What I want to do in this video
is start exploring entropy. When you first get exposed
to the idea entropy it seems a little bit mysterious. But as we do more videos we'll
hopefully build a very strong intuition of what it is. So one of the more typical definitions, or a lot of the definitions
you'll see of entropy, they'll involve the word disorder. So it might be considered
the disorder of a system. Now with just that
definition in your head, I want you to pause this video
and I want you to compare this system to this system. I want you to compare
this room to this room, and ask yourself, which
of these has more entropy. And then I want you to compare
the moon here to the sun, and these clearly aren't
at scale, the sun would be way more massive or way larger if I was drawing it to scale. But which of these
systems has more entropy? Alright, so I'm assuming
you've had a go at it. So when you look at
these rooms you might say okay this room over
here, this looks ordered, It's a clean room. And this over here looks
disordered, it's a messy room. So if all you had is this
definition, you'd say okay maybe this one is more disordered, maybe this one has more entropy. And you wouldn't be
alone in thinking that. In fact, even in a lot
of textbooks they'll use this analogy of a clean
room verses a messy room. And the messy room
somehow being indicative of having more entropy. But this isn't exactly the case. This form of disorder
is not the same thing as this form of disorder. So let me make this very, very clear. So something being messy, does not equal entropy. To think about what disorder
means in the entropy sense we're going to have to
flex our visualization of muscles a little bit more, but hopefully it'll all sink in. Entropy, this kind of a
disorder is more of the number of states that a system can take on. What do I mean by states of a system? Well if I have a container like this, and if I have four molecules that are bouncing around. So I have this magenta molecule,
I have this blue molecule, I have this yellow
molecule right over here, and then I have a green molecule. Well this would be a particular state, a particular configuration. But that system these
molecules are bouncing around could take on other configurations. Or it could take on other states. Or maybe the yellow molecule is over here, they bounce around enough
for the yellow molecule to get there, the blue
molecule to get over here, maybe the pink molecule is now over here, and the green molecule is now over here. And so a system can take on
a bunch of different states. I've just drawn two
states for this system. But there could be many, many
more states for this system. So each of these are a
particular state for the system. So imagine this system
where I have this box with the four molecules in it, and let's compare it to another system where I have a larger box. And let's say it has even
more molecules in it. Let's say that it has
two yellow molecules, let's say that is has a blue molecule, let's say that it has a green molecule, let's say that it has a
magenta molecule, this is fun. Let's say it has a mauve
molecule right over here. So this system that is
larger, there's more places for the molecules to
be and there's actually more molecules in it. This can actually take
on more configurations or more states. I've just drawn one of
them but there's many more. If you imagine these
molecules all bouncing around in different ways there's
many, many different states that it could take on. So the system without even knowing what the actual molecules are doing at that given moment in
time, we would say that there's more possible states relative to this one, this
has fewer possible states. And because this system over
here has more possible states, more configurations, it would take more to tell you exactly where everything is. We would say that this has more entropy. So when we talk about disorder,
we're really talking about the number of states something could have. And it makes sense that
this thing you could imagine there's a lot more stuff moving around and a lot more different
directions and they have a lot more space to move around. So it makes sense that
the system as a whole has more entropy. So when we talk about entropy
we're not talking about any one of the particular states, any one of the particular configurations, we're talking about the system as a whole without really knowing exactly
where the molecules are. In this example with the rooms, we're just talking
about particular states. Messy is a particular state,
clean is a particular state. But we're not talking about
the number of configurations that a room could actually have. In fact if this room is
larger, this room actually could have more configurations. And if we're talking
about the molecular level if this room was warm
and this room were cold, and actually if this room is
just larger, it's going to have more molecules in it. And those molecules are going to be in way more configurations
that they could be arranged so there could be an argument that this actually has a higher entropy. And so using that same
reasoning, let's go back to that comparison of
the moon and the sun. Which of these would have more entropy? Well let's think about it. The sun is larger, it has
way, way more molecules and those molecules are
moving around way faster and they're hotter and they're
moving past each other. While the moon is small, it's
cold, it has fewer molecules. It's for the most part rigid, it doesn't have a very high
temperature so these things aren't moving around a lot. It has way fewer states,
way fewer configurations than the sun does. So the sun's entropy, if
you view it as a system. If you view the sun as a system,
it's entropy is way higher than the moon. It's entropy is much larger
than the entropy of the moon. Think about it, how much
information you would need. You would need a lot of
information if someone wanted to tell you where every molecule or every atom on the moon is. But you would need even more
to know where every atom or molecule for in a given
moment on the sun is. If you're just looking at
the sun, wow all these things are moving around and
it's this huge volume. And they're very energetic
and all of these molecules. So hopefully this starts
to give you a sense of what entropy is. And you might say okay this is all fun intellectual discussion,
what's the big deal? But the big deal is that to some degree you can describe the
universe in terms of entropy. As we learn in the second
law of thermodynamics, the entropy in the universe
is constantly increasing. We are constantly moving to a universe with more possible states, which has all sorts of
interesting implications.