You're making the (very common) mistake of taking a poetic English-language interpretation of a physical law -- which is necessarily lossy/imprecise, since the actual law is mathematical -- and over-interpreting the words without referring back to the actual law.

You can see the law (in the context of thermal & statistical physics) at https://en.wikipedia.org/wiki/Entropy_(statistical_thermodyn.... You can of course argue that 'disorder' isn't a good way of translating the maths into English, but shrug, it's the one people seem to have settled on. And of course, that's orthogonal to whether the actual law is true or not.

'Information' is another way to translate. See https://en.wikipedia.org/wiki/Entropy_(information_theory)

Personally, I don't like the description of entropy as disorder.

Mathematically, it's a measure of spread of a probability distribution (the more spiked a distribution, the lower the entropy, which is an 'ordered' state insofar that things are arranged in specific places instead of randomly thrown all over the place).

Depending on your point of view, I would describe entropy in physics as microscopic indeterminacy (essentially the number of microscopic states that are part of your statistical ensemble defined in terms of macroscopic constraints), or as microscopic freedom (essentially the volume of microscopic phase space accessible to time evolution of a system in thermodynamic equilibrium).

I think the response you got pointing out that "disorder" is a poor approximation of the actual physical law is the best explanation but it's probably dissatisfying.

I like this analogy from Sean Carroll, explaining the difference between disorder and complexity: the moment you first pour cream into your coffee, the coffee-cream system is low entropy. All the cream is at the top, all the coffee is at the bottom, none is mixed together. It's very easy to describe the system. If it was stored as data, you could compress the data very easily. After you stir the coffee for a while and it's all mixed up, it is in its highest entropy state. It's all smooth and mixed together. This is also very easy to describe: everything is mixed up. It's in the middle where you get all the neat swirrles and interesting patterns. We're living in the middle state, between the low entropy moment at the big bang and high entropy heat death of the universe. The galaxies and clusters and life are the swirles.

It might be easier to view entropy of a state as sort of the probability that that state would occur after randomly arranging all of its parts (usually particles). In fact this is pretty close to the actual definition.

Here's an example: Suppose you had a container and you put some marbles at the bottom such that there are reasonably large gaps between the marbles. Now if you close and then shake the container hard (this is the 'random arrangement' process), then it is with high probability when you open the container that the marbles will be arranged reasonably spread out across the bottom. In this sense, when the marbles are spread kind of far apart in the container, it is in a state of high entropy (probability).

There is also the chance that when you open the container the marbles form a perfect straight line at the bottom. However, this is much more unlikely, so that you would consider this a low entropy state.

Now, consider the universe in place of the container, and subatomic particles as the marbles. Randomly configuring all of these particles, it would be really hard to end up with a stars, galaxies, humans. These are like straight lines in the marble example. It is much more likely you just get a soup of somewhat uniformally distributed particles (as in the marbles just being sort of randomly spread out from each other). This is what you describe as "a perfectly uniformly distributed of zero temperature mass (or maybe absoute zero, not sure) of grey energy is the perfect order". It wouldn't really be 'perfect' in some senses of the word though, which may be your cause of confusion. It would be more like if you took a snapshot of the static on an old TV.

The common depiction is of a bunch of particles of two kinds, sorted into separate compartments by kind, which will mix if a divider is removed. In this picture, every part of one kind receiving a partner of the other kind, that can be called a state of order. If we take heat instead, every particle swinging differently is more chaotic--at least in my understanding--than all synching up so that their speeds relative to each other are zero ... 0 degree is just not higher order, because "high" is associated with high frequency (or energy or order).

In your shaky example, you transmit energy to the system by shaking, so if shaking a certain way, you'd well expect standing waves, if shaking a bit more you'd pulverize the marble and ultimately a hot plasma with density gradients. I wonder how hard you'd have to shake and swirl to eventually get a black hole, for which the notion of entropy doesn't even really make sense, if you aren't inside.

>Why is this a measure of "disorder"? In my eyes, a perfectly uniformly distributed of zero temperature mass (or maybe absolute zero, not sure) of grey energy is the perfect order?

Order here means something specific.

A sand castle has more order, in that sense, than sand thrown around (e.g. the default state of sand in a beach) -- the sand in the castle is ordered in specific ways to represent something.

>I would call a perfectly uniformly smoothed out heat-death of the universe perfect order (i.e. the opposite of chaos).

Again, chaos in this sense means (to put it in layman terms) that nothing is put in some particular order. The "perfectly uniformly smoothed out heat-death of the universe" means nothing is explicitly ordered in some way -- any chunk of that universe that you take will have an equal distribution.

Here's another example:

A layered cake has an order (e.g. chocolate, cream, biscuit, marmelade, biscuit).

A layered cake mixed up on the blender on high, has no such order, it's all a chaos (even though it's smoother).

Entropy is more accurately defined as hidden information, or the number of possible microstates that a system in a certain macrostate could have. Here's a great lecture by Leonard Susskind on the topic: https://www.youtube.com/watch?v=n7eW-xPEvoQ

What distinguished macrostates from each other? What distinguishes a macrostate from a microstate?

I'm trying to learn all this, I have the same issue. So far my best interpretation is that order means energy-transfering organization, a solid is ordered, a gaz is not. It's not to be seen as complex vs simple, a machine is more complex than a bunch of cold molecules, but it's would be less chaotic in that sense.

Another definition is the number of possible microstates that can be reached. A cold universe of evenly distributed particles would be the upper limit of these microstates.

ps: coursera just started this https://www.coursera.org/learn/statistical-thermodynamics

>> a perfectly uniformly distributed of zero temperature mass ... is the perfect order

At max entropy, things would not be uniformly distributed: equal distance between each atom. Rather they would be randomly distributed. There'd be some clumping but without much pattern. If such a system were of near infinte size, the number of variations of its alignments would far exceed the much smaller near-infinity of slightly or somewhat more ordered possible systems in the same universe. Especially in the case of your uniformly ordered one, which is almost unique in that universe.

This is entirely incorrect. Our solar system started out as a gas cloud of randomly distributed atoms which then proceeded to become atoms organized into spheres called planets. This happened spontaneously and is not the result of energy entering or exiting the system.

Almost all atoms started out in a state of random distribution before transforming themselves into almost perfect spheres orbiting in an almost perfectly circular orbit around a giant glowing sphere called a star. These stars then organize themselves into beautiful ordered spirals called galaxies. Entropy always increases and most people think high entropy is a state of random distribution, but the organization of atoms in the universe is definitely not heading in that direction.

Thanks to gravity the universe will not become a place where atoms are perfectly randomly distributed. This does not make sense from an intuitive perspective and observational as well.

Strange right? Entropy has not reversed. What's going on most people don't have an intuitive grasp of what the true definition of entropy is.

Allow me to elucidate.

The "disorder" that entropy refers to can actually take on many forms. In the case of our solar system it is perfect spheres that orbit another glowing perfect sphere. In the case of food coloring dispersing in a glass it is atoms randomly distributed.

Entropy simply put should not be called a law it is really a consequence of probability. If the organization of atoms is in a high probability state than it has high entropy if it is in a low probability state than it has low entropy. Put it this way: atoms and gravity by probability are more likely clump into perfect spheres rather than stay in a perfectly randomly distributed gaseous state. Spherical planets are then according to this definition entropy, at a higher state of entropy than a gas dust cloud.

Seem crazy right? It seems like entropy is reversing... randomly distributed atoms organizing themselves into clumps of perfect spheres... The reality is nothing crazy is going on. Intuitively we know gas dust clouds organize them selves into spherical planets and solar systems. It's your definition of entropy that is off. Are intuitive notions of disorder and chaos are clashing with what entropy defines as 'disorder' and 'chaos'

Wait, what happens if we look into the collapsing of the galaxy from an informational-theoretic view of entropy?

As far as I know, thermodynamic and informational-theoretic entropy are the same except for the Boltzmann constant. It certainly seems to me that the informational entropy of the galaxy is lower than the original gas cloud.

That is, if I wanted to describe the state of a single atom in the gas cloud (lets presume the number of atoms is constant) using a perfectly tuned compression algorithm, I'd need more bits to do it than if I wanted to do the same for an atom in the current galaxy (again using a compression algorithm perfectly tuned to that situation).

Perhaps, because the gas cloud was cold, but the galaxy is 'hot' we actually need more bits because the individual particles can go faster, and thus have a larger range of possible speeds? Is this indeed enough to compensate for the much easier to describe location? Do I need to take more than just location and speed into account?

I'm less familiar with the information perspective of this topic.

Why would you need more bits to describe a single atom in a galaxy vs a single atom in a gas cloud?

If a set amount of bits are required to describe an atom then that amount will not change whether or not the atom is in a galaxy or a gas cloud.

If we have a lot of similar locations, we can use compression to reduce the amount of bits required.

A basic example of this compression would be to take the current location and represent it with two parts. The first gives the location accurate to the nearest light-second, and the second gives the location within that cubic light-second.

Now, we can do huffman-coding [1] on the first part. In a gas cloud, the atoms are distributed over all possible cubes of light seconds. In a planetary system, they are concentrated in a much smaller set of planetary light seconds. This would make the huffman-coding a lot more efficient.

There are almost certainly smarter compression methods than what I just described, but the above serves as an illustration. The information-theoretic entropy of a distribution can be seen as a lower bound on the average amount of bits needed when applying compression to the distribution. I believe (am not sure) that this is a tight lower bound (i.e. there exists a compression method that gets as close to the lower limit as you want)

> This happened spontaneously and is not the result of energy entering or exiting the system.

This is not true: gravitational collapse usually produces energy in the form of heat that radiates away, making the surrounding universe more entropic.

When you look at the universe as a whole as a closed system this is happening to every particle in general. The system is organizing atoms into perfect spheres while making heat radiation randomly distributed. There is still a division here, still a form of order and organization happening spontaneously.

However this system is still ascending into higher entropy. What is wrong here is your notion of what entropy is. You think that high entropy as something similar to very random but uniformly distributed noise. This is not what entropy is. The definition is more complex and can encompass very organized structures as well.

It always confuses me as well (and I have at least some Physics background, having done a year as an undergrad). I think this is because I confuse it with the statistical measure of the entropy of a distribution, where a uniform distribution will maximise entropy.