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I'm going to do one more
video on entropy.

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Maybe I'll do more
in the future.

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But I thought I would at least
right now do one more, because

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I really want to make clear
the idea of entropy as a

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macrostate variable.

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So let me write that down.

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An S, which is entropy, is
a macrostate variable.

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I'm going to write macro
in bold red.

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It's a macrostate
state variable.

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And I want to emphasize this.

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And I talked a little bit about
it in my previous video,

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but I think even then I wasn't
as exact as I needed to be.

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And the reason why I want to
say it's macro is because

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there's a very strong temptation
to point to

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particular micro states and
say, does this have higher

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entropy or lower entropy
than another?

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For example, the classic one.

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Even I did this.

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Actually, let me make a
bigger, thicker line.

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So you have this box that
has a divider in it.

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We've gone through this
multiple times.

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Let me draw the divider
like right there.

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OK.

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So at first if we have a
system where all of the

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molecules are over here-- so
that's our first scenario.

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And then our second scenario,
we've studied this a lot.

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We blow up the wall here.

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And we actually calculated
the entropy.

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Control.

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OK.

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Let me copy it and then
I'm going to paste it.

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Let me put these next
to each other.

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All right.

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So I have these two things.

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And then the second time,
I blew away this wall.

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Let me blow it away.

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Let me erase the wall there.

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And then we said, once the
system reaches equilibrium

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again-- remember, these
macrostate variables, like

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pressure, like volume, like
temperature, like entropy, are

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only defined once the system
is in equilibrium.

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So once the system is in
equilibrium again, these

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particles are now-- I wanted the
same number of particles,

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so let me erase some of these
particles, let me move them.

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Let me see if I can
select some.

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There.

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So we'll have a more even--
Let me just redraw.

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1, 2, 3, 4, 5, 6,
7, 8 particles.

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Let me erase what I have. And
I'll make it with a more even

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distribution.

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So then, once I blow away the
wall, I might have 1, 2, 3, 4,

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5, 6, 7, 8.

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Now, the reason why I'm doing
all of this is because there's

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a temptation to say that this
state, what I just drew you

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when I, you know, made sure to
blow these away and draw 8

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more, I drew a microstate.

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This is a microstate.

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Anytime someone is actually
drawing molecules for you,

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they're drawing a microstate.

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Now, I want to be very clear.

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This microstate does not have
more entropy than this

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microstate.

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In fact, microstates you
don't have entropy.

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Entropy does not make sense.

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What you can say is a system--
and this time, I'm going to

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draw it without the particles.

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That if I have a container
that is this big, that

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contains-- so it has
some volume.

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So volume is equal to v1.

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Its temperature is equal
to a t1, and it has 8

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particles in it.

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This has some entropy
associated with it.

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And what we can say, is if we
were to double the size of

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this container, which we did by
blowing away that wall, now

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all of a sudden our volume is
equal to 2 times v1, if we say

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this is double.

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Our temperature is still
equal to t1.

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We saw that a few videos ago.

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And we still have 8 molecules.

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The entropy of this
system is higher.

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So now entropy is higher.

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And I want to make this very
clear, because you never see

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it drawn this way.

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People always want to draw
the actual molecules.

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But that confuses the issue.

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When you draw actual molecules,
you're showing a

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particular state.

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For example, this system, if
we were to actually measure

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the microstate, it could be--
there's a very, very

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infinitesimally probability--
but all of the molecules, all

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8 molecules might
be right there.

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I mean, it's almost, you know,
you could wait for the whole

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universe to come and go, and
it might not happen.

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But there is some probability
it would happen.

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So you can't assign entropy
to a particular state.

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All you can do is assign it
to a particular system.

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I want to be clear about that.

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So even I talked about
a clean and dirty

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room and all of that.

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Clean versus dirty room.

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And the point I was making is,
the entropy of a room is not

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dependent on its cleanliness
or its dirtiness.

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In fact, you could kind
of view these

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as states of a room.

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But even more, these
really aren't even

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states of the room.

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Because when a room is clean, or
a room is static at a macro

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level, they're static.

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If my books or lying like--
you know, sometimes people

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look at a deck of cards and
say, oh, if I have all my

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cards stacked up like this, or
if I have all my cards that

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are all messy like that, that
this has higher entropy.

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And I want to make
it very clear.

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I mean, maybe you can kind
of make an analogy.

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But that's not the case.

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Both of these systems
are macrostates.

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For example, it's not like
these cards are vibrating

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around any more than
these cards are.

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It's not like these can take
on more configurations than

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these cards can.

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So when you talk about entropy,
you're trying to take

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a macro variable that's
describing at a micro level.

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And the cards themselves are not
the micro level, because

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they're not vibrating around
continuously due to some

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kinetic energy or whatever.

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It's the cards' molecules that
are at the micro level.

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And if these cards, if you have
the same mass of cars as

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you have here, and if they're
at the same temperature, the

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molecules in these cards can
take on just as many states as

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the molecules in these cards.

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So they're going to have
the same entropy.

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Entropy is a macrostate
variable, or a macrostate

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function, that describes
the number of states a

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system can take on.

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So here, I would view the
cards as a system.

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And what we care about is not
the number of configurations

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the cards themselves
can take on.

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The cards aren't constantly
vibrating and changing from

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one thing to another.

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It's at the atomic level, at the
molecular level, that as

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long as we're above absolute
zero, which we pretty much

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always are, things are going
to be vibrating around

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continuously, and continuously
changing its state.

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So it's almost impossible
to measure the state.

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And since it's impossible to
measure the state, we use

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something like entropy to
say, well, how many

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states can we have?

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And I mean, all of these things,
entropy, whether we

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call it internal energy, whether
we look at entropy,

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whether we look at pressure,
volume, temperature.

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These are all, if you can think
about it in some way,

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these are shortcuts around
having to actually measure

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what each molecule is doing.

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And entropy, you can kind of
view it as a meta shortcut.

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I mean, temperature tells you
average kinetic energy, this

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tells you all of the energy
that's in it, this tells you,

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you know, how frequently the
molecules are bumping against

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a certain area.

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This tells you, on average, kind
of where the outermost

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molecules are.

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Entropy is kind of a, you
can almost view it

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as a metastate variable.

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It tells you how many states,
how many micro

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states can we take on?

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And so I just want to make this
very clear, because this

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is often confused, and there's
a very, very, very strong

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temptation to point to a
particular state and to say

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that that has higher entropy
than another, that somehow

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this state is more entropic
than that state.

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That's not the case.

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This system is more entropic
than this system,

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than this half box.

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It has more volume.

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If it has the same temperature
with more volume, then its

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particles can take on more
possible scenarios at any

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given moment in time.

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Anyway, hopefully you found
that a little bit useful.

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I just want to make it very,
very, very clear.

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Because this is often, often,
often confused.

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It is a macrostate variable for
a system, where a system

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is composed of things that are
bumping around randomly.

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Every millionth of a second,
they're changing states, so

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it's very hard to even measure
one of the microstates.

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You can't point to a microstate,
and say, oh, this

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has higher entropy
than another.

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Anyway.

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See you in the next video.

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