First of all let me say thanks again and
but more to the point is that.
You know giving a talk on this topic here
Virginia Tech is like bringing coal to
Newcastle now for some of you you may not
know what cold it is let alone Newcastle.
So I should change that to it's
like being peaches to Georgia.
And the reason is that there are lots
of experts here on this fear.
You know the kids so on and so
I hope I have something to tell you
that you don't know in any case it's
it's it's a kind of a personal perspective
not equilibrium it's an extremely
large feel and even if you might
know your grandfather a lot you may
not have seen certain aspects so I hope
this would bring you something new and
he went the other thing is that this talk
is prepared with students in mind so
there are lots of simple things that
there are lots of pictures and so on and
so they experience in the audience if you
want to ask me about something a little
bit more please do so afterwards students
please feel free to ask OK All right.
All right so let me give you the outline
first of all what is normally
clear in statistical mechanics and I
already told you that there are many many
ways to look at this I'm going to
give you a personal perspective so
is my version of it and then one is Why do
you want to study this funny subject and
then answer it from curiosity
driven to dollar driven research.
And finally I'll tell you a little
bit about what is being done at
various places.
I will state is because I'm in the feel
good cycle there as well anyways so
there are the rides your problems and so
on and so forth but I want to thank my.
Longtime collaborator and friend
the other one who has gone to become dean
at our state and that's part of the reason
for that I would hate business and
plus many many people around the world so
here we go.
So instead of learning programs that make
let me begin with physics which I hope
you all know and this is my view of
the spectrum of physics then one end
is static switch is boring and doable on
the early dynamics which is exciting and
doable is a color code here everything
there is purple is equilibrium or
start Hades or whatever and red or
green tend to be the other then so
faced with a spectrum is a good fit is
what do you do while you start with
the doable and you sneak a little bit
off and you try to do something here and
there is what I call steady states and
what our stage States periodic
question periodic understandable chaos now
in the year physics is a big field here
in any case the whole point is that
this is interesting and doable OK So
let me give you some examples of the
things that you know classical mechanics
that's pretty boring there's nothing
to do in fact on the other hand the for
all dynamics if you tell
me what the forces are and
you want me to tell you
what except he is even
though there is every cause there
may it's not particularly easy.
Now on the other hand you can switch.
Off a little bit of steady state and
periodic States once you periodic States
and so on there's lots of that go
on to you and them Electra statics
graduate students you agree this is
neither interesting nor doable correct.
Sure your professors with disagree and
say yes is doable and
I would give you the right
grading on the other hand.
I guess here we use your book Andy.
But there in my days we all
grew up with Jackson and.
And in chapter seventeen Jackson tells
you how undoable for you and them and.
You may or may not remember so
given this what do you do where you sneak
off a little bit you dooming you do static
you do E.C. you do power generation and
all of modern technology is played on
the right so it's sitting over here so
in this context I put equilibrium is that
Mike over there and you expect me to put
no one equilibrium state like over here
right no I'm not going to put that.
So let me give you some pictures I like
to illustrate with some pictures and
so equilibrium here is what appears
to be a very peaceful scene and
what you think it's equilibrium and
so on so forth but
no almost everything that you see is known
equilibrium for example the sun over there
makes this beautiful sunset you would
agree that it's not in equilibrium and
the house for example would fall down and
so on what might be in this picture is
equilibrium is a speed of thirty boring
water right that might be equilibrium
so it may look boring but
is far from trivial So
let me illustrate I understand
that you don't use this book but
some people use this book for
teaching sat next that states a matter.
Do you know where then they are here you
know and so you know what I'm about to say
so this comes from of course Google and
you can tap forwards and backwards so
I will show you the introduction so
paragraph one point one The very first
thing the most man who spent much of
his life studying statistical mechanics
died in one thousand nine
hundred six by his own hand.
Horn carrying on the work similar
to the even like him forty.
Now if you're our to thank you OK.
The first paragraph of this book is so
wonderful but you should go get it.
So you know that I left a space for
the beginning of the next paragraph
perhaps you would be wise to approach.
If you get if you fail you will
stand my course you can just think
about poor Boltzmann and beer and
friends then you both feel so bad so
this is what I mean by it may look boring
but equilibrium is highly nontrivial
So that was equilibrium stand there so
here's feel some theory.
And the word is.
You have no idea how to describe any
of the things in here you are trying
to survive and by the way this is not.
A professor is this is
a graduate student and
so thought professor is
sitting in the lab telling you
turn right turn left turn right turn left
so you are sort of scared to live there.
That is what is meant by fearsome fury So
what I'm about to tell you about in this
colloquy is when we sneak off a little
bit from the thought I live in studies.
So here's a picture of Monica again most
of the interesting you see is not
equilibrium this is my wife actually and
we are in a canoe and you can see
that we're trying to go somewhere and
then only problem is the state
it's just this little ripple right
you know very well there is soon as
I stop paddling it will go away and
dad on the other hand is very interesting
phenomenon sitting right there so
this is an example of not equilibrium
stench so what distinguished
equilibrium from not equilibrium when
steady state the word steady state means
time independent people to be you
know if you change the time scale in
which you look at the time scale but very
time to you look at it it looks a thing so
what distinguishes remember
now purple is equilibrium so
we start with equilibrium
the fundamental hypothesis to
say that the probability of
finding each configuration on.
All the same for an isolated system
that's where you start it so
pictorially are drawn they call a system
completely surprised around it and
the probability is just proportional to
this delta function because as long as
the configuration of the right energy it's
all equal outside there's nothing and
from this very simple hypothesis you get
to a viable definition of temperature
Have you ever thought about when you are
in high school you start to learn about
energy and momentum and philosophy and
all the stuff you say what is hot in coal
you go in the shower in the morning it's
hot or cold What's this hot and cold have
to do with energy momentum and so on and
so forth it was modern No one question.
Both men came along and give you a viable
definition and then you can bend our
couple this system that you want to
a bath at a particular temperature and
now because the energy is no longer
conserved they can exchange energy and
now you see that the probability
distribution is given by the famous
sportsman factor where the temperature
answers to this key and
want to be cheap so now you know
something about these two guides and
that's what you learn when
you go to a course and
that statistical mechanics and
be able thing you learn is that it led to
this highly this successful description
of system inter-modal Librium but
the whole point is that there is no two
hundred pounders anywhere everything is
stationary the only thing you are asked to
do is to calculate average or you already
given this guy how do you calculate
averages for example what is the average
energy system you would take the
Hamiltonian try to calculate this object.
Notice there is no trace of time
anywhere in the SO description.
So if you insist on imposing a dynamics so
instead of just having P.
of C.
you one out of C.
then how do you get back
to dis picture and.
The simplest way to get there is to
use the master equation and then on.
And you have to obey detailed balance so
what the hell with detail power this
outcome and tell you about that
in a minute so first of all
I'll tell you about the month equation
this is an incredibly simple equation OK
how those the probability of a system
in a configuration change with time
well it says well you could
start off somewhere else and
it comes in with some rate and
you could start at your place that C.
and you go I want some rate OK for
simplicity think of a system which
is discrete So the C's are just.
Think of a bunch of zeros and
ones and it's all discrete and
then these are just rig OK That
changes the system from C.
prime to see the way that I've written
it so here you can think of it this way
here's the configuration you specify rate
for coming in and you specify a rate for
going up so you can make sure
that you start from here and
this has a dynamic so you can think
of a water analogy every one of these
tubes is a configuration of
the height is the probability and
there are some pumps that pump
in from one to the other and
that's what these are they're just pump
water from one tube today mix than they
would be on the pumps they come in and
you want to specify these rates and you
have to specify these rates in some way to
make sure you're going to equilibrium but
before I get to equilibrium let me
point out to you that this thing inside
the packet carries a many meaning it
says what goes out in this is the amount
of water that comes in Think of it as
water this is the water that goes out
that's the water that comes in and so you
can think of this is a current instead of
water now this is probability so
is probability current and
this probability current
will play a role so.
Detail balance so when I was studying.
Learning about this to begin with.
The thing that I was told is that if
you're going to try to put this on
a computer and try to simulate the whole
thing then these rates are not or
they have some outrageous to add but you
make make sure they will be detail about
once and what is the job and you make
sure that the forward rate compared to
the backward rate going this way compare
that our way or the ratio is the spokesman
factor so if you swallow that it's
OK if you tell me so I'll do it.
And if you do that and you say I didn't
even ask why but at the time but
you see immediately why it's good because
you'd be use the state rates then
the stationary state namely the one in
which this is zero that's what you mean by
stationary zero if you plate rates that do
this then those rates would make sure that
the star which you mean to the stationary
state that's what the star stands for
will do because when you put it in
here they just cancel or you get zero.
So I was very happy.
However if you think a little bit about.
This while still probability current and
now you would make sure there
are about once a means in this
purple color stationary state
every single current is zero.
OK.
For every pair of C.N.C.
prime What does that remind you of that's
a live remind you of this boring subject
course electrostatics there are no
currents anywhere OK All right so
we're reading what if you now we have good
graduate student say have another one and
do what you tell me did they were
going to finally be twelve hours so
I was you know would the world live up.
Well it turns out that the stationary
States there exists I won't bore you
about the mathematics but
it says that if you store and.
Fisher and state and they may.
In fact a unique of a circuit but
never mind the point is that
under those when you violated your
balance the net currency would be
independent because the stationary
state is in time independent but
now they don't have to be zero so
if they're not zero and
you are in stationary then the current
special form curve looks right
because they tell otherwise they
would build up somewhere and
deplete somewhere the height of the water
is all the same though they don't do
currently that should remind you of
meter statics current the spring so
this is really the major distinction
is piece current which I call K.
star now it is a function
of true configuration so
there are many many more of these current
standard probabilities this is just
a function of one variable just going to
variables it's a very simple is what goes
on is what comes in and you would find
these currents and they are in general
not equal to zero so you can ask well do
they correspond to any physics are you
just talking mathematics and if so how do
you produce them answer first one is yes
of course otherwise I wouldn't be talking
to you dancer this second one is make sure
you get away from the conditions that
take you to equilibrium so for example
coupling to more than one energy reservoir
or coupling to one particle reservoir or
whatever your life do you remember that
picture that I drew at the beginning and
the canonical ensemble and
they're all the core answers zero So
what I'm telling you is now that you
should consider a system where you
take energy from one reservoir and
dump it into another reservoir and
then you can specify rate which does this
and in general it does not obey beach or
balance and then what happens is
that when you specify those rates
you have no idea what the story is and
you don't know what a story is in general
you make this reference because this is
the foremost solution as to what these.
Given the rates it's not particularly
useful I won't bore you with that so you
look at this thing and you say well why
should I look at a system like this and
here's a good example this is the second
largest equilibrium steady state
that affects your daily namely
the planet this is the one the spigots
which affects your daily right and
you get energy from the sun and you dump
energy out of that most fear like a friend
of mine likes to put it this reservoir is
sitting at five thousand Celsius this one
is sitting at three degrees Celsius and
you can think of it that way well that one
is a little bit too big How about you.
And what do you need to make sure that you
don't go away you better eat something and
you better spread it out otherwise
you're not going to do very well so
imagine putting yourself into this
situation how long would you last.
Answers.
How long would you live just imagine
putting yourself into an isolated chamber.
Come on seventy years now.
Few days right usually you
think a few days right so
because I drew that picture I thought
of eating I forgot about breathing.
So if you actually put your in there
you're lost maybe about three minutes.
I stop you from breathing and
stop you from breathing in or
out it's just three minutes so
that's the difference that's why
it's known equilibrium stage state is so
important when you're experiencing
one yourself so this is my personal
perspective of non equilibrium
steady state of any questions or
comments before E three of being else.
OK All right all right so why do we
studied it well the answer really given
your curiosity did all of the research I
don't know why it takes a little bit for
this to show up.
OK so the blue is curiosity
the red is dollars and
so curiosity driven from fun then
games now if you just do fun and games
your number then get funded through you
better say these are fundamental issues.
So through the other end
which is to talk about
well practical applications on term
implications and that's the reason for
the subtitle of the talk pure and
applied theoretical physics.
OK fun and games let me show you some fun
and games we all do with computers and
you know how to play computer games and
to me something very simple ones to
incredibly surprising unpredictable
results very good examples Conway's Game
of Life How many people know
Conway's Game of Life fantastic so
I don't have to warn you not ever to play
that game one week before your finals.
You get sucked in and you're done.
The point is that these computer games are
actually all the models that we work words
when we want to model something signal
stock market say epidemics say whatever.
You you want the.
Population dynamics and so
on you write some models and
they're actually computer games or they go
on to real life games they're also simple
very surprising and predictable I'll give
you two Example one is Paul's kitchen and
the other one is just boss
boys kitchen has to do with
Thomas spore who is a grandson of the old
here he is the University of Denmark and
you remember that picture what do you do
in the kitchen that reminds you of this
washing dishes right you pour
dish water into the dish and
the water then goes into the sink all
right why is this interesting wow
because when you pour water
into this case now and dish but
I think typically when the water is fast
enough you will make a hydraulic jump like
this you force in this way or parts of
the boys because they don't wash dishes
correctly or
maybe just stick it in the washer so
this is a paper and
tired of creating corners and
kitchen things published in Nature
not a cheap Journal one thousand nine
hundred eight not a long time ago
you pour water onto a plate that is
circular which had some legs and here
is the water that goes in and it makes
this beautiful hydraulic thing in because
you do it in the lab is nice and circular.
So why does it deserve a Nature
paper if you are just this high
powered the lips to different heights
need circles become polygons like that.
And Pentagon is not the only thing the
rest of the paper has octagons triangles
and even a geometrically
impossible to go on to some
known equilibrium is the states if I turn
off the faucet you know what happens and
all right let me go to something else this
is just fall back into of all landfill
what they did do they put a lot of
little steel balls tiny guys or layer
on aluminum plate like this where you get
the steel balls you go to bicycle shop and
buy some ball bearings and
you put they put a.
Loud speaker below it and driver were
different frequencies and amplitudes and
so on and typically of course you just get
a bunch of this is not a very good picture
but it's supposed to show lots of little
balls bouncing around just like what you
think is molecular chaos and so
on Bob It turns out that if you drive
a different AM to cheers and frequencies
a portion of the gas condenses on there is
falling like this you see is the piece
of earth falling it doesn't move at
all Meanwhile the outside is
coexisting with it bouncing around so
how the heck can this happen what is going
on is energy is going into the system and
energy is disappearing because of
the collisions and what have you and
due to that thing you find in a city state
that you don't get into a more equal
Librium this can condense things so
in fact this is the thing that got him
on I felt a person like that fellow here
for this for this non-equal instant.
Cast on that was just last year
anyway all of this fun and
games and let me talk about fundamental
issues because we can't just have fun and
games and so I don't understand why it's
time anyway so let me give you a lift
our one thing is that we don't know
how to compute these things can we
predict it somehow can we have processes
sizes somehow can guess it somehow so
that's an important thing so non-equal
been conditioned on means you tell
me the rules are games of life that's very
easy would I have predicted you know on.
Gliders and glider guns and
all those things and so on so
well here are these things you need are do
they have some of that memory limits and
that's what surprisingly because
some systems it depends on
where you take it to infinity this way
First all the way to infinity first and
gives you very different things and
so this was about you Matt geometry
dependent on a dynamic Are they equally
trances like detail balance and
so on and so forth we have some answers
to that and do we can we understand
the implications of a car loops and B.T.O.
balance violation are in
the electrodynamics when you talk about
the car loops and so on you eventually
have a gauge theory is their number line
gauge theory and so on and so forth and so
it keeps going on like this but
what is the fundamental concern is how
do these complex patterns emerge from
very simple rules for a few particles.
So I mean two hundred dollars given so
I don't know the students probably
don't know that every ten years there's
a committee in the National Academy
of Sciences on various types
of Sciences this one a solid state every
ten years they try to formulate what they
think are the important questions and
itself listen to it and so
this committee in twenty ten challengers
three years them has to do with
non-equal evince that night here's one of
them how do complex phenomenon from simple
ingredients just wonder why mention
what happens far from equilibrium and
why exactly exactly that
what is the physics of life
I think hope I have convinced you there
is no life in so most quickly program and
then the others have to do with something
that you're very strong and all and
then energy demands and
information technology so.
Interesting question what
would happen in three years
let's see what they come up with so.
The other is major funding agencies the
O.E. and they also have these committees
and they also come up with not six but
five challengers they're essentially
the same as the other one except that they
use more words they are control freaks.
And they drop life.
So there you are here's one of
them how the remarkable power
to emerge on the blah blah blah blah
blah blah blah blah blah blah but
it's basically the emergence one how do
we characterize and control you see this
where control control far from equilibrium
the other three have to do with Nano and
so on they drop Life All right so
practical applications where can you use
any understanding of known equilibrium
physics you can see that I'm start of with
something at the very very small level
go through atomic levels go through
our life you know our scales
up to global levels and
all the way to the Big Bang this
literally goes from zero to the yada.
Literally in the higher spectrum is
where you can apply all these things and
the two examples I gave one is
there weather which is here and
the other one is on all kinds
of things at the human scale so
I hope you have convinced your wife
you should study for the fact that
there is both fun and also money and
then he questions before I go on to next.
Now.
Out OK All right.
So what do we do so you see the blue
is the fun and games part and
then the red is we make noises about
how it would be applicable and
we used a range of methods and
this is a bunch of people that work with
me but this is really what we do OK.
Remember we're serious so we say that.
And we drink wine and we talk and so
on and so forth in very nice surroundings.
This is an institute in
Germany in Dresden so
are big more seriously simple models
like the large number of models that
we study is under the title
driven diffusive systems and so
what driven means is that driven is out
of equilibrium and diffuse it is a key
word that is associated with conservation
laws were to be energy or particle and so
on and so forth and that they where
the and now you can drive many things you
can drive a single species of particles
now would for example be the ising model
of for those who are not familiar
with ising model you have a lot is
like checkers you have a lattice and you
put particles on the various squares and
you move them around according to the
rules remember the rate that was telling
you about if you could prove put more than
one species different kinds of drives and
so on so for that many things you can
do the other thing is to now allow
get rid of the conservation law but
still allow diffusion and
birth death processes and now there
are many many types of things you can do.
In the interactions between the you these
guys they can live and they can die and
you can talk about population dynamics and
so on and so forth but let me
focus on this for the time being what I
mean by trivial if you use of systems and
give you some examples is to take
objects that is then dimensional and
give you some examples and
that indeed dimensional space so
protein synthesis I think there is a huge
biological physics component in this but
I haven't and you or I would already know
what protein synthesis is all about here
it's the picture I think all of you have
seen this picture before you take D.N.A.
you and the bed you get them are Nate and
the they are mine and
carries the genetic information for
making proteins ribosome comes along
get someone and goes and reads the.
And so the beat and the speed
eventually wraps up become approaching
what are proteins Well there
are important ones like hemoglobin and
if you don't have hemoglobin you're not
going to be able to have oxygen carrying
around are OK so
you better make those all the time and so
that's the idea of protein synthesis So
here's a microgram
of what it looks like there's
a standard picture of them on A and
they don't do it one at a time before
one finishes another one can start so
you can have a whole bunch of them on
the thing and it looks like traffic and
gets into traffic jams and
die you can imagine now I
can model this by looking at a lighter and
then I put particles in and
they move along and then they leave at
the end of it and so the apology is called
this process initiation how the ribosome
comes on and they go along and
this process is call you don't question
it refers to them to the protein that is
being made and terminations domination so
this mathematical ball though
comes under the fancy name of a totally
symmetric simple exclusion process
it's symmetric because the right
was I'm strong go backwards.
And simple exclusion instead Don't sit
on top of each other so that was it.
So let me show you when
that model was created so
they had created independently
by chemists Julian years.
In one hundred sixty eight sixty
nine this is actually Carroll and
they don't feel and he tries to
model model the whole situation
exactly and so
on I don't know why does that.
Then quite independently in one
hundred seventy there's a completely
different approach by mathematician and
they tried to prove theorems and
things like that is all he
tried to prove theorems and
this is the totally symmetric extrusion
process and the true actually.
We're not understood to have something
to do with each other until our good
ten fifteen years later and
we were asked to write a review in recent
years twenty eleven of how this model
is related to biological transport and
there's more than protein synthesis
that has many other things as well so
this is the example of a zero dimensional
object there just point particles
moving along a one dimensional space it's
now you can keep going there's a long
list here I won't go through all of
them let me just talk about polymers for
men sedimentation polymers
are one dimensional object and
under gravity they would come down slowly
being driven and how they land and
so on and so forth and how they come and
so and so forth is of some interest
maybe another thing that is of
interest here surface closed in
in that is sitting over
here now have these but.
You have a growing surface on the M.B.E.
that the surface itself
is moving right and so you want to
know how the surface moves and so
that's being driven and for
the experts in the audience K.P.C.
and so on so forth comes into this this
whole game you don't have to do just one
Osprey sheets you can go to
many more than one species.
This is a good example because
all of your drive course and
the previous example you should remind
you of a highway cost come in and
go out and now you can have cars
going in opposite directions and
they don't collide hopefully but if you
have some comping over here you know
if you have company on this plane you know
that we come to feel that Lane How many
of you have driven along places where
there is some accident here and
then all of this other lane
completely slows down interactions
of two species going in different
directions so where are they.
Applied Biology which are already
mentioned in engineering chemical
engineering in gas permeation that's
like gas moving through our porous
media how do they get impeded and
so on if you try to drive them
on traffic social networks you can talk
about opinions epidemics and phone so
forth all the way up to Joe logical
sciences are needless to say
the climate and so
on is it's a nonequivalent system and
here are the two symbols again that I mean
or I can't say that I've been using So
all right so that for
a lot of talk about what we do so
what have we learned so far from all
this working with simple models and
things like this and there are many
surprises which we didn't expect and then
there are things well they're expected so
let me talk about the surprises for us OK.
One of the first one that we ran
into is for iconic it is response
normally when you go to the wall when
you turn up the thermostat the energy in
this room goes up that's your normal
expectation in known equilibrium
systems that we play with it is very
frequent that you go to the wall and
you turn up a thermostat and
energy goes down.
And it keeps coming up
in surprise because we
would take systems in equilibrium
that we understand very well and
then instead of having one reservoir
with two reservoirs and when we turn up.
The control parameter and one of the.
Resin was the system response
in the opposite way and
that's something which you know we observe
we can understand where it would
come from but we don't have.
Really general overall understanding
in that sense OK you have it
anyway the way that it comes
about is sufficiently easy.
We published a paper in America is this
the teaching John also of your student
you can go and
read this this is perfectly readable.
Paper that you can try to understand
what negative responses about.
The other one is the lack
of a theory of law and
all of you know that if you
take equilibrium a system and
you bring in do it will be in with System
piece of there is no more exchange and B.
and C.
on the same state and you can bring a C.
together and there would be no more
Exchange where youth energy or particle or
whatever that's a fuel flow rate in
equilibrium would be be in equilibrium C.
means automatically is in equilibrium with
c This does not exist in an equilibrium so
far we have not found any universal way of
saying under what circumstances
if any where we know the serial
would occur so that's how bad if
there is no zero of existence of
new shows United States that's
the whole reason for doing not equal B.
instead named after all this is
the new stationary States you
haven't seen polygons before in
water have you them so they are this
one example how did they come about
the changes in the phase transitions you
could before surly becoming second order
second order become first can change your
mythology classes and all of those generic
long range interactions is also another
thing that it's important because one of
the things you learn about equilibrium
sent back is that if the interactions are
short range of I can only talk to you and
you can only talk to your neighbor and
so on so for
then the correlation of the rumor
dies exponential here it.
But in non equilibrium there
are many situations where
you have long range correlations despite
the fact that everything is local so
there's a whole long range or
many many many other things that we are.
Can.
Talk about being surprised OK at least we
can talk about something that we expected
on day.
Three expected one says that you know
I was drawing this picture where
the energy is flowing this way right
from one reservoir and so on you can
run the movie backwards because we don't
get energy from the outer atmospheres and
it goes into the sun so time reversal has
to be right here we should be able to find
time diverse to various After all that's
what car loops side goes one way and
not the other way so
this idea of having loops.
Things that go around a way
brings to the idea of
angular momentum after all if
something goes around that way
you know one of the first things you think
about is angular momentum or you could or
could physicists I'll tell you about what
anger management is about a little bit.
Right right away but
the whole idea of this probability and
a mantra is that there was
the probability fourteen says so
or to City is a very important
concept in in fluid dynamics and
what did these things do but they exist
and so on so let me just illustrate now so
first let me make a beat each will on this
stationary distribution and the current So
the idea is that if you you
look at the cool correlation or
covariance of let's say two quantities but
at different times these are.
Very bones that describe this system so
they can be exist in peace and
what have you over gases or
they can be where the where
the station is and so on and
so forth so you look at.
Correlations at different times but
you look at the empty symmetric part so
remember this thing is done in the.
Steady state so it doesn't depend on the
overall time but only on the difference so
this will be the same for cheap but
if you look at the empty symmetric part
then automatically it is going to be odd
in time so what do I mean by the end
what I mean if I draw a picture like this
so suppose the thing is two variables
first of all if it's only one variable
you can't have taken the symmetry for
that's pretty obvious so there's that
at least two variables there is of X.
component of Y.
component and if you look at each
trajectory it will look something like
that bouncing around over some average
point when you still cast a process
that's what you expect So what you can
do is to label two particular points.
And take the cross product
between those two vectors so
when you do that where you
are what you are doing is that you
are looking at the area span between
these two vectors one at one time and
one at a later time OK why do
you look at that wow if you
differentiate this thing respect to time
one then you are looking at Cross V.
When you differentiate this you get v and
are crossed we use that anger momentum.
OK And you remember from Kepler that
when talking about areas the band per
unit time is being a constant the negative
momentum conservation all the same so
this is the probability version
because this is not real space but
configuration space so we're looking
there and he symmetric thought of this
the angle man the real and
dimension message divided by tall and
take toy Cuisia OK but if you don't have
to do that you can look at the generic
point now when you look at the time lag
correlation like this remember I just
drew a picture of one of these parents and
you calculate the number and they
keep changing I think guys are bouncing
around the place when you look at them.
And not only can you study date
time average which is Davidge in
this quantity but you can study it in the
higher distribution are they very big that
they go around this way or that way at
any particular time how often do they go
this way versus stuff where and so on so
here is a schematic picture of what
I'm trying to tell you you go to the lab
you take God data on the blue X.'s and
the red wise as a function of time and
it would look something like this and
experimental The should be
happy with this picture because
they never look like a constant and
always trickles around like crazy and
so you take that thing and
you plot it in the X.
Y.
would bounce around like that and
now you can take that histogram
of the thetan point he said or
point and
you would get the problem the stationary
distribution assuming that you're sitting
in the stationary state already so
in the lab that's how you can find peace
star in addition you can see how it
turns around and how it gives you
the curls around the situation and
get probability angular
momentum a probability current
the fact that they might turn around
more one way than the other way
this is something you can see in the lab
and you should be able to measure it so
this is a schematic picture now I
give you a real picture from above it
does not look familiar from the picture
there over showing you before on
the axis here is a little bit funny but
it came from the two.
Articles one is by now it's published but
it was in the archives when I downloaded
it so the tiger is broken detail balance
remember we're talking about detail
balance reveals you know my genealogy and
so on talk about skinning as so what is
this thing that they have plotted and
it has to do with third Jhelum
doing things in active matter which
means that they get A.T.P.
to get energy from the A.T.P. and zones.
Before and
they do funny things and the place
where I first found out about this was
when I went to an A.P.S. meeting in.
Twenty fifteen and I saw this normally
quite Libyan phase transitions right and
I thought wow this is fantastic let me
go here what Nick to follow he factory
is talking about the you know about
missions here so in a fantastic lady So
here's what you're talking about so
what you're looking at is a general
which is just a little hair from say in
your ear there was a little hairs and
you can see it go back and forth and
you know make goals and they're decompose
the motion in terms of the various modes
this mode this mode this mode and so
on and the plot you saw is the amps
at you of true of the modes
OK And you can see them going through
a periodic motion and plotted and
so on and that movie is actually
taken out of a science article and
this time it's in twenty sixteen and
I went to another A.P.S. thought and.
Discussed quite a bit with when
I could graduate students and
we're trying to you know understand
this in terms of probability and
the momentum so
this is a real on data from their lab
opted to move down to two of the two
modes going back and forth and
this is the around the average the Ampeg
you you know obviously goes around
something and so when you plotted it you
can see there it goes around like this
it doesn't it's not very random
it's just very very periodic And
so if you like that it's
very prominent manifestation
of detail downs violation it really
goes around one way into us and
go around the other way but
away I talk about population dynamics
you can also make a similar plot for
the population of links and hairs.
It goes around one way and the reason
it goes around one way is because
Lynx eat hairless has never eat like this.
So it is a meaningful description so
this is actually what
is the article talks about is that it is
very obviously no Nickleby in system.
Many other things that you study they
don't display this kind of rotation
in fact these other modes of study and
they don't do this and so
what are the characteristics and
what are the implications
of non-obvious ones what I call subtle
manifestations and that is the work that
is in progress in trying to understand
how we can count to rise and so on.
Let me give you another illustration
remember there are two logos one is
one is you and the other one is
the climate so here is how it.
And so apart from the obvious daily and
seasonal cycles are there
other manifestations the fact that we
are actually getting energy from one and
out to the other and so
on are there any be yes but
many of these other manifestations are
subtle and here's what I mean by subtle by
subtle I mean the average angular
momentum is supposed to vanish for
equilibrium States however when
you collect the data the average
angle mentum is going to bounce around and
so as a standard deviation
if the standard deviation is much larger
than the average you scratch your head and
say who I believe it is you know how
can I believe that me go back again so
how can I believe it if the average is
much much less than the standard deviation
So that's what I mean by subtle So
let me go to back to this picture again so
you're doing something like this and
their idea is that when you
collect the data you time series you can
form this combination which is a function.
Time and you can then make
the distribution out of all this these
data points OK for each time you
can make such a combination and
you can make a distribution and so
here is a paper that are submitted to
win the friend in climate science and
associated with probability angular
momentum in the climate system and
what I'm going to tell you about is
two quantities are is associated
with their Nino and one is called D twenty
I'll tell you what that is the other one
is called the No three red and blue in
your picture in your two coordinates and
this is real data from nine
hundred sixty two twenty sixteen
every three months there is
a point of these two variables and
you can pop them around and
you can show that it actually oscillate so
now or tell you what these
two funny variables are.
So all you would recognize
this picture and you so
El Nino is when this side
suddenly warms a lot and so
what they do is they make little boxes in
the Pacific used mean zero one two three
and this is No three three point four four
and they take the average temperature
in this region Here's a picture of
what it looks like Sony No three is in
units of degrees Celsius is
the average temperature in this region
OK that was what this other plot
was that's what this things is
the degree Celsius or the deviation
from their average what is the twenty OK
how many of you know that there ocean
actually has two layers of water.
So I should tell you the funny story is
that when I got involved in these climate
scientists I asked him a very naive
question that if I could tie a water
molecule in the Pacific how long does it
take to go around to more or less the same
place and instead of getting an answer
they said do you want new water all water.
Why.
The near water is the water there's
just fallen down as rain or
from the river and that takes about a year
to go around and that's comparable to what
you're aware of the junk from the tsunami
in Japan is washing up in California
your two later they're all water goes
down to the bottom and comes back up
takes thousands of years that's what
makes climate science difficult can
OK third turns out that the new world
is on top and the waters down there and
there is a sharp divide between
the warm water on the top and
the cold water on the bottom and
this is called the thermal cloud.
And this stuff goes around very slowly and
that stuff is driven by the wind and
goes around very fast.
And this thermocline because of the fact
that there is what you would normally
is tilted at some angle but during a Nino
years when it gets hot over here it
kind of pushes to
the the thermocline down so
the twenty is what is the average
depth of the thermocline
of twenty degrees Celsius so
that's what twenty to twenty stands for
and so these two variables are apparently
have nothing to do with each other
are actually related So
here is that plot again B.
twenty one sell your New You want THIS IS
NOW YOU KNOW WHAT THIS IS degrees Celsius
deviations from the average
OK this is the deviations
in centimeters from the average that's
what the twenty four and that's
the data they have collected if you take
the data they have shown you before and
calculate the momentum angular momentum
and plotted the histogram what you see is
on the listing on the right hand side and
what you see is that most
of the guys are sitting over here
by the way the blue is the data and
they are orange is the theory
the so-called linear theory that is.
Used to describe it.
And you know here's what happens that
negative ones as well as positive ones
these kind of like two experimental
details just a lot lot like true expansion
of the case but one has a steeper slope
and the other one has a now or so and so
you can see that the average is
going to be small compared to
the standard deviation so in equilibrium
this part is symmetric so it tells
you that the average is zero but symmetric
is never quite seven hundred right so
if you really want to see subtle non
equilibrium you have to make the plot and
do statistical analysis on
the asymmetry associated
with it so
there is a serious circulation and
there are double exponential
tailless that can be understood and
so on and so forth and I have already
mentioned that a couple of times.
Are OK so we recently had
the book shop interest then.
The idea is that not equilibrium
people should talk to their
climate fluctuation people and
this is a picture of Galileo's dialogue
that's why I talk about Galileo so
much and this is the fifth is this idea of
non equilibrium this is too simple
harmonic oscillator is thrown into two
different term about as you can understand
everything completely about it and
there's the other system which
is incredibly complicated.
All right so let me quickly go through
the range of methods are the simplest
one is Monte Carlo and
that's very easy to do their series
expansions which are little bit tough you
have a look at different thing questions
which means you do discrete theories and
discrete time and let us do this and
they went through differential equations
the ordinary differential equation and
stochastic differential equation so
those of you who are going on to this
deal should study about that you can do
you feel theory quantum field theory.
If that is the goal for your theory and
at the end is difficult mathematical
methods which we want this broad
conclusions I hope I'll convince you
that on equilibriums that is famous for
many exciting frontier awful surprises and
open questions from fun to
the fundamental don't forget fundamental
begins the word fun begins with F.
U.
N.
and today practical and so on so who
are there lots of ways to do things and
so come and
join the party Thank you very much
Iran.
I left you speechless.
Emergence.
Well.
Usually emergence is associated with
something a little bit dynamic in nature
but the simplest version of it is
what we call collective behavior
if you put a bunch of things together and
you know how say two of them interact
pairwise can you say what would
happen to a bunch of them and
the typical answer is we don't really
know what would happen sometimes we know
sometimes we don't know and in the case
of physics we can put dies in Moscow.
Mr ising didn't manage to show
that there's a place transition
on target date for
the two dimensional one so that one way or
thinking the word emergence what
kind of behavior can I describe.
And I have a funny story to tell is
that if you google me you'll find
that I'm associated with the research of
children's behavior that's three hits and
that this came about because I
got an interview by one of these.
You know P.R. person from the social
trying to explain to her co-operative
phenomenon and I didn't want to talk about
Isaac models I said well just look at kids
you put thirty kids in through a closet
who want kind of behavior can you expect.
They will fight them there do everything
put the same thirty kids on a big field
with a thought cabal What do you get
some relatively well behaved kids so
she understood that so the right of
use children be curious my research.
You have a question.
Yeah the question is that if you couple
more than two reservoirs what would happen
and their answer is no because we don't
even understand what happens when we have
just one going to the other our you
can certainly do that you can do even
more fancy things like do energy going
one way and particles going the other way
I mean we have done things like that but
the problem is that we
already have trouble with one of them
to try we keep getting surprises and
so yes we can do it but then in
the end you publish a paper he says
look what I found that don't ask
me why it's like that it's not
very satisfying that's the situation but
you're right I mean you know we obviously
take in much more than one reservoir
we do much more than just eating we.
Read we.
Take information that's
the other thing which is very
complicated that we don't
know what to do about it or.
Yes.
Yes.
Right right right so on there used
to exploration of what is out there
and those tools are mainly computer and
we're trying to get
you know experimentalists real experiments
that show us real systems as opposed to
simple models and this is a part
of the fun about coming here and
there they are for you know so which not
throughout our where life I don't know but
I do anyway that's the exploratory
phase where you go out there and
you try to do your explore new things and
is literally like going in there
jungle you don't know when you're thirty
and then once you do that the first set of
tools is that you tried to write down
equations what you think is going on.
So you want to write variables associated
what you think is happening so for example
let's say I want to describe epidemics
then I would write down any question for
how the number of infected individuals
evolve is a function of time and
I'll try to solve it and now these
equations are typically not just simple
equations twenty questions with annoyance
so you know where you get infected
is a probability why you don't always get
infected when you're in come in contact
with with a sick person so
that's the whole long list you start with
the simplest that you can do which is
computer simulations finding exposure
to add up there find an experiment
to find a friendly experimentalist.
And do this like they like their.
Case they were talking about and
then you go through different parts of
mathematics that you learned
in graduate school so
far we don't have anything
fancy new to describe.
That.
Almost never it's not this
is actually providing the.
Variance.
OK so we raised on the conservation
of angular momentum.
So let me turn the question around for you
if I look at the general dynamic process
typically the force between them is not
central and if it's not central then
you don't have any of the conservation but
nevertheless you go and talk about it and
Nevertheless you can use angular momentum
a way of characterizing what is happening.
OK characterizing the fact that
it goes around one way and
not the other way one
way more than the other.
So most of the things that we run
into the reason of conservation.
And the other question that people tend
to ask me socially wrangle momentum
is talks when you talk about talks and
again in physics we tend to come
from given the force what is the.
Reaction right so here you are given
the rates that already tells you about how
the orbit looks you don't specify the top
for us you can go and find out the talk
if you didn't see it but it's the other
way around you don't specify to talk and
ask you where you go that's where
angular momentum becomes important so
the process is ever in writing down
as first order in time it's there's
no inertia so
it's very different in that it's.
OK So on the question is about inertia and
again that's something we learn very much
in physics that if you don't do anything
through a particle you would just
keep going that's Galileo so
we don't have anything like that in our
statistical mechanics in the following
sense we typically think of
a still plastic process and
this is the classic process
tends to be dissipated.
And noisy so.
You in real physical systems of
course there is in their show and so
on so all the things that I'm talking
about can be applied to particles and
so on so forth in the low mass regime so
you would have something that looks like M
A M mixed up or dark plus is equal to and
then on this side is deterministic
forces noisy forces and
dissipated minus on the OK
in the small mass limit so
we take VASTA then you have an equation
that is first order in time so
you're just leave is equal to something or
another and that's the level at which we
want to play with things because if
we add inertia then it's very good
if you it's not easy to imagine why how
do you add inertia except in the physical
case it's kicks up in New Mutants can't if
I say I variables at the squad's epidemics
what's in the ocean and so on so
that's the that's a very long
winded we're saying is that if we don't
focus just on physical things that
are already there because I may then
we can't as we'll weigh in there and
just one first order equation.
And that's already hard enough.
OK I question.
So.
It's really like.
Your.
Thought playing with the computer.
You know I mean.
Is this implies there is such an enormous
feel and so little there is no.
Almost anything you do would be
progress in the sense of discovery if
nothing else and then of course
you would be up to you to try to.
Model it try to understand what it is that
you found you know how to get a hold of
these so it's buried there are there many
ways that you can you can participate so
some people say.
This is a place where it's
at the beginning yes well.
You should you can ask me to come
back to give my public lecture
on what is physics there's a there's
a slide in there this is physics is that.
I don't know what are you aware of this
particle maybe you're not referring to
this article but there's an article in
Nature of physics that physics is dead and
then of course there's
a subtext there physics and
this is the nature of physics two
thousand and four I think it was so.
My my responses physics is
only if you find it is a very.
Natural phenomena.
My definition of physics is.
Quantitative understanding of nature and
then you can't have a.
Thank.