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Disorder, as I understand it, is basically a measure of entropy. This does not seem correct to me, and appears to be a result of our macroscopic bias.

Not only does the beginning of the universe appear to make more sense when one thinks in terms of disorder to order, but so does its end. A particular form of disorder (not necessarily maximum) could have started the big bang (dark matter or anti-matter might be related to this); the universe is essentially returning to a perfect equilibrium, or zero, state. Energy at the end of the universe would be indiscernible from energy that naturally pops in and out of existence (also probably related to the big bang) so, effectively the universe ceases to exist.

Meanwhile... in other parts of the void or multiverse.. energy continues to pop in and out of existence (or just strange things occur), and even though the probability is ridiculously low, eventually an unstable disorder emerges, which causes a big bang type event... repeat.

Related to: Entropy is...disorder?

I was not satisfied with the answers to the above question due to them not focusing on a small enough scale (energy). They were focused on molecules, atoms, or their known components.

Note: one cannot consider an atom to be ordered (see comments below), and even a uniform cluster of energy would not be considered ordered unless its surroundings were in the same state; thus, it would seem the universe has to expand in order to become more ordered.

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closed as unclear what you're asking by Norbert Schuch, tfb, John Rennie, user36790, ACuriousMind Jun 7 '16 at 13:20

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    $\begingroup$ Isn't the consideration (counting) of microstates small-scaled enough? $\endgroup$ – Steeven Jun 7 '16 at 7:14
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    $\begingroup$ Is there a question here? If so, what is it? $\endgroup$ – tfb Jun 7 '16 at 7:21
  • $\begingroup$ "Truly ordered state (assume you arrange a sculpture from atoms) " His example would actually be massive disorder (atoms are not uniform), and only appears to be order to us thinking at that scale. Micro-states of individual energy particles at near-maximum entropy would be orders of magnitude more ordered.. $\endgroup$ – user2800679 Jun 7 '16 at 7:22
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    $\begingroup$ @user2800679 no. $\endgroup$ – tfb Jun 7 '16 at 7:27
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    $\begingroup$ My general advice to those who worry about disorder and entropy is to learn to understand why the original definition is based on reversible heat flow. That ought to clear a lot of phenomenological and philosophical problems up. $\endgroup$ – CuriousOne Jun 7 '16 at 7:51
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Tl,dr: Entropy is the right definition, because it's incredibly useful in the description of statistical and thermodynamic systems. Whether or not it quantifies "disorder" in whatever sense of the word is completely irrelevant - it just so happens that it can be interpreted that way.


Entropy is not a measure of disorder. At least not really. Then again, if you count information theoretic entropies, there is more than one entropy.

Let's start with the classical definition: A very useful thermodynamic concept is that of a heat engine. This is a contraption, which can transform heat energy into work or vice versa. When considering such heat engines, it turns out that while energy conservation is undoubtly necessary, it is not enough to fully describe heat engines. In particular, it doesn't really capture irreversibility. It was then realised (by Clausius) that you also needed what today is known as the second law of thermodynamics and with it, entropy. In short: entropy is conserved for irreversible processes. This implies that entropy is the right physical concept: it correctly classifies heat engines according to their capabilities and it can correctly predict reversibility in isolated and closed systems (among other things).

Shortly thereafter came Boltzman's statistical definition. Given a macroscopic state, it counts the number of microstates that a system can possibly be in and weighs them according to their probability. The more microstates a system can be in, the higher its entropy. Now if you posit that any microstate is (a priori) equally likely, this will give you the definition of Boltzman's statistical entropy. In view of a better microscopic understanding of the world, Boltzman saw the need to describe macroscopic systems in terms of their microstates. On the one hand, since the number of microstates is huge (sometimes formally infinite), this is a hopeless undertaking. On the other hand, not every single aspect of the microscopic world will result in a differen macroscopic behaviour, so there is hope that you can capture the microscopic properties in a few simple measures that you can then use to derive the macroscopic (thermodynamic) entropies such as temperature, volume, etc. This is essentially why entropy was introduced.

The beautiful thing is that the two definitions turn out to be consistent.

This is essentially, where you have things backwards: Entropy is not supposed to be a measure of disorder, it rather happens to be a measure of disorder in the precise sense that a system is more disordered, if the number of microstates that lead to a given macroscopic state is large and their probabilities are close to equidistribution. In this sense, a solid state is more disordered and a gas is less disordered, because in a crystalline solid, the number of configurations of the atoms is clearly more limited.

In other words: The precise meaning of "disorder" in thermodynamic systems is defined via entropy and not the other way round. The reason that makes physically sense is that entropy is not (a priori) meant to be a measure of disorder. Entropy is used to a) quantify reversibility/irreversibility in heat engines, and b) define useful quantities for macroscopic systems based on only the microscopic states of the system. The fact that the second law exists can be seen as one possible "proof" that entropy is the right definition: it captures an extremely important concept in our theory of the world.


Further notes: As I said, there are other entropies - especially in information theory. They are various measures of how much information content a system has or how much information is accessible, etc. While they are very useful in information theoretic contexts (the Shannon entropy for instance characterises the maximum lossless compression rate without prior knowledge), it is not always clear how these entropies relate to statistical physics and it is an active field of research.

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  • $\begingroup$ Thank you. Please forgive my ignorance.. but I don't quite get it. So, disorder is defined via entropy; what I'm failing to understand is why it's disorder, and not order. if the universe were to convert all of its energy into heat, that would be considered maximum entropy, correct? But if that were to occur, there would no longer be atoms, their components, movement, and space and time might even break down, no? so, in that state, wouldn't micro-states on average, for the total energy of the system, be closer to uniform (more ordered) than it is currently --akin to a gas vs a solid? $\endgroup$ – user2800679 Jun 7 '16 at 18:12
  • $\begingroup$ The thing is that a uniform distribution is the most disorder you can get in this definition. An analogy is the following: If you order your books in a closet, there is bascially only one such state. If you distribute your books around your room, there are many different distributions that lead to an outcome that looks equally messy (in order to distinguish the distributions, you'd need to look closer). This means that the messy room has a higher entropy: it has more possible distributions of books. It's the same with the universe. But in the end, "disorder" is a language definition... $\endgroup$ – Martin Jun 7 '16 at 18:40
  • $\begingroup$ I think I see the issue now.. Okay, so in your analogy you have books, a bookshelf, a desk, etc. It makes sense then that one's idea of order would not be synonymous with uniformity; however, imagine that room was a giant black box (the system) with nothing in it but books, and every one of those books was exactly the same (energy). In this situation order would not be having the books clumped up in a particular section of the box; instead, order would be uniformity; thus, even a random distribution would likely have greater order than if they were all clumped in X location. $\endgroup$ – user2800679 Jun 7 '16 at 19:17
  • $\begingroup$ AKA, our mundane everyday definition of order is arbitrary, and does not necessarily take into account the entire system. When the system is taken into account, measure of order is measure of uniform distribution. $\endgroup$ – user2800679 Jun 7 '16 at 19:29
  • $\begingroup$ @user2800679: Yes, our mundane everyday definition is in some sense arbitrary. It's in a sense a matter of language. "More entropy means more disorder" is closest to the everyday definition, if you consider microstates of the system (but I'm not completely convinced that's always the case). That's why I argue you shouldn't even think of it that way at first. You should first learn how it is really defined and why it makes sense. Then you are free to try to find an everyday description. $\endgroup$ – Martin Jun 7 '16 at 22:26

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