What is "order" and "disorder" in entropy? [duplicate]

Question

What is "disorder" in entropy?

Entropy is measurement of "disorder". (Some says it's not "disorder")

I had read "disorder" and "order" of entropy in my book. But I was wondering what "order" and "disorder" actually represent. As Boltzmann said,

$$S=k\ln \Omega$$ Where $\Omega$ is number of microstates.

Disorder actually means lackness of order. So order means in entropy that particles move symmetrically. But particles move randomly we just can say with possibility where it is located but we can't say absolutely where it is at time 't', that's what is known as disorder, isn't it?

Answer 1

Here is a slightly different take on this.

Imagine a deck of playing cards in which each suit is sorted out and all the cards in each suit arranged in descending order. This deck has a lot of order built into it. If you dropped a whole randomly-shuffled deck of cards onto the floor and then scooped them all up, it is extremely unlikely that they would assemble themselves into that sorted order.

Furthermore if you dropped the sorted deck onto the floor, it is extremely likely that after you scooped up all the cards you would find them all scrambled up, out of order.

The sorted deck has low entropy, which becomes high entropy when you shuffle them randomly.

The random deck of cards has high entropy, which becomes low entropy when you sort them out again.

But that entropy reduction required the expenditure of work, which produced an increase of entropy somewhere else in the process of furnishing that work.

In our universe, systems always tend naturally towards states of greater entropy as time goes by. So we see china plates shatter into lots of pieces when dropped on a concrete floor, but we never see those pieces spontaneously jump into the air and re-form themselves into an unbroken plate.

Answer 2

Entropy is dependent on the number of microstates. If entropy is a measure of disorder, then 'order' is also related to the number of microstates--the number of different ways a system can be in a given state.

If you roll 6 dice, there's only one way you can get a total of 36: every die is a 6. This is a well ordered state, you know exactly what's going on with every die. If you have a total of 35, this is slightly less ordered: one of the dice is a 5, and it could be any of them. So you know most of the dice are 6, but each one has a 1/6 chance of actually being a 5. If the sum was something like 21, this would be very disordered (135246 or 635241 or 333444 or 526152 or...).

On the macroscopic scale, disorder tends to be related to homogeneity. If you pour milk into coffee, the system would be well ordered if the milk and coffee didn't mix: there's only one way for every atom to be exactly where it was put. But there's a million ways for the milk to become dispersed into the coffee and we have no idea which one is actually going to happen, so it is the more disordered and far more likely state. The more disordered a state is, the more ways that state can be achieved, and the more probable it is that it will occur.

Answer 3

The use of the terms order and disorder in descriptions of entropy can be the source of confusion, and is unnecessary. It is better to think of increasing entropy as meaning the averaging out of energy among multiple particles.

Whenever particles interact, energy passes between them. If you have one very energetic particle which subsequently interacts with many others with less energy, it tends to lose more and more of its energy with each interaction. At first, it has a lot of energy to pass-on to any particle with which it interacts, so it spawns, as it were, other particles with more energy than the rest, and they in turn interact with other particles and so on in a cascade. The effect is that the high level of energy initially focused in a single particle is gradually diffused among all the particles. With increasing time a sort of equilibrium's reached in an isolated system, at which the energy is randomly distributed among the particles. In principle it is possible for the particles to interact with each other so that once again the energy becomes more concentrated among a tiny fraction of them, but the odds of that happening are vanishingly small.

So, if you want to retain the use of the words order and disorder, you should assume that order refers to conditions in which a relatively large amount of energy is possessed by a relatively small number of particles within a system, while disorder refers to conditions in which the energy is more randomly dispersed among the population of particles.

Answer 4

In general, "order" and "disorder" are not really well-defined or quantifiable. You could just declare that disorder is quantified by entropy, but I find that our intuitive notion of disorder doesn't always agree with what we get when we calculate the entropy. So unless you have some idea already in mind of what you mean by order, I would avoid thinking about entropy in those terms.

If you want an intuitive way of thinking about what the Boltzmann entropy $S = k \log \Omega$ tells us, instead of disorder, I would say that entropy is a measure of ignorance. This might seem like it's not any better: how the heck are we supposed to quantify ignorance? After all, you've never seen anyone write down a formula like \begin{align} \text{ignorance} = \ldots \end{align} However, we can be more specific and say that (Boltzmann) entropy measures our ignorance of the microscopic state of a thermodynamic system, given that we know the values of macroscopic observables: $T$, $V$, $N$, etc. In other words, the entropy tells us how much knowledge about the microscopic degrees of freedom we are leaving out when we describe a system using thermodynamics.

This description is basically just restating the definition of the Boltzmann entropy in plain English, so it's practically tautological. Nevertheless, I think it offers a much more precise way to think intuitively about what entropy means than trying to make sense of "disorder." It also gives us a cute way to describe what the second law tells us; we can say (with our tongue not too far from our cheek) that "our ignorance always increases." (A claim I certainly find to hold well beyond the scope of thermodynamics.)

Answer 5

Orderness and disorderness in thermodynamics is used to measure the net heat or work one can extract from system. Take a simple classical example.If two persons stand on opposite sides of block and start exerting force,the block doesn't move.On the other hand if two persons stand on the same side of the block and push it,it does move. Entropy is a device which measures such things,if things are happening randomly so that work input cannot be extracted as output.