# Order and disorder

1. Oct 24, 2013

### danihel

Hi,
I'm sorry and hope this forum allows people who don't study but are interested in physics to post their primitive questions:
I like watching documentaries and in every documentary on physics that i watched when it came to entropy, it was simply described as disorder as if that was a thing.
Is it only me being retarded? I mean, to me- "order" is a word that points to just anybody's personal preference of organization of things in any sort of dimension (being it space/time, alphabet or numbering system...) based on his current practical needs or cultural bias. Maybe Jackson Pollock had different concept of order than Rothko. Is an English garden of higher entropy than a French one? There is a individual sense of order just like there's a sense of beauty but there is no universal "order".
One of the few things i know about entropy is that it manifests as dissipating heat and as the entropy grows with time and heat dissipates it leads to homogeneity. What confuses me even more is that homogeneity gives me the impression of order rather than disorder and the beginnings of big bang although hot seem to me much more homogenous than the universe at this point.

It fascinates me very much but this important topic confuses me more than anything else from classical physics, if anyone could help me make the meaning of entropy a little more clear I would be very grateful.

2. Oct 24, 2013

### hilbert2

Basically, the idea is that because there are a lot more ways how things can be in "disorder" than ways how they can be in "order", it is statistically extremely probable that a system of a large number of molecules is at any given moment moving towards a state of higher disorder.

In statistical mechanics, entropy of a macrostate (macroscopically observed state of a physical system) depends on the number of microstates (combinations of states of individual molecules) that correspond to that observed macrostate. Therefore, increase of entropy is basically a statistical phenomenon, a system is very likely to move towards a state that can be achieved in many ways.

3. Oct 24, 2013

### danihel

@hilbert2: Thanks a ton! So can i throw the words "order/disorder" out of the window and just say: "Antropy is the measure of probability of a particular state of a physical system to be delivered by random movement of its components(particles)?"
So a limited set of particles in a physical system can be assigned a limited number of combinations of vector quantities and all the combinations of quantities give rise to a lesser number of combinations of states as the time passes.. and the state that is produced by most of the combinations of vector quantities is of highest entropy?
So the universe started at the most improbable state and ends at the most probable? Seems like the universe is losing it's ridiculousness :)

4. Oct 24, 2013

### the_wolfman

In classical mechanics we define entropy as $S = -k_B \sum_i p_i \ln p_i$.

With this definition in mind, we call states with low entropy "ordered" and states with high entropy "disordered."
Thus, we have very carefully defined what we mean by "order" in the physical context. There is no ambiguity.

Be careful here. Homogeneity can be used to describe systems of both high and low entropy.

Case 1) Imagine that you roll 1,000 dice, and they all come up 6. This is a very ordered result (low entropy) but it is also very homogeneous.

Case 2) Imagine a situation where you take ten different colors of paint and mix them together to get a a uniform (homogeneous) brown. if you look at the pain under a powerful microscope you'd see a random mixture of all ten colors. This is a state a maximum entropy or disorder.

5. Oct 25, 2013

### danihel

@the_wolfman: Thanks a lot! I'm afraid the only thing i understand from the equation above is (S) as entropy and (k) as Boltzman's konstant, but i guess i would need to study more physics to understand the rest.
Still, could anyone please tell me, based on my second post, whether i understood the point of entropy right?

6. Oct 25, 2013

### hilbert2

Yes, you understood the point.