Life, Emerging Structures, and the Second Law of Thermodynamics
Introduction
"A theory is the more impressive the greater the simplicity of its premises,
the more varied the kinds of things that it relates and the more extended the
area of its applicability. Therefore classical thermodynamics has made a deep
impression on me. It is the only physical theory of universal content which
I am convinced, within the areas of the applicability of its basic concepts,
will never be overthrown." -- Einstein (1949)
This document investigates the emergence of structures, particularly living
organisms, and the relationship of this process to the Second Law of Thermodynamics.
The level is fairly elementary, and grew out of course notes for a liberal
arts Physics course at the University of Toronto. The structure of the document
is:
A very brief overview of the Second Law of Thermodynamics. Further information
on the Second Law of Thermodynamics is available here.
A similarly brief overview of Chaos. Further details on this are available here.
Discussion of systems in which order arises from disorder, despite the
Second Law of Thermodynamics.
An introduction to Cellular Automata.
A discussion of evolution and maintenance of life on Earth.
Parts of this page and the pages it uses require Flash; the player is available
free from http://www.macromedia.com/.
Other parts use Java; the Java run time environment is available free from http://java.sun.com/.
Illustrating the Second Law of Thermodynamics
There are many many different equivalent ways of stating the Second Law of
Thermodynamics. Here is one of them:
The total disorder of all the participants in any physical process "never" decreases,
but it can increase.
The entropy is a measure of the disorder of a system. This
definition can lead to confusion since it is a measure of the lack of
order, while we usually think of physical quantities as measuring the presence of
some property, not its lack. In fact, the negative of the entropy, the negentropy,
is a measure of the order of the system. Here, then, are two more equivalent
statements of the Second Law of Thermodynamics:
The total entropy of an isolated physical system "never" decreases.
The total negentropy of an isolated physical system "never" increases.
Here is an example. We say that the upper arrangement of the red and
blue spheres is more ordered than the lower arrangement. The upper arrangement
has all the red spheres on the left and all the blue ones on the right;
the lower arrangement has the spheres randomly distributed between the
left and right.
If we shake the box containing the spheres, we would expect to end up
with an arrangement that looks more like the lower one than the upper
one: the disorder of the system increases.
If we think of the red spheres as being hot molecules and the blue ones
as cold molecules, then we see that if we start with the left side hot
and the right side cold, the system will evolve into a state with equal
temperature on the left and right side.
Clicking on the blue button to the right will illustrate the Second Law
of Thermodynamics. The animation is in Flash, and will appear in a separate
window. It is by Vera Fleischer and is used by permission.
The first part of the animation is an increase in disorder, and the second
part is a decrease. The first part is what you might expect if you randomly
shake the sentence and let the letters just arrange themselves wherever they
wish. The second part is very very unlikely to happen spontaneously through
some sort of shaking process.
You may wish to note that when the letters are arranged into the quote by
Einstein, they contain information which we can read. When they are scrambled
there is not anything readable. Thus the order, the negentropy, can be associated
with information.
You may have noticed that above in three places I put the word never in
quotation marks. The reason why is because for systems with many participants
although it is unlikely that the entropy will decrease, it is not impossible.
Above we used an animation with 342 letters and 68 spaces. To the right
is the same sort of animation but for only 2 letters. Now when the two
letters re-form to spell is,
the result is not as improbable as the case where all 342 letters come
together to give us the beginning of Einstein's statement about thermodynamics.
As you may know, the air in the room in which you're probably reading this
has bazillions and bazillions of air molecules, all moving around in random
directions, colliding with each other, etc. If all the molecules suddenly rushed
up into the far corner by the ceiling, we would say they have become more
ordered. But the chances of this happening, causing you to suffocate, is very
very unlikely. In fact, since a bazillion is such a large number
we can pretty well ignore the possibility of it happening. But since the probability
of it happening is not exactly zero, I put the quotation marks around never.
Technical Note: a bazillion is defined to be a power
of ten whose value is much much larger than 342.
Illustrating Chaos
In the late 17th century Newton triumphed and managed to use his newly
formulated Laws of Dynamics and Law of Universal Gravitation to solve
the problem of the Earth in orbit about a fixed Sun.
The Earth moves in a nearly circular orbit about the Sun.
Our Physics students learn to solve this system in their first year of
studies.
Newton then turned his attention to the second most simple gravitational
problem: two fixed Suns and one Earth. He was amazed to discover that
he could not solve it.
Others tried to solve this famous "three body problem" and also failed.
At one point there was a cash prize for its solution.
It turns out that this system is chaotic and is not analytically
solvable. However, computers can produce an approximate solution
that is as close to correct as we wish to make it. Among the properties that
this system, and all chaotic systems, possess is that it exhibits Sensitive
Dependence on Initial Conditions. This is sometimes called the "butterfly
effect" because if, say, history were chaotic
then whether or not a particular
butterfly landed on a particular flower in the Himalayan mountains in
1837 determined the outcome of World War II.
I have done a Flash animation of the solution to the three-body gravitational
problem. In it you can have up to four non-interacting planets that begin with
almost identical initial positions and speeds. As the animation progresses
you can see that after a while the "orbits" radically diverge.
The blue button to the right accesses the animation in a separate window.
The number of planets is chosen in the lower-right corner of the window.
Can Order Arise From Disorder?
Consider a gravel road, such as are still common in many rural areas.
The photograph to the right, taken by Donald Simanek of Lock
Haven University of Pennsylvania in 2005, illustrates.
When first graded, crushed limestone of a variety sizes are laid down
essentially randomly on the surface. And yet over time the road becomes
rutted, the horizontal hills of stones and valleys of hard subsurface
below, that can be seen in the photograph.
The ruts developed from traffic, especially
near abrupt curves where cars had to brake to slow down. They were shallow
at first but got rougher and deeper with time, and have a characteristic
spacing.
This system, then, became more orderly as time went by. But this is not a
violation of the Second Law of Thermodynamics, because that law only talks
about the total entropy of a system that is not interacting with anything outside
of it. Here the road is interacting with the traffic that causes the rutting.
If we consider the total entropy of the gravel and the traffic, it will necessarily
increase: the decrease in entropy of the gravel is more than matched by the
increase in the cars and trucks traveling on the road.
Here is a beautiful example, also from Prof. Simanek. It
is a picture of sand dunes in the desert, and you can clearly see that
the sand has ordered itself into ripples. These were caused by the wind
blowing over the desert.
So here the increase in order of the sand was accompanied by a larger
increase in the disorder of the wind.
Cellular Automata
Cellular automata provide another way to think about order and disorder. One
of the best known automata is the Game of Life, devised by John
Conway in 1970. This example is played on a large checkerboard-like grid. One
starts with a configuration of cells on the board that are populated, and then
calculates the population in succeeding generations using three simple rules:
Birth: an unoccupied cell with exactly 3 occupied neighbors
will be populated in the next generation.
Survival: an occupied cell with 2 or 3 occupied neighbors
will be populated in the next generation.
Death: in all other cases a cell is unoccupied in the
next generation.
Despite the simplicity of the rules, truly amazing patterns of movement, self-organising
complexity, and more arise in this "game."
To the right is a Flash animation of the simplest possible
configuration that changes from generation to generation but never grows
or dies out. It is called a blinker.
Click on the Step button to step from generation
to generation. In this mode the number of occupied neighbors of each
cell is shown.
Click on Play to resume playing the animation.
Here is a small taste of some of the things that can happen in this
game. This example is Gosper's "Glider Gun" and this
implementation of it is from Wikipedia.
Every 30 generations a glider is generated and travels to the
lower-right.
You should be aware that this sort of behavior did not arise just by
accident. The initial state leading to this behavior was carefully crafted
in 1970 by R. William Gosper, Jr., and several student colleagues at
M.I.T. It won a $50 prize offered by Conway as the first known infinitely
growing pattern.
The pattern, the glider, moves. But the squares are just becoming occupied
or unoccupied; they are not moving.
You may wish to notice that in this implementation, when a glider goes out
of the picture it simply disappears. Other variations of the Game of Life have
an object that disappears on one side of the window wrap around and re-appear
on the opposite side.
Clicking on the blue button to the right will access a Java implementation
of the Glider Gun that has this "wraparound" property. It will
appear in a separate window. This implementation is by
Mitchel Resnick and
Brian Silverman at M.I.T.
We have seen that the Glider Gun generates ordered gliders every 30 generations,
and that the generation process is chaotic: it exhibits the butterfly
effect.
This system does not violate the Second Law of Thermodynamics. Imagine that,
like Conway in 1970, we are playing the game on a checker board (actually Conway
used a Go board). If we just shake the board to reposition the pieces, then
clearly the system of board and pieces are not isolated, so the Second Law
does not apply.
There is an added part of this story however. If we just shake the board the
rules for where the pieces will land is just classical mechanics, and the number
of pieces is constant unless some fall off the board. But in the Game of
Life different rules govern
which cells will be occupied in the next generation.
Also, the Glider Gun shows that unpopulating a single occupied square or populating
a single unoccupied one often leads to drastic changes in the time evolution
of the system. This is reminiscent of the Sensitive Dependence on Initial
Conditions that characterises all chaotic systems. You may also recall
that non-chaotic systems become chaotic as some parameter describing the system
changes, and in fact the Glider Gun is right on the edge of being a true chaotic
system.
There are many different rules that are used in the study of these cellular
automata. One well known rule set is by Brian Silverman and is called Brian's
Brain. The rules are:
Birth: an unoccupied cell with exactly two occupied neighbors
will by populated in the next generation.
Death: every occupied cell dies in the next generation.
Rest: if an occupied cell dies it must wait one generation
before it can be populated.
Clicking on the blue button to the right will access a Java implementation
of Brian's Brain in a separate window. This is also by Mitchel
Resnick and Brian Silverman at M.I.T.
We see that although glider generation in Life requires a carefully controlled
initial state, the Brian's Brain rule set makes it very difficult to avoid
making gliders.
Recently a rule set called Rule 110 has been receiving a
lot of attention. One starts with a pattern on a row, and the rules
determine the population of the row under the current one in the next
generation. The rules are given below, and the Flash animation to the
right illustrates for a starting configuration of a single occupied
cell. In the rule table below a 1 indicates a populated cell;
a 0 indicates
an empty cell.
current pattern
111
110
101
100
011
010
001
000
new state for center cell
0
1
1
0
1
1
1
0
In the 1990's Matthew Cook proved that such a rule set can be a model
of any computer.
To the right is an more complete but non-animated example
of Rule 110 for a starting configuration of a single occupied cell. The
figure is from Wikipedia.
It has been proposed that cellular automata may form a useful model
for how the universe really works, possibly supplanting Physics. We've already
mentioned some people; other contributors to this idea include Konrad
Zuse in 1967, Edward Fredkin in the early 1980's, and more recently Stephen
Wolfram in 2002. Wolfram's work in particular is the outcome of nearly a decade
of work, which is described in a mammoth 1200 page self-published book modestly
titled A
New Kind of Science.
Evolution and Sustaining Life on Earth
Warning: at the end of this section I will indulge in some ranting and raving
about energy sources.
A vivarium is a sealed ecosystem. A large clear container has some
soil, water, plants, perhaps some snails, etc. in carefully controlled proportions
placed inside. The container is then totally sealed and placed in the sunlight.
This ecosystem can survive for a long long time with no maintenance required.
In fact, with care a vivarium can be constructed that initially increases the
total amount of biomass inside until it reaches a steady state. What does the
Second Law of Thermodynamics say about this? That there is no problem: although
the system cannot exchange matter with the outside, energy from the sunlight
is streaming through the ecosystem so it is not really closed. If you place
the vivarium in a dark closet, the Second Law will take over and very soon
you will have a high-entropy foul-smelling goo of decomposed biomass.
We can think of the Earth as being very similar to the vivarium. The exchange
of matter between the Earth and space is fairly negligible, but energy from
the sunlight is streaming through the system. In fact during the day about
1400 Joules per second (nearly 2 horsepower) reaches every square meter of
the Earth's surface. A similar quantity of energy is radiated away into space
from the Earth as thermal radiation.
Millions of years ago the Earth had no life and had a relatively high entropy.
Now life has evolved, and the Earth contains about a trillion kilograms of
ordered low-entropy biomass. And this all occurred because of the energy from
the Sun that streams through the Earth's system. The rule set that governs
this process is given by physics, chemistry, biology, and evolution.
This is not the appropriate place to discuss evolution,
which I believe to be a fact.
Now let's consider some energy sources that we use.
1. Solar Panels and Heaters
Solar panels directly convert sunlight to electrical energy. In addition,
in many parts of the world the majority of hot water heaters are on
the roofs of the houses and use sunlight directly to heat the water.
My uncle was fond of talking about my aunt's solar powered clothes
dryer: a common clothes line strung between the house and a
convenient nearby tree.
This photograph is by David Anderson, and is in the public domain.
2. Hydroelectric Power
We build dams that extract energy
from water that is flowing downhill. But how did the water get on top
of hill? The heat from the Sun evaporated the water in the oceans and
lakes, and rain then deposited some of it on top of the hills and mountains.
Thus hydroelectric power is generated from solar power.
The photograph is of the Grand Canyon dam. It was taken by Steven
Pinker at Harvard, and is used by permission.
3. Wind Power
Wind turbines and windmills extract energy from the wind. But what causes
the wind? The sun heats up the air in tropical regions, which causes it
to rise. Near the poles the air cools down and falls. So there is a continual
circulation of air rising near the equator, traveling north and south
high above the Earth's surface, falling nearer to the surface near the
poles, and traveling back to the tropical regions nearer the surface. The
fact that the Earth is rotating on its axis causes the wind to swirl, but
the energy of the wind is also solar.
The photograph is of the wind turbine at Exhibition Place in Toronto.
4. Biomass
We extract energy from biomass in a variety of ways. This includes burning
wood, possibly to run a steam engine, extracting ethanol from it, etc.
Or course, the energy got into the biomass from sunlight, so this too
is solar power.
These energy sources are all sustainable and renewable.
In the language we have been using in this document, this means that they treat
the Earth as an open system and thus allow our low-entropy ecosystem to survive
and prosper.
Let us continue thinking about energy sources.
5. Petroleum, Coal, Natural Gas. These energy sources are
also ultimately from the Sun: biomass from hundreds of thousands of years ago
became trapped in the Earth as oil, coal and gas deposits. However, these energy
sources are not renewable: they are no longer being produced. Thus they all
treat the Earth as a closed system. The Second Law of Thermodynamics predicts,
correctly, that these energy sources will necessarily produce problems with
entropy: some common names for this entropy are pollution, greenhouse gases,
and global
warming.
6. Nuclear Power. This is the direct conversion of mass to
energy in accordance with the most famous equation in the world: E= mc2. Note
that because the speed of light c is such a huge number, a nearly
unimaginable amount of energy is available to us from small quantities of mass.
Thus when we hear experts quacking about an energy crisis they are
wrong. However, we do have an entropy crisis, and the Second Law of
Thermodynamics assures us that nuclear power generation on
Earth in wrong in principle: it treats the Earth as a closed system and necessarily
will lead to problems in sustaining our ecosystem.
In this regard, the source of the Sun's energy is also nuclear. However, the
Sun is some 150,000,000 km away from the Earth. So if we just think about
the Earth, the energy streams through and we can "beat" the Second Law of Thermodynamics.
Of course the total entropy of the Sun plus the Earth plus the rest of outer
space is increasing.
Finally, I mention an idea which seems to re-emerge every few years.
Imagine we put a large array of solar panels on a satellite in stationary
"geosynchrous" orbit above the Earth. We may then transmit
the energy to the Earth's surface with microwaves.
Perhaps technically feasible, this scheme keeps the Earth as an open
system, and so at least in principle is correct.
About This Document
This document was written by David M. Harrison, Dept. of Physics, Univ of
Toronto, harrison AT physics.utoronto.ca in
February 2006. This is $Revision: 1.4 $, $Date: 2007/03/30 11:35:25 $ (y/m/d UTC).
The photographs of the road ruts and the sand ripples are from Professor
Donald Simanek at Lock Haven University of Pennsylvania, and are used by
permission. The original source of these photographs is a discussion of similar
issues to those discussed here, but with an emphasis on questions of evolution,
creationism, and intelligent design; it is at http://www.lhup.edu/~dsimanek/philosop/design.htm.
The animated gif of Gosper's Glider Gun is from Wikipedia,
and being good open-source folks I believe they have automatically given me
permission to use it in this document.
The Java implementation of the Gosling Glider Gun and Brian's Brain were written
by Mitchel Resnick and Brian
Silverman at M.I.T. in 1996. Our copies were supplied by Brian Silverman.
I have heavily changed the text that accompanies the animations. The original
site is http://llk.media.mit.edu/projects/emergence/contents.html.
The large non-animated example of Rule 110 is also from Wikipedia.
I've had the solar satellite drawing sitting around my discs for so long that
I don't remember where I got it. Contact me if it is yours and you wish me
to remove it or give you a credit.
