this video is sponsored by ground news I
used to think that entropy is a measure
of disorder um if you look at my room
for example this is pretty ordered so
it's very low entropy but give it a few
hours and it'll become highly disordered
very high entropy so look the entropy of
the universe naturally tends to increase
the second law of Thermodynamics it all
makes perfect sense or does it if you
pour milk into coffee then there's a
point in time where the milk and the
coffee are just mixing together right
but then after a few more minutes if you
give it some time then eventually it'll
all be nice and mixed so look over here
did the universe just go from highly
disordered to being ordered meaning did
the entropy of the universe decrease no
this is actually low entropy State and
this is actually High entropy state but
how does that make any sense and when
you think from the point of view of
order and disorder it was all confusing
for me and that's why entropy and second
La of therms actually did not make a lot
of sense
until I started reading P1 lectures oh
my God then my mind was blown so the
goal of this video is not just to
ReDiscover the ideas of entropy or the
second law of themodynamics no no no
it's also to gain a deep intuition
behind why it's called the error of time
or how it makes its way into information
Theory or how does it even allow life to
exist in the first place so if you're
ready for this let's begin so fman where
do we start fman says mahes since we on
a journey of rediscovery forget what
whatever you know about entropy or
second law of Thermodynamics which is
easy for me and look at these two videos
one of them is a video that's being
played in forwards and another one is
just the reverse of it which one is the
reverse and I'm like that's pretty easy
the second one because coffee and milk
spontaneously does not unmix itself so
that's the Reversed one but Fon asks why
I mean look at it at the microscopic
level if you could see individual atoms
or molecules in motion then in one of
the cases you might see a motion that
looks like this it's completely called
lighting and it's moving in a very
random manner now if you look at the
reverse of it it looks like this and fin
ask mes now can you tell which is going
forward in time and which is going
backwards in time and I'm like no now
you can't tell both of them look like
they're going forward in time there's
there's no distinction between them so
this means at the microscopic level you
know you cannot tell whether atom's
motion or moleculars motion is going
forwards or backwards in time and yet
if you look at the collection of these
very same atoms at a microscopic level
you can tell whether you're looking at
something that's going forwards or
backwards in time in other words atoms
or moleculars motion is completely
reversible the laws of physics whether
you consider classical mechanics or
quantum mechanics whatever does not care
about going forwards or backwards in
time does not distinguish between them
so it's completely reversible and yet at
the macroscopic level the collection of
these very same atoms and molecules
their processes are are purely
irreversible how how do you get these
irreversible processes from completely
reversible events that is a key question
and I'm like wow you know people say
that learning is about asking the right
question and this is a profound question
how do you get irreversibility from
completely reversible microscopic events
what's going on over here fan well since
the motion of every single particle like
atoms or molecules is complet completely
reversible the answer does not lies in
physics but because when you consider
the collection of large number of atoms
or molecules that's where the
irreversibility comes which means the
answer actually should lie in
statistics wow but fin one statistics
I'm pretty bad at it and F says don't
worry we'll do it step by step in fact
we'll start with a warm-up example
consider you have 10 marbles with you
and you have a box and you're going to
close your eyes and you're going to
throw these marbles randomly into the
box after throwing all of 10 of them
you'll get some pattern right I'm going
to show you two patterns and you have to
tell me which one's more likely so
here's the first one you might get a
pattern that looks like this after
throwing them into the box and the
second pattern you might get it looks
like this mahes which of these two
patterns look more likely to you once
you have thrown them randomly in fact if
you can answer this correctly then
that's it you'll be able to ReDiscover
everything else all by yourself so those
Saks are pretty high I'm like that's
peasy the second one and F's like why
I'm like well that's because what I mean
what's the chances of it getting like
you know all the marbles lining up right
next to each other that should be very
low the second one therefore is much
more likely and Fon says all right let's
compute this and I'm like wait a second
how do we do the math that looks
complicated no no no we'll we'll
simplify in fact what we can do over
here is we can um assume that there are
five rows and there are you know eight
columns which means there are total of
40 slots now come come over here and
think of it this way okay mahes what is
the you know probability of the first
marble which you throw lands exactly
over here how do you compute that well
think about it there are slots and the
chances of Landing in in any one of
these slots is exactly the same so the
probability of Landing in this
particular slot is 1 out of 40 right
okay now what is the chance of the
second marble Landing over here well
again now there are 39 slots available I
mean we we can assume that if it lands
on top of this marble we will repeat the
experiment okay so there are 39 marble
slots available and each one is equally
likely so now the chances of Landing
over here is 1 over 39 similarly the
chances of Landing over here is 1 over
38 and so on and so forth and of course
we need to do a little bit more work to
actually compute the probability but
that's not important what matters is
this is how we would go about it right
if you do the first one now let's try do
the second one and see what we get again
mahes what is the chance of the first
marble Landing over here exactly it's 1
over 40 what about the second marble
Landing over
here 1 over 39 and so on and so forth
this means the probability that you
would get for this specific pattern is
exactly the same as you would get for
this pattern they're both equally likely
or both equally
unlikely wait a second that why why that
does not make any intuitive sense what's
going on over here well think of it this
way here you said what are the chances
that all the marbles will land right
next to each other so this must be
highly unlikely right but the same is
the case over here what is the CH what
are the chances that you know one marble
lands exactly one square to the right
another marble lands exactly two squares
to the left and so on and so forth if
you think of it that way even this
pattern is very very unlikely isn't it
yeah that makes sense so that means any
pattern must have the same probability
yes any pattern you take must have
exactly the same probability it's just
that the pattern on the top looks much
more ordered to us and therefore we
think that it's much more rare but as
the match shows us it's not any more
rare than any other pattern that you
take which is incredible if you think
about it but F why did my brain make
that mistake because I did not pause and
try to verify my conclusion as a result
I had an error in my judgment and that's
a simple this is a simple example mes
sponsor you're also supporting my channel so now back to rediscovering OV
now let's see if you can answer an
original question using a simple example
let's consider a gas which is trapped in
one corner of a a small box and then
we'll let go of it and we know naturally
that the gas tends to expand again this
is irreversible yet at the microscopic
level we know that all the molecules are
you know their motion is completely
irreversible so why does this happen
well let's see if we can answer this
question first of all we can identify
three distinct stages of this particular
gas let's say it goes from being in one
corner to it occupying the half of the
box and then occupying the complete box
over there our big question is why
doesn't it go backwards let's try to
answer this question by looking at
things microscopically so over here in
this particular case we can model this
by saying hey it's kind of like that
marble where we have 40 slots but we are
restricting those 10 marbles to only 10
slots because we're asking them to be in
one particular Corner how many ways can
you arrange that well if you have 10
Marbles and you have to restrict them to
just 10 slots there's only one way to
arrange that like this so there's only
one Arrangement available to get this
particular um this particular state but
now for this particular State it's kind
kind of like modeling it and saying that
hey now those 10 marbles can occupy you
know half the box which means about 20
slots they can occupy 20 slots how many
ways can you arrange them well now there
are a lot of ways you can arrange them
because there'll be a lot of empty
spaces right in fact if you do the math
it turns out the total number of
Arrangements would be a staggering about
.18 million that many Arrangements will
now be available for this particular
State and finally for the fully exponent
gas we can model it by saying that hey
now these 10 marbles can occupy all the
40 Slots of our box and now because
there are more empty spaces there are
even more Arrangements available over
here in fact if you add them up turns
out you'll get
850 million Arrangements again the
numbers are not important how we got
that is not important but you can kind
of intuitively Mak sense right more
empty space means more number of ways
you can arrange them so the number
should be very high so look the total
number of Arrangements we have is 850
+18 + 1 which is about 850 million
Arrangements all right so now let's
let's imagine that our gas is in this
state our question is what's going to
happen in the future well it can go
backwards right because at the
microscopic level everything is
reversible so it can go backwards but
what is the probability let's figure
that out what's the probability of it
going backwards well if it has to go
backwards then how many Arrangements do
we have that goes backwards well there's
only one Arrangement belonging to this
particular thing out of 850 million
arrangements so if all of these
arrangements are equally likely the
chances of this Arrangement
spontaneously occurring from here is 1
over 850 million and the chance of that
is almost zero that's why the chances of
gas going back is almost zero similarly
what is the chance that the gas can stay
in that same Arrangement because they
have so many Arrangements it's possible
the gas can stay in that same state well
again there are .18 million Arrangements
available for this particular state so
the chances of you know picking any one
of these is18 million out of the total
850 million which is is again almost
zero so the chances of gas staying in
that state is also pretty much zero now
what is the chances that the gas goes to
this state well for that we ask how many
arrangements are available there are 850
almost all the arrangements over here
belongs to this state so the probability
of getting that is almost
100% so look right in front of your eyes
we have the answer to our original
question why is it that even though at
the microscopic level things are
reversible each every single Arrangement
is equally likely so things are
reversible what happens at a macroscopic
level at the macroscopic level the
number of Arrangements belonging to this
one is so much low that it cannot go
backwards for all practical purposes the
chances of going backwards is zero there
and the number of Arrangements available
for this one is so much High the the
chances of it going forward is much more
you know it's almost 100% and that's why
at the macroscopic level it goes in One
Direction things tend to be IR
reversible does that make sense so now
we can Define what entropy is let's
first introduce some jargons what we see
at the microscopic level we call them
macro States so macro state is basically
what you see at the macros level um
there are three differ macro States over
here okay now for each Macro State the
number of different Arrangements that
you have is what we call the micro
States because that's the microscopic
level all right now what is entropy
entropy is a measure of of the number of
micro States that's what we Define
entropy as and now we can understand why
this is low entropy because it has only
one micro State and therefore very low
entropy but this one has a lot of micro
States so there is very high entropy and
so if you take any system the chances of
the entropy decreasing is negligibly low
and that's why we can now intely come up
with second law of Thermodynamics which
would we can say that the entropy of an
isolated system will never
decrease beautiful isn't it but fin then
wait a second shouldn't we say that the
entropy of a closed system and we'll
come back to closed system a little bit
later as to why it is called a closed
system anyways shouldn't it be shouldn't
we say that it is most it will most
likely not decrease because it's all
about probability there's a good chance
I mean there's a very tiny chance it can
decrease well fan says yeah technically
mahes you're right but look at the
numbers I mean even with just 10 Marbles
and 40 slots look the chances of it
going back is so low now imagine what
would happen in the realistic case where
we have 10 to the 27 atoms and we're
dealing with so many more empty spaces
and so many more slots the chances of it
going back would be astronomically low
so yes technically there's a small
chance that a gas in a room will
spontaneously go into a corner but the
probability of that is ridiculously
small it's so small that you'll have to
wait more than the age of the universe
something like that right and so what's
fascinating to me is that this whole
irreversibility is just probabilistic
it's not laws of physics but it's the
laws of statistic it's math that makes
things irreversible that is
awesome anyways we can now also
understand the whole idea behind order
and disorder when we say something is
ordered we basically mean a macro state
in which there are less number of micro
States less number of way to arrange
that and we say something is disorder
what we really mean is a macro state in
which there are more number of micro
States more number of ways to arrange
that that's what we mean but now that we
have a much more concrete definition of
micro State and micro States let's not
use the word order and disorder anymore
now let's go back to our coffee and the
milk example why does it go from this
state completely being you know
separated to mixing together why doesn't
it go backwards well again if we can
model it we can say that this one is
kind of like having a micro State like
this there's only one arrange for that
and therefore this has the lowest
entropy lowest number of micro States
over here it's kind of like saying that
hey you know what you can mix or here in
this particular section probably coffee
and milk particles can mix so now we
start getting more number of
Arrangements available and so the number
of micro States increases and therefore
the entropy is higher okay but in this
particular case it's kind of like saying
hey you know what the coffee particles
and milk particles can occupy whatever
States It Whatever slots it wants and
now you will have the highest number of
arrangements for this and therefore this
is the highest entropy and so now you
can see why is this low entropy because
there are less number of micro States
this is high entropy because there are
more number of micro States and
naturally you tend to go from a macro
state of low entropy to a macro state of
high entropy its probability beautiful
isn't it and this now explains why
entropy decides the arrow of the time if
you look at things at a microscopic
level you can't tell whether you're
looking at an evolution that's going
forward in time or you're going
backwards in time because all micro
states are equally likely so there is no
error of time at the microscopic level
but it's only when you look at its
corresponding macro States the picture
becomes much more clear it is evident
that as we go forward in time we can
only go towards macro state that has
high entropy because that's a high
probability chance and that's the reason
why at a macroscopic level things are
irreversible giving us a particular
Arrow of time from the past to the
Future so what's profound and blows my
mind away is that the arrow of time does
not come from physics it actually comes
from statistics and probability that is
insane if you ask me understanding why
entropy of an isolated system can never
decrease makes perfect sense when you
think in terms of micro States or does
it finally I think I can break the
second law of Thermodynamics very easily
just go back to that particular gas and
I'm just going to introduce a piston
over here and I'm just going to flick
that piston and then look the gas gets
compressed doesn't that mean that the
entropy of the gas is reduced I've brok
on the second law of thermodynamics now
in my heart I know this does not break
the second law of Thermodynamics but
this is the most powerful way to learn
when you learn something new try to
critique it try to break it and see what
the logical flaw is that's how you
deepen your understanding and gain
Mastery your teachers may not like it
but that is the best way to learn so
over here I now know that entropy is a
number of micro States compressing the
gas reduces the number of micro States
so shouldn't the entropy reduce answer
in terms of the number of microstates
fan and fman says yes mahes as you
compress the gas the number number of
ways you can arrange the particles will
reduce so you might think that it
reduces the number of micro States but
so far we ignored something see when you
compress a gas this way it Heats it up
meaning it increases its temperature
temperature is a measure of the average
kinetic energy which means now there is
more kinetic energy for these particles
if you give it more kinetic energy you
can distribute that kinetic energy in
various ways and each of them now adds
to to its micro States so although in
this model there is only one way to
arrange that particles but there are so
many ways to arrange that kinetic energy
distribute that kinetic energy that you
end up with lots and lots of micro
States so you have a lot of micro States
because even kinetic energy can be
distributed for a given particle
arrangement so when you compress a gas
this way the number of micro states does
not decrease in fact it actually
increases and I'm like this makes so
much more sense now this is the reason
why if you have a if you have a gas at
high temperature it has a high entropy
compared to an identical gas of low
temperature it has lower entropy well
earlier I should think that high
temperature means more Randomness but
now we can think more concretely high
temperature means more kinetic energy
available so there are more ways in
which you can distribute it adding to
the number of micro States increasing
the entropy beautiful isn't it but wait
we're not going to give up there's
another way to try and break this law of
thermodynamics what if we could compress
this gas without increasing its
temperature one way to do that is by
introducing Maxwell's demon James
Maxwell came up with an interesting
thought experiment he asked what if
there was a hyper intelligent being or
some kind of an advanced computer system
whatever it is we're going to call that
Max steon if she could learn the
positions and the velocities of every
single particle then she can have a trap
door over here and she can make sure
that whenever there's a high energy
particle coming from the right to the
left she allows that particle to go
through but if there's a high energy
particle coming from the left to the
right she will not allow it to go
through this way she can ensure that all
the high energy particles from the right
will eventually end up towards the left
in other words she would have compressed
the gas without changing its kinetic
energy there you have it we have reduced
the entropy of the system what you got
to say about that finin and fan says M
first of all calm down okay second of
all you are right the entropy of the gas
might have reduced but what about the
entropy of the Maxwell's Demon's
brain let's consider the state of her
brain before and after she learns about
the velocities and the positions and all
of that okay now before learning about
the position and the velocities she has
no information and we can model that by
saying that all the bits of that
particular part of her brain is zero
right so no information means all zeros
and how many ways can you arrange all
zeros in a particular section of the
brain there only one way all zeros
there's only one Arrangement you have
which means this represents low entropy
because there's only one micro State now
once she learns about the positions and
all of that that specific part of the
brain will now have some information and
how do we model some information well
she will have some zeros and some ones
how can you now arrange some zeros and
some ones there are so many ways to
arrange it you can arrange it this way
and this way and this way so there are
so many Arrangements available that
means the number of micro States
explodes which means this now represents
High entropy so just by learning she
hasn't done anything else just by
learning about the position just by
acquiring information the entropy of her
brain has exploded it's makes sense
right so earlier the gas had high
entropy and her brain had low entropy
now once she finishes all her tricks the
gas gets compressed and ends up having
low entropy but her brain ends up having
high entropy if you consider the total
entropy of the the system it would not
have reduced at Max it would stay the
same but it would not reduce and for me
what's blowing my mind at this point is
look at how far we have come just by the
idea of micro States we can Now
understand that when something acquires
information its entropy must increase
the number of micros increases the
entropy increases acquiring information
increases the entropy of that object
this is how entropy makes its way into
information Theory this is is beautiful
isn't it but wait I have another silly
idea to break the second law of
Thermodynamics I'm not going to stop
what if I just take a hot gas and just
keep it in touch with a cold gas then we
know heat will start flowing from the
hot gas to cold gas until the
temperature equalizes and in doing so
look the uh the temperature of the hot
gas has reduced meaning the entropy must
have reduced the number of you know the
kinetic energy has reduced number of
Arrangements has reduced so look I have
reduced the entropy of the gas and fan
says yes but remember the second law of
Thermodynamics says the entropy of an
isolated system cannot decrease an
isolated system is where you cannot
exchange matter or energy this first box
is not an isolated system it is
exchanging matter or exchanging energy
with something else so now we need to
look at the whole thing together and
compare its entropy and see what happens
if you think in terms of particle
Arrangements well it will be the same
because same number of particles and the
same volume everything else is the same
so we need to think in terms of the
kinetic energy Arrangements over here
well in the first case because all the
high kinetic energy is restricted to the
left and all the low kinetic energies is
restricted to the right I can arrange in
multiple ways but that restriction means
there are less number of ways I can
arrange you know I can have this
Arrangement on the other hand over here
there is no restriction I can take the
total energy and distribute it arrange
it however I want so you can see
obviously there will be way more
Arrangements available over here this is
very similar to how if you restrict
coffee and milk on one side then there
is less number of Arrangements where if
you allow them to mix there will be more
number of Arrangements the difference is
instead of particles mixing it is the
energy that is mixing so clearly this is
at low entropy and this is at high
entropy and so indeed when you go from
here to here look the entropy is
increasing but look look we now have a
new perspective on entropy we thought of
entropy in terms of micro States entropy
in terms of information but now we can
think in terms of ENT ropy as how
concentrated the energy is low entropy
means the energy is very concentrated
High entropy means the energy is more
spread out so the universe's entropy
tends to increase because energy tends
to spread out more because there are
more number of micro states that way
this is the reason why heat tends to
flow from a high temperature region to a
low temperature region because that way
the energy gets more spread out the
number of micro States increases we now
have an intuition behind the most
fundamental law as to why heat flows
from high temperature to low temperature
it's all about the number of micro
States and probability amazing isn't it
but I have one final question fin one
final counter what about refrigerators
if you have a refrigerator in a room and
it's not yet turned on then it is like
this where the entropy is very high the
temperature everywhere is the same but
the moment I turn on the refrigerator it
pumps the heat out and we go to this
state and look fin one we just saw that
this not just the refrigerator but the
refrigerator and the room the entire
State entire system is at low entropy so
hasn't the entire system gone to lower
entropy hasn't it broken the second law
of Thermodynamics what are you going to
say about that and fan says mahes
remember this now is not an isolated
system because refrigerators require a
power supply so you need to also
consider the power supply as a part of
your isolated system so let's do that so
if if you consider the power supply like
say a battery then a battery has a lot
of concentrated energy o juicy low
entropy energy so if you look at this
entire system now there is a very low
entropy energy over here so the overall
entropy is pretty low then when you turn
on the refrigerator it uses this low
entropy energy to pump out the Heat and
in doing so look at what has happened
the entropy of the RO room and the
entropy of the source has gone up and so
if you compare it to what it was before
look the entropy of the refrigerator's
inside is lower than before but the
entropy of the room and the power source
is much higher than before because the
energy is much more distributed than
before which means the overall entropy
ends up
increasing refrigerators I used to think
that they try to fight the increase in
entropy they try to fight the second law
of Thermodynamics but you you can see
they don't fight it they too help in
increasing the entropy they reduce their
local entropy but increase the global
entropy they too are riding the wave of
the second law of
Thermodynamics but what's more
interesting is that in order for a
refrigerator to work in order to be able
to lower your you know local entropy you
need a low entropy energy source if you
have a low entropy energy source you can
do this increase the number of micro
States and this second of thermodynamics
will love you and that's exactly what
life does for example if you take plants
and you know plants and trees and
everything they take the low entropy
energy from the Sun and they use that to
you know reduce their local entropy so
that they can stay alive and they can
stay ordered if you may and in doing so
they increase the global entropy
increasing the number of micro States
increasing the you know the entropy of
the whole universe so life does not
fight the second law of Thermodynamics
life also rides the way of second law of
Thermodynamics it's it's used up in
increasing it also increases the global
entropy so as far as second law of
Thermodynamics is concerned life is an
entropy increasing machine and in doing
so now it creates fruits and vegetables
and animals will use the low entropy
energy in the fruits and vegetables to
keep their local entropy you know small
to reduce their local entropy and again
increasing the global entropy
life is an entropy increasing machine
and this also helps me understand a
confusion that I always had before so I
used to always think that hey what does
it mean when we say that don't waste
energy or don't consume too much energy
because energy can neither be created
nor destroyed right well now you can see
what we talking about when we say that
don't waste energy what we really mean
is don't waste low entropy energy okay
low entropy energy is the one that can
be you know that is useful to us High
entropy energy is useless to us so when
we talk in our terms we are consuming
energy what we really doing is we are
consuming low entropy energy and making
the entropy you know the entropy of the
energy higher that's what we're
continuously doing and we're increasing
the entropy of the universe this also
means we can Now counter people who say
that hey you know there's ENT there's
energy all around us channel that ENT
energy inside no you can't channel that
energy inside because that's a high
entropy energy that's not useful if you
want to channel anything Channel low
entropy energy from the fruits or food
into your body not the high entropy
energy that you have outside but anyways
since life is an entropy increasing
machine this means a planet with life is
much more probabilistic than a planet
without life that is amazing right I
would have never thought of it that way
but it indeed is because these are
Global entropy increasing machines
however you all you do need a low
entropy Source something like the sun
and that's why people believe that there
must be life outside as long as you have
a habitable planet and you have the
right ingredients and you have a low
entropy Starlight on it for example
continuously life is an probabilistic
eventually High probabilistic event
eventually life must you know evolve but
guess what's better than a planet with
life planet with intelligent life
because intelligent life not only
increases the global entropy using our
own bodies but we also increase Global
entropy using a lot of things that we
do and so intelligent life is even more
probabilistic than normal life which
means if you have planets with life
there should also be planets with
intelligent life given enough time but
that's a problem because even with a
small amount of time humanity has gone
from living in caves to going to
different planets imagine what could
life do intelligent life do if they had
millions of years they could colonize
galaxies or Galaxy clusters and if they
do so we should see some signs of them
but we don't see anything when we look
out where are they so intelligent life
does not exist meaning life does not
exist exist everywhere this is the
famous for me Paradox maybe a topic for
another video and this is where we're
going to finally stop but we have barely
scratched the surface I mean there was
so much more about information entropy
there's about entropy with gravity and
eventually what happens to entropy of
black holes the holographic principle so
much more if I see interest in that I
will do more research and make a
separate video on that in this video we
will explore why too many neutrons will
make a nucleus extremely unstable
another question that I had for a long
time see you