One of the troubles I find with science education in society
is thinking we understand things because we've oversimplified them. This is one
of my biggest qualms with most things I hear from nonscientists or even a good
number of physical science teachers. One of the biggest oversimplifications I hear is
the idea that entropy=disorder. I can’t remember how many dozens of times I
have heard this and then seen people take it and run with it. I've even seen
some chemistry teachers post videos on YouTube preaching this idea in the
completely wrong context. I have seen a quite a few
videos lately as well as this gem that has been
floating around facebook. While entropy does have to do with disorder in a
sense of the word the common understanding of disorder (like a messy room) has
nothing to do with entropy. So, I’ve decided to clear up the misconception and
attempt to prevent people from associating the word entropy with disorder. If
you get lost in the middle you can go ahead and skip to the bottom few
paragraphs since I’m sure there is no one that’s actually dedicated enough to
read this whole post (if you understand entropy you have no need, if you don’t
you probably have no desire).
First
let me explain the simple example of disorder that relates to entropy (the one
that I’ve heard most). Think of a room full of nicely organized things, then
over time you use the stuff without putting it back. You wear your socks and
throw them on the floor, the desk has pens and pencils randomly laying everywhere,
and your bed is no longer nicely made. Many people would call this a high state
of entropy because of the level of disorder of things in the room. Since the
stuff is not neatly organized with must have high entropy. This actually has
nothing to do with the actual definition of entropy. Mathematically (which is
really the best way to describe it) the entropy of a system is a measure of how
many microstates are possible within a single macrostate. For those of us who
don’t speak geek I will explain. A macrostate describes the contents of the
system and a microstate describes how those contents are arranged. Let me give
an example so it makes sense. If I have 6 coins on a table there would be 6
possible macrostates: 6 coins heads up, 5 coins heads up and 1 coin tails up, 4
coins heads up and 2 coins tails up, 3 coins heads up and 3 coins tails up, etc…
The microstate would then describe which of the coins would be heads up and
tails up. Now that we have that all covered let’s talk about the entropy of
this system.
Like I
said before entropy is a measure of how many possible microstates there are.
High entropy correlates to a high number of microstates, and low entropy is a
low number of microstates. To make things easier to follow I’ll take the number
of coins down to four and let’s say they’re all different (a penny, a nickel, a
dime, and a quarter). Let’s say I’m OCD and I like to have all my coins facing
heads up on the table. I have created a system with very low entropy
statistically. That is because there is only one way to arrange the macrostate
(all coins heads up) which is to have all the coins heads up. So therefore the
number of possible microstates in this macrostate is one. Now lets say I have a
really noisy neighbor who has a huge subwoofer which shakes my table while I’m
gone. The coins will now start flipping on the table all day. If I were to make
any bets on how the coins would be arranged I would say that there would be two
coins heads up and two coins heads down. Why? one might ask. It is because two
coins heads up is the macrostate which has the most number of possible
microstates which means that it has the highest level of entropy in the statistical
sense of the word. Let’s look at it closer. I’ve made a table to make it easier
to follow. You should note that there are 6 different ways of organizing these
coins with two coins heads up and two coins tails up. That’s 5 more microstates
or ways of arranging the coins than having them up heads up or all tails up! So
while I would know to bet on the macrostate, I would also know not to bet on
the microstate as my odds would be lower.
Penny

Nickel

Dime

Quarter

Heads

Heads

Tails

Tails

Heads

Tails

Heads

Tails

Heads

Tails

Tails

Heads

Tails

Heads

Heads

Tails

Tails

Heads

Tails

Heads

Tails

Tails

Heads

Heads

Just to convince that this is the
highest statistical entropy state let’s look at the number of ways you can
arrange the coins with three coins heads up. The number of possible microstates
of this macrostate of the system is 4. That’s still more ways to arrange the
coins than all heads up, but less than two heads up and two tails up.
Penny

Dime

Nickel

Quarter

Heads

Heads

Heads

Tails

Heads

Tails

Heads

Heads

Heads

Heads

Tails

Heads

Tails

Heads

Heads

Heads

This phenomenon is also seen in the
statistics of flipping a single coin many times. If you flip a coin fifty times
you should notice that on average you will get 25 tails and 25 heads. The
macrostate would be flipping a coin 50 times and getting 25 tails and 25 heads.
The microstate would be the order in which you got the 25 tails and 25 heads.
If one were to flip 25 heads in a row it wouldn’t be defying statistics because
each flip has a 50% chance of either heads or tails and the previous flip has
no affect on the next flip statistically. It would be a rare thing to see
however because it would be one of about 126 trillion different ways of
obtaining a 50% heads to tails ratio from 50 flips. While it is true that this
coin flip example does not happen exactly 50% heads and tails 100% of the time,
if one were to take an average of all the unbiased coin flips in the world it
should average to very close to that (to the point of being in practical
language exactly 50%). Now this is just a statistical explanation of entropy,
how does this apply in the real world?
Well it is easiest to see in the
sense of an ideal gas system. This is a system made of gas particles that act
like billiard balls in a container that see no gravity, no air resistance, no
friction, and the collisions are purely elastic (the system does not lose any
energy in the collisions). Let’s say I have all my billiard balls arranged so
that I have slow moving balls on one side of the container and fast moving
balls on the other side of the container with some kind of magical barrier in between.
Now before we continue with this box example I can tell you that on average all
the balls on one side will have the same average speed. How? Because that is
the state with the highest entropy, and the second law of thermodynamics states
that a system will always increase in entropy until it reaches maximum entropy.
This maximum entropy is often referred to as thermodynamic equilibrium. When
one ball collides with another it will transfer some of its kinetic energy to
the other ball. After a long time all of the balls will have collided with each
other multiple times each. Each collision causes each ball to essentially share
its kinetic energy with the other balls. Eventually they will have come to a
point where they all have the same average kinetic energy. If this is true than
there are many ways of arranging this system since I can say that any ball can
be put in any other balls place. If only one ball had all the kinetic energy
then that ball is the only ball that I could rearrange which limits my number
of microstates.
So now we go back to the box with
the magical barrier. Let’s say that there are x number of microstates for each
side of the box. That means there are 2 times x number of total microstates in
the box since the only way I can rearrange this system is by either putting the
fast balls on the right or the slow balls on the right. Now I take the barrier
out, what happens? The fast balls start colliding with the slow balls and after
a certain amount of time I have all the balls with the same average speed
again. That average speed is faster than the average speed of the original slow
balls, but slower than the average speed of the original fast balls. That means
that the balls could all be rearranged to replace any other ball in the box
which correlates to high entropy. Now why would we call this disorder? It is
because this system we know very little about. All I can tell you is the
average speed of each ball in the box. Before I took the barrier away I was able
to tell you a little about the two different average speeds (the slow and the
fast).
Now let’s say I rewind time even
further and say initially I had only one ball that was moving on each side of
the barrier. Well then I can tell you that only two balls are moving at some
exact speed, and the rest of the balls are at rest. You see initially I had a highly
“ordered” system because I had only two balls with any kinetic energy and I
knew exactly what their energy was. After some time the balls bounced around
and collided with other balls causing my information about the system to be
even vaguer. I do not know anything about any one particular ball now, but I
can split the box in two and know that in each half the balls will have some
average speed. Now when I take away the barrier I know even less about the
system, only that all the balls now have one average speed. One could conclude
then that as entropy increases the knowledge one has about a particular system
decreases.
This doesn’t mean that 1010 is a
low entropy organization of ones and zeros because it repeats a pattern (and
therefore probably contains some good information). It merely means that if I
had four binary digits that were changing randomly then after some time I would
end up with a collection of arrangements of two 1s and two 0s (which includes
1010 as well as 0101, 0011, 1100, and 1001). That means that I know have to
guess between 6 options now rather than if they were all 1s I would only have
to guess one out of one option. So when you are trying to get rid of
information on a hard drive there a repeated pattern of 10 is just as worthless
to the NSA as all 1s and then all 0s which is just as worthless as a random
assortment of 1s and 0s which are half 1s and half 0s. The information isn’t
lost in the actual arrangement; it is lost in the number of possible arrangements.
So if there are random 1s and 0s left on your hard drive, but there are more 1s
than 0s it makes the NSA’s job easier because it limits the possible
combinations of 1s and 0s that contained your actual information previously.
But I digress, now I will get to
the whole point of this explanation. Many people say that evolution violates
the second law of thermodynamics since our bodies are highly ordered organisms.
That would kind of be like saying that because you are using your computer
right now you are cheating the laws of physics. In order to get this point
across I’m going to take in terms of massenergy. General relativity states
that mass can be converted into energy and viceversa. This happens all the
time not just in fusion in the sun and fission in power plants but in chemical
reactions. You see our bodies are highly ordered massenergy systems. But in
order to make our bodies (and keep them running) we actually cause more disorder.
For example we eat things which are highly ordered (plant and animal matter or
even synthesized chemicals) and we use up the energy that is provided by the
chemical bonds of this “fuel”. Well over time we get hungry again. That is
because we used this energy and a good portion of it was lost from our body
leaking body heat. That energy was partially radiated as electromagnetic
radiation and partially lost due to convection in the air or conduction in your
clothes/blankets/couch/whatever you are touching. That energy that left you is
now “simple” or “less ordered”. This is just like our nuclear fuels which go
from high energy density (“high order”) to lower energy density (“low order”).
It’s the same with fossil fuels and basically anything that could be rearranged
into a lower energy state. This is what is theorized by some to be the “heat
death of the universe” or when the entire universe will reach thermodynamic
equilibrium. All the higher ordered massenergy of the universe could
eventually all become the same lowordered mass energy in some form. This would
be like everything in the universe evaporating into radiowaves. While no one
knows how the universe will end (if it ever “ends”) this goes to show that
evolution has no impact on the second law. Yes it is creating “higher order”
out of “lower order”, but the total “high order” being converted to “low order”
was a net loss in the end.
In conclusion: entropy isn't what
most people think it is, and is a very abstract thing that is hard to
understand. The one thing I've learned about physics: if you think you know
what you’re talking about, you probably don’t.
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