1
00:00:00,000 --> 00:00:00,550


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00:00:00,550 --> 00:00:03,705
The second law of thermodynamics
tells us that

3
00:00:03,705 --> 00:00:06,580
the entropy of the universe
is always increasing.

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00:00:06,580 --> 00:00:10,610
So the change in entropy for
the universe, when it

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00:00:10,610 --> 00:00:13,030
undergoes any process,
is always greater

6
00:00:13,030 --> 00:00:14,260
than or equal to 0.

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00:00:14,260 --> 00:00:17,210
And we showed in the previous
video that it has a lot of

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00:00:17,210 --> 00:00:18,460
implications.

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00:00:18,460 --> 00:00:20,940


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00:00:20,940 --> 00:00:23,070
Regardless of how you define
your entropy, whether you

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00:00:23,070 --> 00:00:27,520
define entropy as equal to
some constant times the

12
00:00:27,520 --> 00:00:30,660
natural log of the number of
states your system could take

13
00:00:30,660 --> 00:00:35,080
on, or whether you define change
in entropy to be equal

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00:00:35,080 --> 00:00:37,870
to the heat added to the
system divided by the

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00:00:37,870 --> 00:00:40,390
temperature at which it is
added, either of these

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00:00:40,390 --> 00:00:42,660
descriptions, combined with
our second law of

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00:00:42,660 --> 00:00:46,830
thermodynamics tell us things
like, when you have a hot body

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00:00:46,830 --> 00:00:52,890
next to a cold body-- so say
this is T1, and then I have T2

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00:00:52,890 --> 00:00:55,970
over here-- that heat will
flow from the hot

20
00:00:55,970 --> 00:00:57,160
body to the cold body.

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00:00:57,160 --> 00:00:57,730
And we showed that

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00:00:57,730 --> 00:01:00,010
mathematically in the last video.

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00:01:00,010 --> 00:01:02,960
That heat will flow
in this direction.

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00:01:02,960 --> 00:01:05,170
Now, one of the commenters on
the last video said, hey,

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00:01:05,170 --> 00:01:07,260
could you cover Maxwell's
demon?

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00:01:07,260 --> 00:01:10,250
And I will.

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00:01:10,250 --> 00:01:14,900
Because it's an interesting
thought experiment that seems

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00:01:14,900 --> 00:01:16,540
to defy this principle.

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00:01:16,540 --> 00:01:19,420
It seems to defy the second
law of thermodynamics.

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00:01:19,420 --> 00:01:23,240
And it has a very tantalizing
name, Maxwell's demon.

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Apparently, though, it was not
Maxwell who called it a demon.

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00:01:27,300 --> 00:01:28,260
It was Kelvin.

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00:01:28,260 --> 00:01:32,080
All these guys, you know, they
all meddle in everything.

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00:01:32,080 --> 00:01:37,160
So Maxwell's demon.

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00:01:37,160 --> 00:01:40,440
And this is the same Maxwell
famous for Maxwell's equation,

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00:01:40,440 --> 00:01:42,760
so he obviously dealt with
a lot of things.

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He's actually also the first
person to ever generate a

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color image.

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00:01:46,590 --> 00:01:48,430
So this is in the mid-1800s.

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So all around a fairly
sharp individual.

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00:01:51,890 --> 00:01:54,290
But what's Maxwell's demon?

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00:01:54,290 --> 00:01:57,000
So when we say something has
a higher temperature than

43
00:01:57,000 --> 00:01:59,440
something else, what
are we saying?

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00:01:59,440 --> 00:02:01,730
We're saying that its average
kinetic energy of its

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00:02:01,730 --> 00:02:05,500
molecules bumping around
here-- that the average

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00:02:05,500 --> 00:02:08,690
kinetic energy of the molecules
here-- is higher

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00:02:08,690 --> 00:02:12,440
than the average kinetic energy
of the molecules here.

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00:02:12,440 --> 00:02:15,550
Now notice, I said its average
kinetic energy.

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00:02:15,550 --> 00:02:17,240
And we've talked about
this multiple times.

50
00:02:17,240 --> 00:02:19,020
Temperature is a macro state.

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00:02:19,020 --> 00:02:21,940
We know that at the micro level,
all of these molecules

52
00:02:21,940 --> 00:02:23,130
have different velocities.

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00:02:23,130 --> 00:02:25,670
They're bumping into each other,
transferring momentum

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00:02:25,670 --> 00:02:26,630
to each other.

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00:02:26,630 --> 00:02:28,540
You know, this guy might
be going super

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00:02:28,540 --> 00:02:30,040
fast in that direction.

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00:02:30,040 --> 00:02:32,290
This guy might actually
be going quite slow.

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00:02:32,290 --> 00:02:34,360
This guy might be going
super fast like that.

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00:02:34,360 --> 00:02:36,080
That guy might be going
quite slow.

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00:02:36,080 --> 00:02:37,520
It's just a hodgepodge
of things.

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00:02:37,520 --> 00:02:39,130
You could actually draw
a distribution.

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00:02:39,130 --> 00:02:43,260
If you knew the micro states
of everything, you could

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00:02:43,260 --> 00:02:44,650
actually draw a little
histogram.

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00:02:44,650 --> 00:02:49,450
We could say, for T1--
let's say this is

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00:02:49,450 --> 00:02:51,850
on the Kelvin scale.

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00:02:51,850 --> 00:02:55,280
So you could say, look, my
average temperature is here,

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00:02:55,280 --> 00:02:58,050
but I have a whole distribution
of particles.

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00:02:58,050 --> 00:02:59,745
So let's say this is number
of particles.

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00:02:59,745 --> 00:03:03,420


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00:03:03,420 --> 00:03:04,580
And I won't put a scale there.

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00:03:04,580 --> 00:03:05,890
You'll get the idea.

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00:03:05,890 --> 00:03:08,220
So I have a bunch of particles
that are at T1, but I have

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00:03:08,220 --> 00:03:10,340
some particles that could be
really close to absolute 0.

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00:03:10,340 --> 00:03:11,860
I mean, it'd be very few, but.

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00:03:11,860 --> 00:03:14,760


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00:03:14,760 --> 00:03:16,710
And then you have a bunch that
are maybe at T1, and then you

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00:03:16,710 --> 00:03:19,120
have a bunch of particles that
could have actually kinetic

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00:03:19,120 --> 00:03:20,740
energy higher than T1.

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Higher than the average
kinetic energy.

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00:03:22,710 --> 00:03:23,870
Maybe that's this one here.

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00:03:23,870 --> 00:03:26,450
Maybe the guy down here is
this guy with barely any

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00:03:26,450 --> 00:03:27,010
kinetic energy.

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00:03:27,010 --> 00:03:29,330
It means there's some guy
who's almost completely

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00:03:29,330 --> 00:03:31,290
stationary, who's, you
know, sitting right

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00:03:31,290 --> 00:03:32,740
around there someplace.

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00:03:32,740 --> 00:03:35,300
So there's a whole distribution
of particles.

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00:03:35,300 --> 00:03:41,230
Likewise, this T2 system right
here, on average, these

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00:03:41,230 --> 00:03:43,670
molecules have a lower
kinetic energy.

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00:03:43,670 --> 00:03:45,780
But you know, there might be one
particle here that has a

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00:03:45,780 --> 00:03:47,370
really high kinetic energy.

91
00:03:47,370 --> 00:03:49,000
But most of them on
average are lower.

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00:03:49,000 --> 00:03:54,500
So if I were to draw the
distribution of T2, my average

93
00:03:54,500 --> 00:03:56,770
kinetic energy is lower, but
my distribution might look

94
00:03:56,770 --> 00:03:58,640
something like this.

95
00:03:58,640 --> 00:04:00,800
It can't go backwards
like that.

96
00:04:00,800 --> 00:04:03,220
It might look something
like this.

97
00:04:03,220 --> 00:04:06,100
Oh, I don't know, maybe it looks
something like that.

98
00:04:06,100 --> 00:04:07,950
Let me try it a little
different.

99
00:04:07,950 --> 00:04:09,500
I'll make it go just as high.

100
00:04:09,500 --> 00:04:12,610
Maybe it looks something
like that.

101
00:04:12,610 --> 00:04:13,690
right?

102
00:04:13,690 --> 00:04:18,760
So notice, there are some
molecules in T1 that are below

103
00:04:18,760 --> 00:04:20,970
the average kinetic
energy of T2.

104
00:04:20,970 --> 00:04:21,269
Right?

105
00:04:21,269 --> 00:04:22,480
There are these molecules
here.

106
00:04:22,480 --> 00:04:26,680
These are these slow
guys right there.

107
00:04:26,680 --> 00:04:30,210
And notice, there are some guys
in T2 that have a higher

108
00:04:30,210 --> 00:04:33,490
kinetic energy than
the average in T1.

109
00:04:33,490 --> 00:04:35,380
So these are these
guys right here.

110
00:04:35,380 --> 00:04:38,710


111
00:04:38,710 --> 00:04:43,480
And so the fast guys in T2--
so even though T2 is, quote

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unquote, colder, it has lower
average kinetic energy,

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00:04:46,320 --> 00:04:50,980
there's some molecules, if you
look at the micro state, that

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00:04:50,980 --> 00:04:53,390
are actually moving around quite
rapidly, and there are

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00:04:53,390 --> 00:04:56,180
some molecules here that are
moving around quite slowly.

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00:04:56,180 --> 00:05:00,090
So what Maxwell said is, hey,
what if I had my-- and he

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00:05:00,090 --> 00:05:02,510
actually didn't use the word
demon, but we'll use the word

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00:05:02,510 --> 00:05:05,940
demon, because it makes it
seem very interesting and

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00:05:05,940 --> 00:05:08,820
metaphysical on some level, but
it really isn't-- what if

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00:05:08,820 --> 00:05:12,210
I had some dude, let's call him
the demon, with a little

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00:05:12,210 --> 00:05:13,630
trapdoor here?

122
00:05:13,630 --> 00:05:14,880
Let me draw a little
bit neater.

123
00:05:14,880 --> 00:05:19,260


124
00:05:19,260 --> 00:05:22,380
So between those two
systems, let's say

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00:05:22,380 --> 00:05:24,120
that they're insulated.

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00:05:24,120 --> 00:05:27,480
Let's say that they're separated
from each other.

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00:05:27,480 --> 00:05:31,830
So this is T1 where I have a
bunch of particles, you know,

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00:05:31,830 --> 00:05:36,210
with their different
kinetic energies.

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00:05:36,210 --> 00:05:38,240
And then, here is T2.

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00:05:38,240 --> 00:05:40,470
And I'm making them separated,
and maybe they're connected

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00:05:40,470 --> 00:05:44,230
only by this little connection
right here.

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00:05:44,230 --> 00:05:45,320
T2.

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00:05:45,320 --> 00:05:49,200
These guys have a slower
kinetic energy.

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00:05:49,200 --> 00:05:52,350
And what Maxwell, his little
thought experiment was, hey,

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00:05:52,350 --> 00:05:56,690
let me say that I have some
dude in charge of a door--

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00:05:56,690 --> 00:06:00,510
maybe the door is right
here-- and he has

137
00:06:00,510 --> 00:06:02,050
control over this door.

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00:06:02,050 --> 00:06:05,350
And whenever a really fast
particle in T2, one of these

139
00:06:05,350 --> 00:06:09,080
particles over here, come near
the door-- so let's say this

140
00:06:09,080 --> 00:06:14,050
guy is flying-- let's say
that guy right there.

141
00:06:14,050 --> 00:06:16,750
He's going super fast. He has
super high kinetic energy, and

142
00:06:16,750 --> 00:06:19,360
he's just going perfectly
for the door.

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00:06:19,360 --> 00:06:20,940
So the demon says, hey.

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00:06:20,940 --> 00:06:21,920
I see that guy.

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00:06:21,920 --> 00:06:23,380
He's coming for the door.

146
00:06:23,380 --> 00:06:27,800
He's going to lift his hatch,
and he's going to allow this

147
00:06:27,800 --> 00:06:30,100
particle to get into T1.

148
00:06:30,100 --> 00:06:33,170


149
00:06:33,170 --> 00:06:35,200
So after he lifts the hatch,
that particle will just keep

150
00:06:35,200 --> 00:06:36,990
going, and it'll be in T1.

151
00:06:36,990 --> 00:06:40,490
And then he closes the hatch
again, because he just wants

152
00:06:40,490 --> 00:06:43,730
the fast particles to
go from T2 to T1.

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00:06:43,730 --> 00:06:48,330
And then when he sees a little
slow, you know, pokey little

154
00:06:48,330 --> 00:06:51,870
particle coming here, one of
these guys down here, he opens

155
00:06:51,870 --> 00:06:54,510
the trapdoor again, and he
allows that one to go.

156
00:06:54,510 --> 00:06:57,820
So then that guy shows
up in here.

157
00:06:57,820 --> 00:07:00,460
So if he just kept doing that,
what's it going to look like

158
00:07:00,460 --> 00:07:01,410
at the end?

159
00:07:01,410 --> 00:07:03,820
Well, at the end, you're going
to segregate-- and it could

160
00:07:03,820 --> 00:07:05,490
take a while.

161
00:07:05,490 --> 00:07:10,660
But you're going to segregate
all the slow particles on--

162
00:07:10,660 --> 00:07:11,380
let me draw it.

163
00:07:11,380 --> 00:07:14,140
I'll make the boundary in brown,
because now it's not

164
00:07:14,140 --> 00:07:15,850
clear which one is-- well.

165
00:07:15,850 --> 00:07:16,920
We'll talk about it
a little bit.

166
00:07:16,920 --> 00:07:18,350
So that's the boundary.

167
00:07:18,350 --> 00:07:19,130
That's his door.

168
00:07:19,130 --> 00:07:20,100
What's going to happen
at the end?

169
00:07:20,100 --> 00:07:22,010
All the fast particles-- some
of them are going to be the

170
00:07:22,010 --> 00:07:25,930
original fast particles
that are in T1, right?

171
00:07:25,930 --> 00:07:29,620
There are some original fast
particles in T1 are going to

172
00:07:29,620 --> 00:07:34,390
be still on the side
of the barrier.

173
00:07:34,390 --> 00:07:37,550
Let me draw-- make sure you
don't get these two confused.

174
00:07:37,550 --> 00:07:38,970
This is a separate picture.

175
00:07:38,970 --> 00:07:41,990
Now all of the fast particles
from T2 are also going to be

176
00:07:41,990 --> 00:07:42,520
stuck there.

177
00:07:42,520 --> 00:07:45,020
Because eventually they're all
going to get close to that

178
00:07:45,020 --> 00:07:47,990
door, if you wait long enough.

179
00:07:47,990 --> 00:07:50,400
So then this guy's also going
to have a bunch of the, what

180
00:07:50,400 --> 00:07:54,110
would originally, in the T2 side
of the barrier, they're

181
00:07:54,110 --> 00:07:55,120
also going to be there.

182
00:07:55,120 --> 00:07:57,460
So you're going to have a
bunch of fast particles.

183
00:07:57,460 --> 00:08:01,410
Likewise, all the slow T2
particles are going to be

184
00:08:01,410 --> 00:08:04,150
remaining on the side
of the barrier.

185
00:08:04,150 --> 00:08:05,850
So these are the slow guys.

186
00:08:05,850 --> 00:08:09,290
And he would have let all the
slow T1-- I shouldn't even

187
00:08:09,290 --> 00:08:11,010
call them T1 anymore.

188
00:08:11,010 --> 00:08:12,630
I'll call them side 1.

189
00:08:12,630 --> 00:08:14,110
Side 1 particles here.

190
00:08:14,110 --> 00:08:17,470


191
00:08:17,470 --> 00:08:19,940
Slow side 1 particles.

192
00:08:19,940 --> 00:08:23,130
So what just happened here?

193
00:08:23,130 --> 00:08:26,380
This was the hot body, this
was the cold body.

194
00:08:26,380 --> 00:08:29,430
The second law of thermodynamics
would have told

195
00:08:29,430 --> 00:08:31,690
us that heat would have gone
from here to here.

196
00:08:31,690 --> 00:08:34,000
That their temperatures
should have equalized

197
00:08:34,000 --> 00:08:35,230
to a certain degree.

198
00:08:35,230 --> 00:08:38,520
So the hot bodies should get
colder, the cold bodies should

199
00:08:38,520 --> 00:08:39,190
get hotter.

200
00:08:39,190 --> 00:08:41,270
They should kind of average
out a little bit.

201
00:08:41,270 --> 00:08:45,550
But using this little demonic
figure, what did he do?

202
00:08:45,550 --> 00:08:47,780
He made the hot body
hotter, right?

203
00:08:47,780 --> 00:08:50,080
Now the average kinetic energy
here is even higher.

204
00:08:50,080 --> 00:08:54,950
He transferred all of these high
kinetic energy particles

205
00:08:54,950 --> 00:08:57,730
to that distribution, so now
that distribution is going to

206
00:08:57,730 --> 00:09:01,170
look-- the way you could think
about it, if you transferred

207
00:09:01,170 --> 00:09:04,450
all of these guys to this guy
over here, the distribution

208
00:09:04,450 --> 00:09:07,150
will now look something like--
let me see if I can do it.

209
00:09:07,150 --> 00:09:10,860
It will look something
like that for T1,

210
00:09:10,860 --> 00:09:12,200
instead of the old one.

211
00:09:12,200 --> 00:09:16,510
And T2-- and he took all the
hot ones away, all the cold

212
00:09:16,510 --> 00:09:17,620
ones away, from T1.

213
00:09:17,620 --> 00:09:19,740
So these guys are going
to disappear.

214
00:09:19,740 --> 00:09:21,340
They're not going to
be there anymore.

215
00:09:21,340 --> 00:09:22,590
And he added them to T2.

216
00:09:22,590 --> 00:09:25,545


217
00:09:25,545 --> 00:09:28,600
So the distribution of T2 is
going to look like that, and

218
00:09:28,600 --> 00:09:32,270
he erased, of course,
these from T2.

219
00:09:32,270 --> 00:09:35,152
He took all of these
guys out of T2.

220
00:09:35,152 --> 00:09:36,880
Let me erase this right here.

221
00:09:36,880 --> 00:09:38,410
That was the old distribution
of T1.

222
00:09:38,410 --> 00:09:40,960
So the T2 distribution now looks
something like this.

223
00:09:40,960 --> 00:09:43,460


224
00:09:43,460 --> 00:09:47,640
So T2, the new average might
be something like here.

225
00:09:47,640 --> 00:09:49,640
This is my new T2.

226
00:09:49,640 --> 00:09:52,590
And my new T1 is going to move
to the right a little bit.

227
00:09:52,590 --> 00:09:54,260
The average is going
to be higher.

228
00:09:54,260 --> 00:09:57,450
So this demon seems to have
violated the second law of

229
00:09:57,450 --> 00:09:58,400
thermodynamics.

230
00:09:58,400 --> 00:10:00,540
Let me box off this
right here.

231
00:10:00,540 --> 00:10:04,810
My little diagrams
are overlapping.

232
00:10:04,810 --> 00:10:07,750
This example shows that the hot
got hotter and the cold

233
00:10:07,750 --> 00:10:08,400
got colder.

234
00:10:08,400 --> 00:10:10,950
So Maxwell's thought experiment
says, hey, we

235
00:10:10,950 --> 00:10:14,030
violated the second law
of thermodynamics.

236
00:10:14,030 --> 00:10:16,530
And this actually
was a conundrum

237
00:10:16,530 --> 00:10:17,280
for many, many years.

238
00:10:17,280 --> 00:10:20,450
Even in this century, people
kind of, hey, you know,

239
00:10:20,450 --> 00:10:22,340
there's something fudgy
about here,

240
00:10:22,340 --> 00:10:23,420
something not quite right.

241
00:10:23,420 --> 00:10:25,260
And the thing that's not quite
right, and I'm not going to

242
00:10:25,260 --> 00:10:27,470
prove it to you mathematically,
is-- and it's

243
00:10:27,470 --> 00:10:31,270
kind of analogous to the
refrigerator example-- is, to

244
00:10:31,270 --> 00:10:37,750
have something here-- to have
some dude, perhaps he's a

245
00:10:37,750 --> 00:10:43,730
demon, here, pulling this
little door when it's

246
00:10:43,730 --> 00:10:47,000
convenient, when the fast
particles are going from this

247
00:10:47,000 --> 00:10:49,690
side or the slow particles are
going from that side-- in

248
00:10:49,690 --> 00:10:52,270
order for him to do it
correctly, he's going to have

249
00:10:52,270 --> 00:10:53,870
to keep track of where all
the particles are.

250
00:10:53,870 --> 00:10:55,540
He'll need to keep track
of particles.

251
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I mean, these aren't balls,
like, you know, macro balls.

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These are micro molecules or
atoms. He's going to have to

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bounce light off of them, or
he's going to have to bounce

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electrons, use an electron
microscope.

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He's going to have to keep
track of these gazillion

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particles that are there.

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And I mean, think about it.

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He might have to have a super
duper-- if it doesn't occur in

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his head, he might have to have
some kind of hardcore

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computer microchip that's
churning away.

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And this would be, actually,
for a computer to do this,

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this would be intensive
computation power.

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And let your computer run for
a little bit and feel the

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microchip-- this is generating
a lot of heat.

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His bouncing off light, or
whatever he's trying to bounce

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off of the different molecules
to be able to measure how fast

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they're going, that's also
going to generate heat.

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He's going to have to
do work to do that.

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He's going to have to
measure everything.

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There's a lot of stuff that's
going on that he's going to

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have to do.

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So the current answer is-- and
it's not easy to prove

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mathematically-- but the current
answer is, if you

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actually wanted to build a demon
like this-- and probably

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in our world today, you'd use
some type of computer with

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some type of sensors-- to
attempt to do this-- and there

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are people who have attempted
to do this, on some level.

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This computer and this whole
system is going to generate

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more entropy-- so the delta S
here is going to generate more

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entropy than the entropy that's
lost by making the cold

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side colder and the
hot side hotter.

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So Maxwell's demon,
and I didn't do

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anything rigorous here.

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I didn't prove it to you.

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But Maxwell's demon, it's
an interesting thought

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experiment, because it gives
you a little bit more

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intuition about the difference
between macro

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states and micro states.

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And what happens at the
molecular level in terms of

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temperature, and how you can
make a cold body colder and a

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hot body hotter.

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But answer is, it really
isn't a paradox or

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anything like that.

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When you think about the entropy
of the entire system,

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you have to include
the demon himself.

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And if you include the demon
himself, he's generating more

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entropy every time he opens that
door-- and maybe there's

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some energy required to
open the door itself.

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But he generates more entropy
when he does all of this than

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the entropy that might be lost,
when say, for example,

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one of these slowpoke particles
kind of just

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00:13:17,130 --> 00:13:20,280
traverses onto that side
of the barrier.

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Anyway, I thought I would just
expose you to that, because

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it's a really neat thought
experiment.

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So I'll see in the next video.