Statistical Mechanics for Chemistry and Materials Science

Key Question Being Explored in This Insight:

Biman Bagchi discusses key concepts in statistical mechanics along with many advanced and modern topics such as nucleation, spinodal decomposition, inherent structures of liquids.

View the page of: Biman Bagchi

Institution: Indian Institute of Science

Explore more insights in:

Chemistry Natural Sciences Sciences

Media Literacy Toolkit

Faculti's Media Literacy Toolkit helps viewers critically engage with academic insights by analyzing the research context, identifying perspectives, and encouraging thoughtful evaluation.

Critical Questions to Consider ▼

What assumptions does the research make?
Are there alternative perspectives not explored?
What are the limitations of the research method?

Bias and Perspective Awareness ▼

This research comes from Indian Institute of Science . Reflect on how the institution's academic focus and research partnerships may shape the questions being explored.

Further Reading ▼

Read the Book

Biman Bagchi discusses key concepts in statistical mechanics along with many advanced and modern topics such as nucleation, spinodal decomposition, inherent structures of liquids.

Image courtesy of interviewee. March 19, 2024

Log-in or Sign-up to Faculti
Currently viewing this subject insight as a guest. You have insight(s) remaining for this month. Login to view 8000+ figures on the platform.

Generating Workspace...

Export as PDF

The speaker discusses their academic journey, which began with a PhD at Brown University and teaching at the University of Chicago. They highlight the lack of modern resources in statistical mechanics for chemistry and biology, leading them to create their own teaching materials—ultimately resulting in the publication of four books, with one being particularly successful in India.

They explain the evolution of statistical mechanics, its relevance in understanding complex systems like liquids and proteins, and the importance of developments from historical figures such as Ludwig Boltzmann and Willard Gibbs. The speaker emphasizes how modern computing has transformed statistical mechanics, enabling simulations and insights into molecular behavior, which were previously unattainable.

Additionally, they touch on the significance of understanding dynamic processes in biology, including DNA repair and protein folding, which require knowledge of non-equilibrium statistical mechanics. The talk underscores the need for students to explore these subjects further, as they hold the key to many scientific challenges and advancements in understanding living systems and diseases. The speaker concludes by encouraging the pursuit of this important field, suggesting that statistical mechanics will continue to be a crucial discipline in science and research.

Language:

Export as PDF

X-TIMESTAMP-MAP=LOCAL:00:00:00.000,MPEGTS:90000

1
00:00:00.195 --> 00:00:03.985
When I, came back from,

2
00:00:04.105 --> 00:00:07.145
I did PhD at Brown, then I was in University of Chicago

3
00:00:08.005 --> 00:00:09.505
and started teaching Stat Mac,

4
00:00:09.505 --> 00:00:11.705
which was not very popular in chemistry

5
00:00:11.725 --> 00:00:12.825
and biology those days.

6
00:00:13.565 --> 00:00:16.785
And I found there's a book which I can teach from,

7
00:00:17.215 --> 00:00:20.425
from the subjects and topics that I wanted to teach.

8
00:00:20.425 --> 00:00:23.585
There are lots of books, which are from 1960s and seventies,

9
00:00:24.165 --> 00:00:27.265
but the tremendous development has taken place in,

10
00:00:27.485 --> 00:00:28.665
chemistry and biology.

11
00:00:29.565 --> 00:00:31.265
Uh, like for example, liquids.

12
00:00:31.725 --> 00:00:34.265
We never didn't have a theory of liquids in sixties.

13
00:00:34.855 --> 00:00:36.425
They all developed in seventies

14
00:00:36.425 --> 00:00:38.505
and eighties with computer simulations

15
00:00:38.645 --> 00:00:40.905
and biology, for example, understanding protein

16
00:00:41.465 --> 00:00:42.905
proteins, protein folding.

17
00:00:43.485 --> 00:00:47.945
So the things that I wanted to start cover in a book,

18
00:00:48.645 --> 00:00:50.945
in a course was not simply not there.

19
00:00:51.685 --> 00:00:53.345
So I had a lot of difficulty

20
00:00:53.365 --> 00:00:54.865
and I started making a lot of notes.

21
00:00:55.605 --> 00:00:57.745
And my students, there are some good students

22
00:00:57.805 --> 00:00:58.985
who started typing it.

23
00:01:00.235 --> 00:01:03.295
So, it, it actually, I have four books now,

24
00:01:03.315 --> 00:01:05.135
but this was the first book

25
00:01:05.165 --> 00:01:07.895
that actually was conceived but got delayed.

26
00:01:08.315 --> 00:01:10.975
Uh, it's a big book because it's 600 pages.

27
00:01:10.995 --> 00:01:13.015
It probably even, we took out some chapters

28
00:01:13.015 --> 00:01:15.135
because it was getting too big.

29
00:01:15.715 --> 00:01:19.295
And I believe that in your course you should teach some life

30
00:01:19.295 --> 00:01:22.095
skill, you know, in the sense that things

31
00:01:22.095 --> 00:01:24.855
that students can take to their work

32
00:01:25.725 --> 00:01:27.415
that was not there in the books.

33
00:01:27.475 --> 00:01:29.135
You know, there are a lot of complicated books,

34
00:01:29.135 --> 00:01:31.775
sophisticated books, but I thought there is no book.

35
00:01:31.775 --> 00:01:33.015
And this book has become quite

36
00:01:33.015 --> 00:01:34.575
popular, actually, at least in India.

37
00:01:35.095 --> 00:01:37.255
I think at least 20 places teach from my book,

38
00:01:37.255 --> 00:01:38.535
which I'm very proud of

39
00:01:38.535 --> 00:01:41.575
because yeah, I was, you know, you, you always write a book

40
00:01:41.575 --> 00:01:42.855
for your own students, right?

41
00:01:42.855 --> 00:01:46.135
You know, that means, so it was though you this concept of,

42
00:01:46.155 --> 00:01:48.975
think globally, but act locally.

43
00:01:49.415 --> 00:01:51.895
I have a chapter in the book which tells why study

44
00:01:51.935 --> 00:01:53.575
statistical mechanics, you know,

45
00:01:53.575 --> 00:01:55.775
like the very first chapter or in the pre phase.

46
00:01:56.265 --> 00:01:57.655
Great deal. I went into it.

47
00:01:58.355 --> 00:02:03.015
Uh, so look, if I want to understand, a, a, a glass

48
00:02:03.015 --> 00:02:04.975
of water is properties to want to predict.

49
00:02:05.465 --> 00:02:06.895
There are some very interesting thing.

50
00:02:06.985 --> 00:02:11.095
Water is same almost everywhere. Okay? Wherever you go.

51
00:02:11.165 --> 00:02:13.655
Okay, forces changing. Many other things are changing.

52
00:02:15.635 --> 00:02:17.815
So the session mechanics has two things.

53
00:02:17.915 --> 00:02:19.855
One is statistics and is mechanics.

54
00:02:20.555 --> 00:02:23.415
Uh, why we need statistics, mechanics,

55
00:02:23.415 --> 00:02:25.175
and Newton's laws of motions should have what?

56
00:02:25.675 --> 00:02:28.335
But no, in this glass of water, I gave you the example,

57
00:02:28.515 --> 00:02:31.495
the zillions and zillions and zillions of water molecules.

58
00:02:31.555 --> 00:02:33.335
And they're very strongly interacting with each other.

59
00:02:33.755 --> 00:02:37.455
We cannot solve neutrons, laws of motion, neutrons, laws

60
00:02:37.455 --> 00:02:40.655
of motion, deals with position, acceleration and forces.

61
00:02:41.795 --> 00:02:44.175
And we solve all these equations together.

62
00:02:44.845 --> 00:02:46.615
Even if you pass, you won't be able to solve.

63
00:02:46.745 --> 00:02:49.215
It'll take you millennium, but a billion years.

64
00:02:49.315 --> 00:02:51.375
But even if you saw what you do with all the data,

65
00:02:52.245 --> 00:02:54.215
it's just not, useful at all.

66
00:02:55.155 --> 00:02:59.925
So in the, this approach was, adopted in a limited way

67
00:02:59.945 --> 00:03:03.845
by a great German physicist called Luman.

68
00:03:04.545 --> 00:03:07.245
Um, and who was motivated by Maxwell in the,

69
00:03:07.245 --> 00:03:10.005
our pre British, physicist story

70
00:03:10.705 --> 00:03:12.885
who conceived DL gas law, what will come to in a minute.

71
00:03:14.135 --> 00:03:18.715
Now, Bolman tried to really go by way,

72
00:03:18.715 --> 00:03:21.555
almost neutral loss of tion, but he converted into priority.

73
00:03:22.455 --> 00:03:24.595
Now, as I said, statist on mechanics is two things.

74
00:03:24.595 --> 00:03:26.995
Static mechanics and priority mechanics is neutral.

75
00:03:26.995 --> 00:03:28.475
Loss of motion. We understand

76
00:03:28.735 --> 00:03:30.115
and we see that you cannot do it.

77
00:03:30.895 --> 00:03:33.635
But then Boman realized that one way

78
00:03:33.635 --> 00:03:35.835
to go will be introduced concept, priority theory.

79
00:03:35.835 --> 00:03:39.425
He was heavily criticized and he committed suicide, and,

80
00:03:40.285 --> 00:03:42.145
but he could not do it all the way

81
00:03:42.145 --> 00:03:44.025
because he made some questionable assumptions,

82
00:03:44.025 --> 00:03:45.345
which, you know, didn't work though.

83
00:03:45.345 --> 00:03:47.505
He got quite too far. He introduced the mechanical

84
00:03:47.695 --> 00:03:49.505
microscopic definition of entropy

85
00:03:50.565 --> 00:03:51.825
on the other side of the Atlantic.

86
00:03:52.735 --> 00:03:56.235
Uh, another great, great brain instance called the,

87
00:03:56.955 --> 00:03:58.915
possibly the greatest brain of that century

88
00:03:59.615 --> 00:04:01.995
was Willard Gibbs at Yale University.

89
00:04:02.615 --> 00:04:04.635
He, he was very close to Maxwell,

90
00:04:04.775 --> 00:04:06.755
and he was following a failure of ulman.

91
00:04:07.595 --> 00:04:10.415
So he now realized that that approach will not work.

92
00:04:11.235 --> 00:04:13.535
So he invented a completely new approach

93
00:04:13.555 --> 00:04:16.535
and something which is really not valued enough.

94
00:04:16.595 --> 00:04:18.255
The most brilliant hypothesis

95
00:04:18.255 --> 00:04:19.495
with the concept concept of ensemble.

96
00:04:20.085 --> 00:04:22.585
He said, look, this glass of water, I give you an example,

97
00:04:22.725 --> 00:04:23.905
has the same property everywhere,

98
00:04:24.165 --> 00:04:26.105
but the molecules are all moving.

99
00:04:26.725 --> 00:04:28.905
So they are all in different states.

100
00:04:29.205 --> 00:04:30.385
We call microscopic states.

101
00:04:30.385 --> 00:04:31.585
All have different orientation,

102
00:04:31.985 --> 00:04:34.145
position momentum are different.

103
00:04:34.605 --> 00:04:37.785
So it's all my glass, glass of water that you have in front

104
00:04:37.785 --> 00:04:39.185
of me and I have in front of me.

105
00:04:39.185 --> 00:04:40.385
They're almost the same. Property

106
00:04:40.905 --> 00:04:41.945
molecules are all indifferent.

107
00:04:42.825 --> 00:04:43.925
He then conceived that.

108
00:04:43.995 --> 00:04:47.205
Okay, then can I consider a six in dimensional,

109
00:04:47.205 --> 00:04:50.245
high dimensional space where each coordinate

110
00:04:50.245 --> 00:04:53.045
for each molecule, so in a number of particles,

111
00:04:53.045 --> 00:04:55.645
there is a six n number of degrees of freedom.

112
00:04:55.905 --> 00:04:57.805
In that space, which is called face space.

113
00:04:58.425 --> 00:05:00.565
My system is described by point,

114
00:05:01.435 --> 00:05:03.935
and my evolution then moves from one trajectory.

115
00:05:04.285 --> 00:05:05.735
Just like in three dimension space,

116
00:05:05.735 --> 00:05:07.415
we see a water molecules falling in the river,

117
00:05:08.345 --> 00:05:11.395
this face space, which mental construction,

118
00:05:11.975 --> 00:05:13.195
all a particle moves.

119
00:05:13.625 --> 00:05:14.995
Then he realized, okay,

120
00:05:15.455 --> 00:05:19.195
if I have can construct mental replica of,

121
00:05:20.165 --> 00:05:22.995
again, zillions, of zillions, of zillions of mental replica,

122
00:05:23.145 --> 00:05:26.475
then each replica will have a different micro state.

123
00:05:27.375 --> 00:05:29.715
But at constant energy, they have the same probability.

124
00:05:30.745 --> 00:05:32.605
So then any concept introduce the concept

125
00:05:32.745 --> 00:05:36.525
of the probability, and it concept many,

126
00:05:36.525 --> 00:05:37.925
very many things followed from.

127
00:05:38.105 --> 00:05:40.765
So if a student wants to remember, anybody wants to,

128
00:05:40.765 --> 00:05:42.805
then these two names Mann

129
00:05:42.805 --> 00:05:44.955
and Willard Gibbs, they're the fathers

130
00:05:45.175 --> 00:05:46.315
of statistical mechanics.

131
00:05:46.815 --> 00:05:50.955
Now they describe these ensembles and that escape priority.

132
00:05:52.095 --> 00:05:54.195
But in real world, we do time averaging.

133
00:05:54.195 --> 00:05:56.235
When you measure the property of a glass of water,

134
00:05:56.335 --> 00:05:57.485
you are doing a time averaging.

135
00:05:57.545 --> 00:05:59.685
You have one glass of water. I have one glass of water.

136
00:06:00.425 --> 00:06:03.965
But we are saying that I can have different ensembles.

137
00:06:04.025 --> 00:06:05.245
But in mental replica,

138
00:06:05.245 --> 00:06:07.285
where each system in a different microscopic states,

139
00:06:07.495 --> 00:06:08.645
those two must be equal.

140
00:06:09.505 --> 00:06:12.485
And those two equal means the is called

141
00:06:12.575 --> 00:06:14.125
equal, time average.

142
00:06:14.435 --> 00:06:17.485
Your averaging and the ensemble average, they have to equal,

143
00:06:17.485 --> 00:06:18.765
they're the fast postulate.

144
00:06:19.105 --> 00:06:23.325
Second, my system must my mental replicas, billions

145
00:06:23.325 --> 00:06:26.645
and billions of them, they must be equally probable.

146
00:06:26.685 --> 00:06:28.925
I don't know anything about them. They have constant energy,

147
00:06:29.275 --> 00:06:31.085
same micro, same microscopic state.

148
00:06:31.235 --> 00:06:32.445
They're equal probable,

149
00:06:32.555 --> 00:06:34.125
that is called equally probable, probably.

150
00:06:34.265 --> 00:06:36.725
So these are the two posterous ational mechanics,

151
00:06:37.425 --> 00:06:39.525
and they're connected by another beautiful concept.

152
00:06:39.525 --> 00:06:41.285
According hypothesis will not go into it.

153
00:06:41.285 --> 00:06:44.165
That's a huge branch of physics and, mathematics.

154
00:06:44.945 --> 00:06:49.925
Now, once I now want to describe the motion

155
00:06:50.025 --> 00:06:54.365
of my system in the face space, so when I have just six,

156
00:06:54.365 --> 00:06:56.325
same dimensional, I I have one point,

157
00:06:56.385 --> 00:07:00.445
but I have many systems, then I'll have a density, density

158
00:07:01.105 --> 00:07:05.125
of, these systems, which like a swar of bee, you know,

159
00:07:05.215 --> 00:07:08.395
which are moving or water in a river.

160
00:07:08.425 --> 00:07:10.795
They're flowing, but flowing in that space.

161
00:07:11.775 --> 00:07:14.275
So I need an equation to describe the flow.

162
00:07:14.815 --> 00:07:17.115
If I have an equation like neutrons equation

163
00:07:18.095 --> 00:07:21.795
to describe the flow of density, density of particles,

164
00:07:21.975 --> 00:07:25.115
not density of particles, density of systems, then I am in,

165
00:07:25.115 --> 00:07:27.875
in, in, in, in, in, in, in, in, kind of business.

166
00:07:28.115 --> 00:07:31.595
I can, I can start describing properties,

167
00:07:31.975 --> 00:07:32.995
how systems change.

168
00:07:33.655 --> 00:07:35.955
And that is what the global equation gives you.

169
00:07:36.105 --> 00:07:37.235
It's a density function.

170
00:07:37.235 --> 00:07:38.635
It's a direct generalization

171
00:07:38.735 --> 00:07:41.115
of you can say hydrodynamic equations.

172
00:07:41.115 --> 00:07:44.035
There are equations like equation continued Ethereum,

173
00:07:44.195 --> 00:07:45.435
conservation of mass.

174
00:07:45.935 --> 00:07:49.795
See, very standard concepts of hydrodynamics

175
00:07:50.615 --> 00:07:54.075
and classical mechanics are used to derive equation

176
00:07:54.075 --> 00:07:55.795
of motion of the density function,

177
00:07:56.015 --> 00:07:57.875
but density function in a face space,

178
00:07:58.415 --> 00:08:00.475
it sometimes puts the students off,

179
00:08:00.495 --> 00:08:03.355
but is a very simple thing based on same concept

180
00:08:03.505 --> 00:08:05.155
that conservation of particles.

181
00:08:05.155 --> 00:08:07.195
You cannot conservation systems here,

182
00:08:07.215 --> 00:08:09.075
you cannot create or destroy system.

183
00:08:10.135 --> 00:08:13.115
And so it just, follows from that.

184
00:08:13.135 --> 00:08:16.635
And it describes your motion of system in a face space.

185
00:08:17.455 --> 00:08:20.475
In my book, the chapter, I think, immediately

186
00:08:20.475 --> 00:08:22.515
after the postulates, the chapter comes

187
00:08:22.535 --> 00:08:26.395
as you have seen, the, these, ideal gas law.

188
00:08:26.645 --> 00:08:30.315
Ideal gas law was formulated by Gaza Boyle

189
00:08:30.315 --> 00:08:32.675
and, this European and British scientists,

190
00:08:33.495 --> 00:08:35.825
because it was seen that the pressure

191
00:08:36.605 --> 00:08:37.825
and volume of a system,

192
00:08:38.295 --> 00:08:40.105
they have very close relation with each other.

193
00:08:41.675 --> 00:08:43.475
Molecules then did not. They, they, they, they,

194
00:08:43.475 --> 00:08:46.075
they had molecules, but they did not know how to in

195
00:08:46.635 --> 00:08:47.675
describe interaction between them.

196
00:08:48.935 --> 00:08:51.475
But our, our systems that determine very interactions.

197
00:08:52.415 --> 00:08:54.715
So first thing they did, the simplest

198
00:08:54.715 --> 00:08:56.205
System is ideal gas law,

199
00:08:56.735 --> 00:08:59.965
where my molecules are considered at the point, part two,

200
00:09:00.195 --> 00:09:01.605
they don't interact with each other.

201
00:09:01.605 --> 00:09:02.805
They're phantom particles.

202
00:09:02.955 --> 00:09:05.525
They pass through each other without any, eh,

203
00:09:06.065 --> 00:09:09.245
but they interact with the wall and they recoil.

204
00:09:09.745 --> 00:09:13.765
That's Maxwell, a recoil, and you get a pressure.

205
00:09:14.265 --> 00:09:16.045
So one could derive that pressure,

206
00:09:16.225 --> 00:09:19.285
and they found that pressure is invar al to volume

207
00:09:20.185 --> 00:09:22.165
and pressure is al to temperature.

208
00:09:22.965 --> 00:09:27.025
And that combined by giving, by using just simple variation

209
00:09:27.415 --> 00:09:31.225
that PV got wat that defines the, ideal gas log.

210
00:09:31.605 --> 00:09:36.185
Now, very fast, we did the, like we just in the air,

211
00:09:36.725 --> 00:09:40.745
let's say we have only oxygen or we have only nitrogen.

212
00:09:40.965 --> 00:09:43.705
That's the one component system, but that is diet.

213
00:09:44.645 --> 00:09:45.665
But we have argon.

214
00:09:45.685 --> 00:09:47.905
We much later, could explain,

215
00:09:47.965 --> 00:09:49.265
do it, explain with the argon.

216
00:09:49.265 --> 00:09:53.465
That's a mono. Monoatomic means a molecule has one

217
00:09:53.935 --> 00:09:54.945
atto, okay?

218
00:09:54.945 --> 00:09:58.025
Like argon diatomic means it has two atoms,

219
00:09:58.095 --> 00:09:59.465
like nitrogen and oxygen.

220
00:09:59.915 --> 00:10:01.065
Their properties differ.

221
00:10:01.885 --> 00:10:05.225
So fast modules that scientists developed was doing testing

222
00:10:05.285 --> 00:10:06.745
or mechanics or ideal gas

223
00:10:06.765 --> 00:10:09.625
or monoatomic that can be easily worked out.

224
00:10:09.735 --> 00:10:12.145
They don't interact with each other. They're simple.

225
00:10:12.665 --> 00:10:14.265
I can go from level equation

226
00:10:14.725 --> 00:10:16.425
to a concept called partition function,

227
00:10:16.485 --> 00:10:18.105
and I can evaluate this pressure

228
00:10:18.685 --> 00:10:20.425
for completely microscopic things.

229
00:10:21.615 --> 00:10:23.995
But you know, when you being dynamics, there's a rotation,

230
00:10:24.875 --> 00:10:26.315
molecules rotate and they ate it.

231
00:10:26.315 --> 00:10:27.515
Sphere doesn't rotate because, well,

232
00:10:27.515 --> 00:10:28.635
it rotate doesn't matter.

233
00:10:29.135 --> 00:10:30.795
But a diatoms rotate

234
00:10:31.135 --> 00:10:34.735
and it vibrates that those degrees of freedom,

235
00:10:34.755 --> 00:10:35.815
we call them degrees of freedom,

236
00:10:35.845 --> 00:10:37.015
need to be taken into account.

237
00:10:37.755 --> 00:10:40.935
And they were done in these, fashion

238
00:10:41.035 --> 00:10:43.575
by introducing certain models that they took bonds

239
00:10:44.085 --> 00:10:48.295
held together by spring, and they rotate like a rigid body.

240
00:10:48.395 --> 00:10:50.695
We all, all these things were known in classical mechanics.

241
00:10:50.915 --> 00:10:52.855
You know, if you take any book of classical mechanics,

242
00:10:52.875 --> 00:10:55.255
you will have harmonic vibrations, you know,

243
00:10:55.875 --> 00:10:57.495
and it will have the rigid rotator.

244
00:10:57.915 --> 00:11:01.015
So those things were now taken into size mechanics

245
00:11:01.315 --> 00:11:03.575
to describe, you know, what we call, you know,

246
00:11:03.675 --> 00:11:07.455
energy function, Hamiltonian, and then one grinds.

247
00:11:07.475 --> 00:11:10.575
The thing is a very straightforward and very simple,

248
00:11:10.835 --> 00:11:14.695
and I just take one, second to tell you one thing, one

249
00:11:14.695 --> 00:11:17.815
of the reason of writing the book when I was teaching,

250
00:11:18.575 --> 00:11:21.575
I thought they, there is certain lack of coherence.

251
00:11:22.455 --> 00:11:25.335
Students really need to know why they're studying what,

252
00:11:25.715 --> 00:11:26.775
and there should be a flow.

253
00:11:27.755 --> 00:11:31.335
So I tried to create that flow. In this, in this book.

254
00:11:31.605 --> 00:11:35.055
This is what I, I I really wanted to talk about because in,

255
00:11:35.425 --> 00:11:39.655
after, when you're doing gas, ideal gas law, mono di

256
00:11:40.405 --> 00:11:42.215
they don't, they don't interact with each other

257
00:11:42.675 --> 00:11:45.135
and they don't undergo any face change.

258
00:11:45.515 --> 00:11:48.095
But, you know, real world raindrops form

259
00:11:48.115 --> 00:11:49.135
and fall on our head.

260
00:11:49.525 --> 00:11:51.655
Then we, liquid crystalizes,

261
00:11:52.835 --> 00:11:54.245
all these things are face changed.

262
00:11:54.245 --> 00:11:56.925
They're only present, all the time.

263
00:11:57.305 --> 00:11:59.285
Uh, acid becoming liquid, liquid

264
00:11:59.285 --> 00:12:00.805
and boil water becoming gas.

265
00:12:01.585 --> 00:12:04.245
But how do we, describe these things?

266
00:12:04.945 --> 00:12:09.405
And, a ideal gas does notify.

267
00:12:09.425 --> 00:12:10.965
It does not undergo in phase transition

268
00:12:11.535 --> 00:12:13.785
because in order to undergo face transition,

269
00:12:14.455 --> 00:12:18.465
they must interact, like in order to formulate, in, in,

270
00:12:18.485 --> 00:12:21.945
in raindrops on the upper atmosphere, molecules must stick

271
00:12:21.945 --> 00:12:25.285
with each other and molecules will stick with each other.

272
00:12:25.635 --> 00:12:26.685
They lose entropy.

273
00:12:26.785 --> 00:12:28.565
We, we come back to entropy a little bit more.

274
00:12:28.565 --> 00:12:31.205
You aspir, I forgot. Now entropy

275
00:12:31.325 --> 00:12:32.685
means molecules are moving around.

276
00:12:33.505 --> 00:12:35.285
Now that translational entropy,

277
00:12:35.285 --> 00:12:36.445
they're rotating, that's rotation.

278
00:12:37.005 --> 00:12:38.325
Entropy is nothing but degrees of freedom.

279
00:12:38.705 --> 00:12:40.005
But when they come together,

280
00:12:40.315 --> 00:12:41.565
they lose the degrees of freedom.

281
00:12:42.415 --> 00:12:44.475
But why they'll do that, they'll do

282
00:12:44.475 --> 00:12:46.035
because they like each other.

283
00:12:46.145 --> 00:12:48.235
There's an attractive interaction between them

284
00:12:48.915 --> 00:12:51.575
and that attractive interaction make them call

285
00:12:52.235 --> 00:12:54.135
and that leads to face transition.

286
00:12:55.065 --> 00:12:57.485
But, and this is not the Skype idea

287
00:12:57.545 --> 00:13:00.205
and all this is, discipline

288
00:13:00.205 --> 00:13:02.445
that discuss face transition is testing on mechanics.

289
00:13:03.075 --> 00:13:04.925
There's great pieces like Landau

290
00:13:04.925 --> 00:13:08.485
and other people who did the Einstein is beat.

291
00:13:09.025 --> 00:13:12.605
So that face transition is completely a subject

292
00:13:12.605 --> 00:13:13.685
of statist mechanics.

293
00:13:14.775 --> 00:13:17.275
How does it form? It does not form itself.

294
00:13:17.275 --> 00:13:18.835
There's phenomenal nucleation,

295
00:13:18.835 --> 00:13:20.435
which is called embryo formation.

296
00:13:21.085 --> 00:13:25.395
Small has to stabilize against a droppy. Then that can grow.

297
00:13:25.395 --> 00:13:28.715
That is nucleation. Sometimes in a rock formation,

298
00:13:28.715 --> 00:13:30.795
in volcanic rock, we find the beautiful patterns

299
00:13:31.345 --> 00:13:33.115
when you suddenly, what the temperature

300
00:13:33.845 --> 00:13:36.925
a lo starts segregating and they form beautiful patterns.

301
00:13:37.185 --> 00:13:38.565
That's this spin competition.

302
00:13:38.565 --> 00:13:40.125
It's a non equilibrium phase transition.

303
00:13:41.585 --> 00:13:44.645
All these things at the purview of this wonderful subject

304
00:13:44.645 --> 00:13:47.205
of size mechanics, you know, it is, it is,

305
00:13:47.905 --> 00:13:49.205
we call it a second pillar

306
00:13:49.265 --> 00:13:50.805
of theoretical physics and chemistry.

307
00:13:50.805 --> 00:13:53.485
Fastest quantum mechanics. Second is ational mechanics.

308
00:13:54.205 --> 00:13:56.805
Entropy is essentially, as I said, is a degrees of freedom.

309
00:13:57.475 --> 00:14:00.925
That means the, there are a very famous law by ulman.

310
00:14:01.025 --> 00:14:03.165
The entropy equal to ulman.

311
00:14:03.445 --> 00:14:06.845
Constant times log of number of degree, number

312
00:14:06.905 --> 00:14:08.325
of, of freedom.

313
00:14:09.025 --> 00:14:11.045
So entropy, essentially peoples a measure

314
00:14:11.045 --> 00:14:12.285
of disorder that's not perfect.

315
00:14:13.245 --> 00:14:14.885
Entropy is essentially the amount

316
00:14:14.945 --> 00:14:17.445
of microscopic space that you have.

317
00:14:18.335 --> 00:14:22.745
Like if I want to go on, tossing a coin

318
00:14:23.015 --> 00:14:27.585
that I get, two sides, then I toss the many times the,

319
00:14:27.685 --> 00:14:31.625
a, a dice, a dai, then I get six side.

320
00:14:32.045 --> 00:14:33.105
So I know number of

321
00:14:33.675 --> 00:14:35.465
after end times, what are the number

322
00:14:35.465 --> 00:14:38.425
of possibilities all together from this sample space.

323
00:14:39.285 --> 00:14:42.905
And, and may entropy is the measure of the sample space.

324
00:14:43.605 --> 00:14:44.985
We call it measure of disorder

325
00:14:44.985 --> 00:14:46.625
because we don't know where it'll be.

326
00:14:47.365 --> 00:14:48.865
All the states are equally probe,

327
00:14:49.655 --> 00:14:51.285
and if you have too much entropy,

328
00:14:51.505 --> 00:14:52.845
you cannot have face transition

329
00:14:52.995 --> 00:14:54.845
because face transition means order,

330
00:14:55.475 --> 00:14:57.405
face transition may go to crystal.

331
00:14:57.405 --> 00:14:59.005
Crystal is highly ordered thing,

332
00:15:00.115 --> 00:15:01.895
but it has entropy, very low entropy.

333
00:15:03.645 --> 00:15:05.345
So you have to remove the entropy

334
00:15:05.345 --> 00:15:06.545
by intermolecular potential.

335
00:15:07.125 --> 00:15:10.225
And that is, is, is, is, is is the fascinating subject.

336
00:15:10.565 --> 00:15:14.605
You know, now, as I was telling the, sixties

337
00:15:14.825 --> 00:15:18.665
and seventies and eighties, also nineties

338
00:15:18.725 --> 00:15:21.785
or tremendous development of the concepts, that's one

339
00:15:21.785 --> 00:15:23.105
of the things I started teaching.

340
00:15:23.225 --> 00:15:26.545
I found that the, my stat Mac books do not have several

341
00:15:26.685 --> 00:15:29.745
topics which are considered advanced talks in theory

342
00:15:29.845 --> 00:15:32.305
of liquids, which is extremely difficult to do.

343
00:15:32.645 --> 00:15:34.465
Uh, one of the first theory of liquids

344
00:15:34.465 --> 00:15:37.425
and the idea that what liquidities was done by JD Burnell,

345
00:15:37.565 --> 00:15:39.625
the famous, I think Oxford or Cambridge.

346
00:15:39.625 --> 00:15:43.255
Cambridge, I guess, who's also one of the father figure

347
00:15:43.255 --> 00:15:44.255
of Histography.

348
00:15:45.035 --> 00:15:47.815
JD Burnell sold something very interesting.

349
00:15:48.235 --> 00:15:51.655
He said, okay, I want to describe I liquid.

350
00:15:51.925 --> 00:15:56.535
What he did, he took a, a collection of marble balls

351
00:15:57.155 --> 00:16:00.205
and he put them in a jar and said, oil

352
00:16:00.665 --> 00:16:02.925
and type packed it, as many as he can put it.

353
00:16:03.775 --> 00:16:06.825
Then he put a paint, a black paint on top of that

354
00:16:07.445 --> 00:16:09.265
and let the paint go through.

355
00:16:10.525 --> 00:16:13.545
Now, after some time or after a day or two, he opened

356
00:16:14.285 --> 00:16:17.815
and he found out where, yeah,

357
00:16:17.915 --> 00:16:19.855
he did the marking one by one.

358
00:16:19.855 --> 00:16:21.575
He took out and marked, the ball.

359
00:16:21.635 --> 00:16:23.655
He found that there's a beautiful pattern

360
00:16:23.655 --> 00:16:27.855
that emerges from the position of just speak to each other,

361
00:16:28.875 --> 00:16:30.765
coin the name radial distribution function,

362
00:16:30.765 --> 00:16:32.845
which is now later measured by neutron scattering.

363
00:16:33.345 --> 00:16:36.005
Uh, so this now, so the theory

364
00:16:36.065 --> 00:16:39.125
of liquids was begin now is extremely difficult thing.

365
00:16:39.125 --> 00:16:40.805
As I was saying, these are called interacting system.

366
00:16:41.025 --> 00:16:43.605
As I said, marble balls, which is a very good description,

367
00:16:44.555 --> 00:16:45.645
like point particle.

368
00:16:45.665 --> 00:16:46.925
Non interacting is ideal.

369
00:16:46.925 --> 00:16:48.485
L gas law, low density gas,

370
00:16:48.745 --> 00:16:50.805
but liquid is other extreme limit of high density.

371
00:16:51.345 --> 00:16:53.845
One order of magnitude, two orders of magnitude,

372
00:16:53.845 --> 00:16:55.445
more density molecules are

373
00:16:55.445 --> 00:16:56.525
really hitting against each other.

374
00:16:58.065 --> 00:17:00.405
How do you do that? Then there was a, this cell theory said,

375
00:17:00.405 --> 00:17:03.205
okay, let me then consider liquid as a solid.

376
00:17:04.365 --> 00:17:05.735
What is so unique out solid.

377
00:17:06.495 --> 00:17:09.375
I can give a cell a volume element to each attom

378
00:17:09.375 --> 00:17:10.895
because it is sitting there, right?

379
00:17:11.715 --> 00:17:13.935
So the concept of li crystalline

380
00:17:13.995 --> 00:17:17.215
or solid state was brought to liquids,

381
00:17:17.485 --> 00:17:18.815
basically motivated by.

382
00:17:19.635 --> 00:17:22.735
So cell theory means it was divide the whole volume

383
00:17:23.125 --> 00:17:24.175
into different cells.

384
00:17:25.175 --> 00:17:29.355
But however, unlike crystal, where the particle cannot move

385
00:17:29.985 --> 00:17:34.115
from OO one, cell to another cell in liquid,

386
00:17:34.215 --> 00:17:35.395
no, they diffuse.

387
00:17:35.535 --> 00:17:37.235
It has an non zero diffusion constant.

388
00:17:37.535 --> 00:17:40.595
So it goes from one cell to another cell.

389
00:17:40.825 --> 00:17:42.475
That particle goes to another place

390
00:17:42.585 --> 00:17:44.955
because there is something called free volume is there,

391
00:17:44.975 --> 00:17:49.655
the volume access, what that crystal and that redistributed

392
00:17:49.655 --> 00:17:52.415
because of the entropy, because these, these space,

393
00:17:52.585 --> 00:17:54.095
there are degrees of freedom available.

394
00:17:54.985 --> 00:17:56.045
So it, so

395
00:17:56.045 --> 00:17:58.325
and so, cell theory is essentially,

396
00:17:58.745 --> 00:18:01.445
you can say solid like theory for liquids

397
00:18:01.445 --> 00:18:03.805
because of the high density that allows,

398
00:18:04.025 --> 00:18:05.925
but allows particles to move and

399
00:18:05.925 --> 00:18:09.125
because particles can move if they have an entropy.

400
00:18:09.315 --> 00:18:10.765
That is called communal entropy.

401
00:18:11.075 --> 00:18:14.245
Certainly wonderful questions. I keep saying that.

402
00:18:14.325 --> 00:18:17.605
Theories of statistical mechanics,

403
00:18:17.605 --> 00:18:21.005
really developed very fast, sixties, seventies, eighties,

404
00:18:21.005 --> 00:18:22.165
that because of computers.

405
00:18:23.385 --> 00:18:27.685
So all these beautiful theories of Mann, Willard, GI

406
00:18:27.825 --> 00:18:32.255
and many other people, they, we, we had them in paper.

407
00:18:32.355 --> 00:18:35.295
We could hardly do it. We could do it only for,

408
00:18:35.455 --> 00:18:36.535
a little bit low density

409
00:18:36.955 --> 00:18:39.415
and with, with just spherical atoms.

410
00:18:39.415 --> 00:18:41.615
But we couldn't do water the system we wanted to do.

411
00:18:41.715 --> 00:18:43.815
We couldn't do protein that we wanted to do.

412
00:18:44.115 --> 00:18:45.175
We couldn't do DNA,

413
00:18:45.435 --> 00:18:47.055
we couldn't do protein Indian interaction.

414
00:18:47.115 --> 00:18:50.615
We couldn't do enzymes, you know, but we,

415
00:18:50.615 --> 00:18:52.255
because we, we had the principles.

416
00:18:52.995 --> 00:18:55.695
We know in principle, if you give me interaction potential,

417
00:18:55.715 --> 00:18:56.735
how molecules interact

418
00:18:56.735 --> 00:18:58.095
with each other, how they talk with each other.

419
00:18:58.795 --> 00:19:01.055
If you give me that, which we quantum mechanics can give us,

420
00:19:02.175 --> 00:19:03.265
then in principle,

421
00:19:03.335 --> 00:19:05.705
test mechanics should give me all the answers.

422
00:19:06.725 --> 00:19:09.345
But it, it cannot because we cannot solve those equations.

423
00:19:09.685 --> 00:19:11.745
As I told you, even computer cannot do

424
00:19:11.745 --> 00:19:13.505
that in the, in, in, in theory.

425
00:19:13.925 --> 00:19:17.185
But then people did something very clever when the computers

426
00:19:17.185 --> 00:19:20.825
came say, okay, I cannot solve thousand of millions

427
00:19:20.825 --> 00:19:22.185
of million, but I can solve hundreds.

428
00:19:22.205 --> 00:19:25.825
So fast simulation was done by bar Alder and Rosen be

429
00:19:25.825 --> 00:19:27.705
and Taylor with only 32 particles.

430
00:19:28.325 --> 00:19:31.465
And lo and behold, even 32 particles of hot sphere,

431
00:19:31.465 --> 00:19:34.225
square face transition, that was a amazing

432
00:19:34.235 --> 00:19:35.905
excitement in 19, late fifties.

433
00:19:36.165 --> 00:19:39.865
And so computer simulation opened the completely new thing.

434
00:19:40.675 --> 00:19:43.415
Uh, so now we started to put in,

435
00:19:43.415 --> 00:19:45.095
that's why the Nobel Prize of Levy

436
00:19:45.195 --> 00:19:48.775
and, Martin car Plus, we, we can do the reactions.

437
00:19:49.235 --> 00:19:51.335
The single molecule spectroscopy got Nobel Prize.

438
00:19:51.435 --> 00:19:53.735
All the Nobel prizes that went into chemistry

439
00:19:53.735 --> 00:19:56.695
and medicine in last few years were all motivated.

440
00:19:56.695 --> 00:19:58.455
That's why Levy one said a very nice thing

441
00:19:58.455 --> 00:19:59.535
when you got the Nobel Prize.

442
00:20:00.035 --> 00:20:02.415
So there is a silent guy in the,

443
00:20:02.435 --> 00:20:04.335
in the room, and that's the computer.

444
00:20:04.485 --> 00:20:07.375
Without this computer, we could not have done anything.

445
00:20:07.555 --> 00:20:09.535
So computer open session mechanics.

446
00:20:09.795 --> 00:20:10.935
Now, I can tell you one thing.

447
00:20:10.935 --> 00:20:15.055
The students, these days, we used to be pen and paper.

448
00:20:15.235 --> 00:20:17.815
We used to probably do a hundred page of calculations a day.

449
00:20:18.875 --> 00:20:21.575
We come in the morning, start to have cup of coffee

450
00:20:21.755 --> 00:20:23.455
and start pushing pencil

451
00:20:23.595 --> 00:20:27.415
and paper, go back at the end at night, very frustrated,

452
00:20:27.525 --> 00:20:30.695
hundred pages in the wash, papers in the wash basket,

453
00:20:31.115 --> 00:20:35.195
all these now students come even in our office,

454
00:20:35.365 --> 00:20:38.075
fancy computer in front of them, they start coding,

455
00:20:38.585 --> 00:20:40.955
they submit a job and they get a result.

456
00:20:42.295 --> 00:20:47.075
So statistical mechanics has been completely redefined

457
00:20:47.425 --> 00:20:49.405
and dis born because of computers.

458
00:20:49.425 --> 00:20:51.445
And there, there are two kinds of simulation we do.

459
00:20:51.745 --> 00:20:55.365
One is Montecarlo, which is very much like your,

460
00:20:55.645 --> 00:20:57.445
I I talked about the postulate.

461
00:20:57.905 --> 00:21:00.685
You know, time average ensemble average is ensembles.

462
00:21:00.685 --> 00:21:01.685
That's what Montecarlo is.

463
00:21:01.945 --> 00:21:04.005
And time average is molecular dynamics.

464
00:21:04.105 --> 00:21:08.115
So two postulation stress mechanics are done

465
00:21:08.115 --> 00:21:09.155
by two different branches.

466
00:21:09.175 --> 00:21:10.795
Now, many other techniques have been developed.

467
00:21:10.795 --> 00:21:13.515
It's just wonderful because of computer simulations.

468
00:21:13.515 --> 00:21:17.235
We can do water now just, we are doing water dyl,

469
00:21:17.235 --> 00:21:18.795
sulf oxide binder mixture.

470
00:21:19.295 --> 00:21:21.115
In my book, I have two chapters,

471
00:21:21.735 --> 00:21:24.595
and again, one of the reason I wanted to write the book,

472
00:21:24.715 --> 00:21:27.515
there are certain things like minimum image convention,

473
00:21:27.515 --> 00:21:28.875
periodic boundary condition.

474
00:21:29.395 --> 00:21:32.675
I thought book conventional books do it very complicated.

475
00:21:32.835 --> 00:21:35.355
I did it very simply by using a simple model

476
00:21:35.355 --> 00:21:36.515
of physics equalizing model.

477
00:21:37.545 --> 00:21:39.605
So I, and they students love it.

478
00:21:39.605 --> 00:21:40.645
It is not taught everywhere.

479
00:21:40.865 --> 00:21:43.845
The, the, that the way in India, this, I think it is being,

480
00:21:44.265 --> 00:21:46.765
the book is being used in University of Chicago extensively,

481
00:21:47.005 --> 00:21:48.485
MIT and several other places.

482
00:21:49.475 --> 00:21:52.365
Important thing when I was writing that, I wanted

483
00:21:52.365 --> 00:21:53.565
to make it simple.

484
00:21:53.715 --> 00:21:55.885
Many, many new simple calculations I did,

485
00:21:55.935 --> 00:21:58.845
which I put it in the book, like you're talking of

486
00:21:59.395 --> 00:22:02.915
dynamic gas, there's no good book.

487
00:22:02.975 --> 00:22:07.725
Uh, word describes rotational entropy of water, for example,

488
00:22:07.725 --> 00:22:10.925
which is try tri anti molecule or ammonia.

489
00:22:12.065 --> 00:22:15.905
I calculated them. The real number of,

490
00:22:16.225 --> 00:22:18.745
rotational entropy and vibrational entropy

491
00:22:18.745 --> 00:22:20.825
of these molecules are in my book.

492
00:22:21.015 --> 00:22:23.425
That was one of the reason I wanted to put as much

493
00:22:23.425 --> 00:22:26.065
as possible that the students can do those problems.

494
00:22:26.945 --> 00:22:28.825
I already wrote a book, just came out

495
00:22:29.405 --> 00:22:31.385
is non-equilibrium Statistical Mechanics

496
00:22:31.475 --> 00:22:33.905
after being the equivalent Statistical mechanics.

497
00:22:34.815 --> 00:22:36.185
What do we do day to day life?

498
00:22:36.375 --> 00:22:39.905
More these days more about time dependence properties, like

499
00:22:40.065 --> 00:22:43.025
how to calculate viscosity, how long it takes

500
00:22:43.085 --> 00:22:44.185
for a protein to fold.

501
00:22:45.125 --> 00:22:49.945
And now if you smoke you in your, in your, in your,

502
00:22:50.425 --> 00:22:53.785
DNA it, there is a a, a nucleic acid's called guin

503
00:22:53.895 --> 00:22:54.945
that become also going,

504
00:22:55.845 --> 00:22:58.625
and that is, sometime we call mutation.

505
00:22:59.065 --> 00:23:01.385
Sometime we call damage because when you smoke,

506
00:23:01.435 --> 00:23:03.945
there is a reactive oxygen species.

507
00:23:04.245 --> 00:23:07.965
The oxid is born into gon that's bad for you

508
00:23:07.965 --> 00:23:09.285
because then a whole thing is,

509
00:23:09.785 --> 00:23:12.085
but why just smoking a few cigarette?

510
00:23:12.145 --> 00:23:13.605
People just continue to leave.

511
00:23:13.605 --> 00:23:16.245
You know, if you one or person or less gets cancer

512
00:23:16.345 --> 00:23:17.405
or anything that,

513
00:23:17.525 --> 00:23:20.405
because in our body there's inbuilt mechanism, there's a,

514
00:23:20.405 --> 00:23:25.205
there's an enzyme called hog one that goes along the,

515
00:23:25.265 --> 00:23:28.645
DNA finds the OxyGo converted back

516
00:23:28.645 --> 00:23:30.645
to guin, this repair.

517
00:23:31.025 --> 00:23:33.205
Uh, you have heard of DNA repair mechanism.

518
00:23:34.045 --> 00:23:36.285
DNA repair is continuously going in your body

519
00:23:36.765 --> 00:23:38.205
continuously right now.

520
00:23:38.825 --> 00:23:41.485
And this thing is a dynamical process.

521
00:23:42.475 --> 00:23:47.285
Then in order for, expression mRNA going to,

522
00:23:47.585 --> 00:23:49.125
our rib nucleus

523
00:23:49.125 --> 00:23:52.405
and getting the, TRN all these things, DNA must open

524
00:23:53.305 --> 00:23:57.115
that we call DNA bubble formation or DNA unwrapped.

525
00:23:57.415 --> 00:24:00.795
Uh, these are dynamical process. So biology is dynamics.

526
00:24:01.335 --> 00:24:02.915
You know, we, I'm talking right now

527
00:24:02.975 --> 00:24:04.795
to you, you are listening.

528
00:24:05.065 --> 00:24:06.115
This is all dynamics.

529
00:24:06.115 --> 00:24:07.515
You know, we are, we are consuming energy.

530
00:24:09.215 --> 00:24:12.315
So equilibrium economics took us very far, even continuing

531
00:24:12.315 --> 00:24:15.195
to work and giving us many answers, you know,

532
00:24:15.695 --> 00:24:18.675
but also we need to do the dynamical process.

533
00:24:19.505 --> 00:24:23.115
Just try to understand how things happen, why they happen.

534
00:24:23.575 --> 00:24:26.315
EBR of stat Mac o often tell you why it happens,

535
00:24:26.735 --> 00:24:28.435
but it does not tell you how it happens.

536
00:24:29.335 --> 00:24:31.355
How it happens is given by non-equilibrium

537
00:24:31.355 --> 00:24:32.995
or time statistical mechanics.

538
00:24:33.815 --> 00:24:36.715
So this is something which is now increasingly people are

539
00:24:36.715 --> 00:24:37.875
working, and that's where I wrote the book,

540
00:24:37.875 --> 00:24:41.915
who just came out, the, a month or two ago.

541
00:24:41.915 --> 00:24:44.435
And, that could have been much bigger booking in.

542
00:24:45.405 --> 00:24:48.785
But I think that more and more students will work

543
00:24:48.845 --> 00:24:50.825
and should work on biological processes.

544
00:24:51.605 --> 00:24:55.065
And, physicists usually find it little difficult

545
00:24:55.245 --> 00:24:57.825
or they kind of model it going to active matter.

546
00:24:57.825 --> 00:24:59.025
And those things which are nice,

547
00:24:59.645 --> 00:25:02.025
but they don't, don't really address the real,

548
00:25:02.055 --> 00:25:04.145
because real problems are really difficult.

549
00:25:04.615 --> 00:25:06.385
What is going on in a cell?

550
00:25:07.165 --> 00:25:09.905
How cytoplasm has all these dynamical processes,

551
00:25:10.445 --> 00:25:13.905
how things are, transported from your cell membrane

552
00:25:14.095 --> 00:25:15.305
outside to inside.

553
00:25:15.765 --> 00:25:17.985
Lot of people are doing a lot of work on that.

554
00:25:18.245 --> 00:25:21.025
You know, in chromosome, these are the active areas

555
00:25:21.045 --> 00:25:23.305
of research, which are all done by social mechanics,

556
00:25:23.765 --> 00:25:24.905
all by social mechanics.

557
00:25:24.905 --> 00:25:26.865
Without testing mechanics, it cannot do anything.

558
00:25:27.725 --> 00:25:31.845
And social mechanics with the computer is the one

559
00:25:31.845 --> 00:25:33.245
that is being used and is the future

560
00:25:34.225 --> 00:25:36.925
and dynamical processes understanding our own life

561
00:25:37.065 --> 00:25:41.005
and our own, diseases, like cancer.

562
00:25:41.225 --> 00:25:44.405
Now, people think that, okay, was Linus Sping correct

563
00:25:44.555 --> 00:25:46.245
that vitamin cures cancer?

564
00:25:46.625 --> 00:25:47.685
He knew what, he knew

565
00:25:47.685 --> 00:25:51.285
that we didn't know the grade Linus spouting what more

566
00:25:51.285 --> 00:25:54.565
and more people think, okay, vitamin C probably could,

567
00:25:54.655 --> 00:25:58.765
block certain receptors and then, it slow on cancer.

568
00:25:59.275 --> 00:26:00.565
Okay? So

569
00:26:00.805 --> 00:26:03.005
whenever you think of, okay, those who take metformin

570
00:26:03.005 --> 00:26:06.245
because of diabetes, they seem to don't get prostate cancer.

571
00:26:06.665 --> 00:26:09.845
Why? Because it seems like the metformin goes

572
00:26:09.845 --> 00:26:12.545
and sits on, those receptors.

573
00:26:12.775 --> 00:26:15.425
Then the, then what, when you block a receptor,

574
00:26:15.935 --> 00:26:17.505
meta matter cannot go inside

575
00:26:18.165 --> 00:26:19.905
and your cancer cell cannot grow.

576
00:26:21.265 --> 00:26:24.685
So these are just beautiful, beautiful problems left,

577
00:26:24.705 --> 00:26:27.285
and I, I, I really wish students do more and more

578
00:26:27.425 --> 00:26:29.245
and they can do anything they want all other things,

579
00:26:29.265 --> 00:26:32.245
but this beautiful subject should be, should,

580
00:26:32.345 --> 00:26:33.925
should actually be pursued.

Quick Answers

Journey of Teaching Statistical Mechanics

00:00:00 - When I, came back from, I did PhD at Brown, then I was in University of Chicago and started teaching Stat Mac, which was not very popular in chemistry and biology those days. And I found there's a book which I can teach from, from the subjects and topics that I wanted to teach. There are lots of books, which are from 1960s and seventies, but the tremendous development has taken place in, chemistry and biology. like for example, liquids.
00:00:34 - They all developed in seventies and eighties with computer simulations and biology, for example, understanding protein proteins, protein folding. So the things that I wanted to start cover in a book, in a course was not simply not there. So I had a lot of difficulty and I started making a lot of notes. And my students, there are some good students who started typing it. So, it, it actually, I have four books now,
00:01:05 - that actually was conceived but got delayed. it's a big book because it's 600 pages. It probably even, we took out some chapters because it was getting too big. And I believe that in your course you should teach some life skill, you know, in the sense that things that students can take to their work that was not there in the books. You know, there are a lot of complicated books, sophisticated books, but I thought there is no book. And this book has become quite popular, actually, at least in India.
00:01:37 - which I'm very proud of because yeah, I was, you know, you, you always write a book for your own students, right? You know, that means, so it was though you this concept of, think globally, but act locally. I have a chapter in the book which tells why study statistical mechanics, you know, like the very first chapter or in the pre phase. Great deal. I went into it. so look, if I want to understand, a, a, a glass of water is properties to want to predict.
00:02:06 - Water is same almost everywhere. Okay? Wherever you go. Okay, forces changing. Many other things are changing. So the session mechanics has two things. One is statistics and is mechanics. why we need statistics, mechanics, and Newton's laws of motions should have what? But no, in this glass of water, I gave you the example, the zillions and zillions and zillions of water molecules. And they're very strongly interacting with each other. We cannot solve neutrons, laws of motion, neutrons, laws
00:02:41 - And we solve all these equations together. Even if you pass, you won't be able to solve. It'll take you millennium, but a billion years. But even if you saw what you do with all the data, it's just not, useful at all. So in the, this approach was, adopted in a limited way by a great German physicist called Luman. and who was motivated by Maxwell in the, our pre British, physicist story

Foundations of Statistical Mechanics and Entropy

00:03:14 - Now, Bolman tried to really go by way, almost neutral loss of tion, but he converted into priority. Now, as I said, statist on mechanics is two things. Static mechanics and priority mechanics is neutral. Loss of motion. We understand and we see that you cannot do it. But then Boman realized that one way to go will be introduced concept, priority theory. He was heavily criticized and he committed suicide, and, but he could not do it all the way
00:03:44 - which, you know, didn't work though. He got quite too far. He introduced the mechanical microscopic definition of entropy on the other side of the Atlantic. another great, great brain instance called the, possibly the greatest brain of that century was Willard Gibbs at Yale University. He, he was very close to Maxwell, and he was following a failure of ulman. So he now realized that that approach will not work. So he invented a completely new approach
00:04:16 - The most brilliant hypothesis with the concept concept of ensemble. He said, look, this glass of water, I give you an example, has the same property everywhere, but the molecules are all moving. So they are all in different states. We call microscopic states. All have different orientation, position momentum are different. So it's all my glass, glass of water that you have in front of me and I have in front of me. They're almost the same. Property molecules are all indifferent. He then conceived that.
00:04:47 - high dimensional space where each coordinate for each molecule, so in a number of particles, there is a six n number of degrees of freedom. In that space, which is called face space. My system is described by point, and my evolution then moves from one trajectory. Just like in three dimension space, we see a water molecules falling in the river, this face space, which mental construction, all a particle moves. Then he realized, okay,
00:05:20 - again, zillions, of zillions, of zillions of mental replica, then each replica will have a different micro state. But at constant energy, they have the same probability. So then any concept introduce the concept of the probability, and it concept many, very many things followed from. So if a student wants to remember, anybody wants to, then these two names Mann and Willard Gibbs, they're the fathers of statistical mechanics.
00:05:52 - But in real world, we do time averaging. When you measure the property of a glass of water, you are doing a time averaging. You have one glass of water. I have one glass of water. But we are saying that I can have different ensembles. But in mental replica, where each system in a different microscopic states, those two must be equal. And those two equal means the is called equal, time average. Your averaging and the ensemble average, they have to equal,

Understanding Statistical Mechanics and Density Functions

00:06:19 - Second, my system must my mental replicas, billions and billions of them, they must be equally probable. I don't know anything about them. They have constant energy, same micro, same microscopic state. They're equal probable, that is called equally probable, probably. So these are the two posterous ational mechanics, and they're connected by another beautiful concept. According hypothesis will not go into it. That's a huge branch of physics and, mathematics. Now, once I now want to describe the motion
00:06:54 - same dimensional, I I have one point, but I have many systems, then I'll have a density, density of, these systems, which like a swar of bee, you know, which are moving or water in a river. They're flowing, but flowing in that space. So I need an equation to describe the flow. If I have an equation like neutrons equation to describe the flow of density, density of particles,
00:07:25 - in, in, in, in, in, in, in, in, kind of business. I can, I can start describing properties, how systems change. And that is what the global equation gives you. It's a density function. It's a direct generalization of you can say hydrodynamic equations. There are equations like equation continued Ethereum, conservation of mass. See, very standard concepts of hydrodynamics and classical mechanics are used to derive equation
00:07:56 - but density function in a face space, it sometimes puts the students off, but is a very simple thing based on same concept that conservation of particles. You cannot conservation systems here, you cannot create or destroy system. And so it just, follows from that. And it describes your motion of system in a face space. In my book, the chapter, I think, immediately after the postulates, the chapter comes as you have seen, the, these, ideal gas law.
00:08:30 - and, this European and British scientists, because it was seen that the pressure and volume of a system, they have very close relation with each other. Molecules then did not. They, they, they, they, they had molecules, but they did not know how to in describe interaction between them. But our, our systems that determine very interactions. So first thing they did, the simplest System is ideal gas law,
00:09:00 - they don't interact with each other. They're phantom particles. They pass through each other without any, eh, but they interact with the wall and they recoil. That's Maxwell, a recoil, and you get a pressure. So one could derive that pressure, and they found that pressure is invar al to volume and pressure is al to temperature. And that combined by giving, by using just simple variation

Exploring Monoatomic and Diatomic Gas Properties

00:09:31 - Now, very fast, we did the, like we just in the air, let's say we have only oxygen or we have only nitrogen. That's the one component system, but that is diet. But we have argon. We much later, could explain, do it, explain with the argon. That's a mono. Monoatomic means a molecule has one atto, okay? Like argon diatomic means it has two atoms,
00:09:59 - Their properties differ. So fast modules that scientists developed was doing testing or mechanics or ideal gas or monoatomic that can be easily worked out. They don't interact with each other. They're simple. I can go from level equation to a concept called partition function, and I can evaluate this pressure for completely microscopic things. But you know, when you being dynamics, there's a rotation, molecules rotate and they ate it. Sphere doesn't rotate because, well, it rotate doesn't matter.
00:10:31 - and it vibrates that those degrees of freedom, we call them degrees of freedom, need to be taken into account. And they were done in these, fashion by introducing certain models that they took bonds held together by spring, and they rotate like a rigid body. We all, all these things were known in classical mechanics. You know, if you take any book of classical mechanics, you will have harmonic vibrations, you know, and it will have the rigid rotator. So those things were now taken into size mechanics
00:11:03 - energy function, Hamiltonian, and then one grinds. The thing is a very straightforward and very simple, and I just take one, second to tell you one thing, one of the reason of writing the book when I was teaching, I thought they, there is certain lack of coherence. Students really need to know why they're studying what, and there should be a flow. So I tried to create that flow. In this, in this book.
00:11:35 - after, when you're doing gas, ideal gas law, mono di they don't, they don't interact with each other and they don't undergo any face change. But, you know, real world raindrops form and fall on our head. Then we, liquid crystalizes, all these things are face changed. They're only present, all the time. acid becoming liquid, liquid and boil water becoming gas. But how do we, describe these things?
00:12:09 - It does not undergo in phase transition because in order to undergo face transition, they must interact, like in order to formulate, in, in, in raindrops on the upper atmosphere, molecules must stick with each other and molecules will stick with each other. They lose entropy. We, we come back to entropy a little bit more. You aspir, I forgot. Now entropy means molecules are moving around. Now that translational entropy,

Understanding Entropy and Phase Transitions

00:12:37 - Entropy is nothing but degrees of freedom. But when they come together, they lose the degrees of freedom. But why they'll do that, they'll do because they like each other. There's an attractive interaction between them and that attractive interaction make them call and that leads to face transition. But, and this is not the Skype idea and all this is, discipline that discuss face transition is testing on mechanics. There's great pieces like Landau and other people who did the Einstein is beat.
00:13:12 - of statist mechanics. How does it form? It does not form itself. There's phenomenal nucleation, which is called embryo formation. Small has to stabilize against a droppy. Then that can grow. That is nucleation. Sometimes in a rock formation, in volcanic rock, we find the beautiful patterns when you suddenly, what the temperature a lo starts segregating and they form beautiful patterns. That's this spin competition. It's a non equilibrium phase transition.
00:13:44 - of size mechanics, you know, it is, it is, we call it a second pillar of theoretical physics and chemistry. Fastest quantum mechanics. Second is ational mechanics. Entropy is essentially, as I said, is a degrees of freedom. That means the, there are a very famous law by ulman. The entropy equal to ulman. Constant times log of number of degree, number of, of freedom. So entropy, essentially peoples a measure of disorder that's not perfect.
00:14:14 - of microscopic space that you have. Like if I want to go on, tossing a coin that I get, two sides, then I toss the many times the, a, a dice, a dai, then I get six side. So I know number of after end times, what are the number of possibilities all together from this sample space. And, and may entropy is the measure of the sample space.
00:14:44 - because we don't know where it'll be. All the states are equally probe, and if you have too much entropy, you cannot have face transition because face transition means order, face transition may go to crystal. Crystal is highly ordered thing, but it has entropy, very low entropy. So you have to remove the entropy by intermolecular potential. And that is, is, is, is, is is the fascinating subject. You know, now, as I was telling the, sixties
00:15:18 - or tremendous development of the concepts, that's one of the things I started teaching. I found that the, my stat Mac books do not have several topics which are considered advanced talks in theory of liquids, which is extremely difficult to do. one of the first theory of liquids and the idea that what liquidities was done by JD Burnell, the famous, I think Oxford or Cambridge. Cambridge, I guess, who's also one of the father figure of Histography.

Exploring Liquid Theory Through Experimental Patterns

00:15:48 - He said, okay, I want to describe I liquid. What he did, he took a, a collection of marble balls and he put them in a jar and said, oil and type packed it, as many as he can put it. Then he put a paint, a black paint on top of that and let the paint go through. Now, after some time or after a day or two, he opened and he found out where, yeah,
00:16:19 - He took out and marked, the ball. He found that there's a beautiful pattern that emerges from the position of just speak to each other, coin the name radial distribution function, which is now later measured by neutron scattering. so this now, so the theory of liquids was begin now is extremely difficult thing. As I was saying, these are called interacting system. As I said, marble balls, which is a very good description, like point particle. Non interacting is ideal. L gas law, low density gas,
00:16:51 - One order of magnitude, two orders of magnitude, more density molecules are really hitting against each other. How do you do that? Then there was a, this cell theory said, okay, let me then consider liquid as a solid. What is so unique out solid. I can give a cell a volume element to each attom because it is sitting there, right? So the concept of li crystalline or solid state was brought to liquids, basically motivated by.
00:17:23 - into different cells. But however, unlike crystal, where the particle cannot move from OO one, cell to another cell in liquid, no, they diffuse. It has an non zero diffusion constant. So it goes from one cell to another cell. That particle goes to another place because there is something called free volume is there, the volume access, what that crystal and that redistributed
00:17:52 - there are degrees of freedom available. So it, so and so, cell theory is essentially, you can say solid like theory for liquids because of the high density that allows, but allows particles to move and because particles can move if they have an entropy. That is called communal entropy. Certainly wonderful questions. I keep saying that. Theories of statistical mechanics, really developed very fast, sixties, seventies, eighties,
00:18:23 - So all these beautiful theories of Mann, Willard, GI and many other people, they, we, we had them in paper. We could hardly do it. We could do it only for, a little bit low density and with, with just spherical atoms. But we couldn't do water the system we wanted to do. We couldn't do protein that we wanted to do. We couldn't do DNA, we couldn't do protein Indian interaction. We couldn't do enzymes, you know, but we, because we, we had the principles.

Advancements in Statistical Mechanics Through Simulation

00:18:55 - how molecules interact with each other, how they talk with each other. If you give me that, which we quantum mechanics can give us, then in principle, test mechanics should give me all the answers. But it, it cannot because we cannot solve those equations. As I told you, even computer cannot do that in the, in, in, in theory. But then people did something very clever when the computers came say, okay, I cannot solve thousand of millions of million, but I can solve hundreds. So fast simulation was done by bar Alder and Rosen be
00:19:28 - And lo and behold, even 32 particles of hot sphere, square face transition, that was a amazing excitement in 19, late fifties. And so computer simulation opened the completely new thing. so now we started to put in, that's why the Nobel Prize of Levy and, Martin car Plus, we, we can do the reactions. The single molecule spectroscopy got Nobel Prize. All the Nobel prizes that went into chemistry and medicine in last few years were all motivated.
00:19:58 - when you got the Nobel Prize. So there is a silent guy in the, in the room, and that's the computer. Without this computer, we could not have done anything. So computer open session mechanics. Now, I can tell you one thing. The students, these days, we used to be pen and paper. We used to probably do a hundred page of calculations a day. We come in the morning, start to have cup of coffee and start pushing pencil and paper, go back at the end at night, very frustrated,
00:20:31 - all these now students come even in our office, fancy computer in front of them, they start coding, they submit a job and they get a result. So statistical mechanics has been completely redefined and dis born because of computers. And there, there are two kinds of simulation we do. One is Montecarlo, which is very much like your, I I talked about the postulate.
00:21:00 - That's what Montecarlo is. And time average is molecular dynamics. So two postulation stress mechanics are done by two different branches. Now, many other techniques have been developed. It's just wonderful because of computer simulations. We can do water now just, we are doing water dyl, sulf oxide binder mixture. In my book, I have two chapters, and again, one of the reason I wanted to write the book, there are certain things like minimum image convention, periodic boundary condition.
00:21:32 - I did it very simply by using a simple model of physics equalizing model. So I, and they students love it. It is not taught everywhere. The, the, that the way in India, this, I think it is being, the book is being used in University of Chicago extensively, MIT and several other places. Important thing when I was writing that, I wanted to make it simple. Many, many new simple calculations I did, which I put it in the book, like you're talking of

Understanding Entropy and Biological Processes

00:22:02 - word describes rotational entropy of water, for example, which is try tri anti molecule or ammonia. I calculated them. The real number of, rotational entropy and vibrational entropy of these molecules are in my book. That was one of the reason I wanted to put as much as possible that the students can do those problems. I already wrote a book, just came out
00:22:31 - after being the equivalent Statistical mechanics. What do we do day to day life? More these days more about time dependence properties, like how to calculate viscosity, how long it takes for a protein to fold. And now if you smoke you in your, in your, in your, DNA it, there is a a, a nucleic acid's called guin that become also going, and that is, sometime we call mutation. Sometime we call damage because when you smoke,
00:23:04 - The oxid is born into gon that's bad for you because then a whole thing is, but why just smoking a few cigarette? People just continue to leave. You know, if you one or person or less gets cancer or anything that, because in our body there's inbuilt mechanism, there's a, there's an enzyme called hog one that goes along the, DNA finds the OxyGo converted back to guin, this repair. you have heard of DNA repair mechanism.
00:23:36 - continuously right now. And this thing is a dynamical process. Then in order for, expression mRNA going to, our rib nucleus and getting the, TRN all these things, DNA must open that we call DNA bubble formation or DNA unwrapped. these are dynamical process. So biology is dynamics. You know, we, I'm talking right now to you, you are listening.
00:24:06 - You know, we are, we are consuming energy. So equilibrium economics took us very far, even continuing to work and giving us many answers, you know, but also we need to do the dynamical process. Just try to understand how things happen, why they happen. EBR of stat Mac o often tell you why it happens, but it does not tell you how it happens. How it happens is given by non-equilibrium or time statistical mechanics. So this is something which is now increasingly people are
00:24:37 - who just came out, the, a month or two ago. And, that could have been much bigger booking in. But I think that more and more students will work and should work on biological processes. And, physicists usually find it little difficult or they kind of model it going to active matter. And those things which are nice, but they don't, don't really address the real, because real problems are really difficult. What is going on in a cell?

Transport Mechanisms and Disease Research Advances

00:25:10 - how things are, transported from your cell membrane outside to inside. Lot of people are doing a lot of work on that. You know, in chromosome, these are the active areas of research, which are all done by social mechanics, all by social mechanics. Without testing mechanics, it cannot do anything. And social mechanics with the computer is the one that is being used and is the future and dynamical processes understanding our own life and our own, diseases, like cancer.
00:25:44 - that vitamin cures cancer? He knew what, he knew that we didn't know the grade Linus spouting what more and more people think, okay, vitamin C probably could, block certain receptors and then, it slow on cancer. Okay? So whenever you think of, okay, those who take metformin because of diabetes, they seem to don't get prostate cancer. Why? Because it seems like the metformin goes and sits on, those receptors.
00:26:32 - meta matter cannot go inside and your cancer cell cannot grow. So these are just beautiful, beautiful problems left, and I, I, I really wish students do more and more and they can do anything they want all other things, but this beautiful subject should be, should, should actually be pursued.

Faculti AI can make mistakes

Research

Policy

Analysis

Data

Originals

Explainers

Podcasts