrational. I have also seen the abject amateurishness and the lack of rigor on this forum, and so I won’t waste my time here any longer.

          • It’s Karl Popper. Not Karl Pooper. I’ve also had my Kuhn and Feyerabend. Popper said nothing of that sort. You are just putting words into his mouth. Disgusting intellectual dishonesty.

          • @Satish Chandra

            Kuhn and Feyerabend! Really!! Hasnt helped you much I see. And it is very clear that you have never read Popper.

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