The Problem With Heat

RocketCat sez

The Second Freaking Law of Thermodynamics! The only thing that cheeses off sci-fi fanboys more is Albert "No FTL for You" Einstein. Thermodynamics gets the the goat of not one but two sets of sci-fi-guys, when it tells them You Can't Do That.

Group Primus is highly urinated because they can't have Run Silent, Run Deep in outer space because the heat of your shivering body can be spotted at a range of one hundred times the distance between Terra and Luna.

Group Secundis is highly urinated because heat radiators give their macho space warships a big fat glass jaw.

Neither group can seem to get it through their heads that attempting to avoid a scientific law is like letting go of an anvil over your foot and daring the law of gravity to start something. Especially when your main motive is to see your favorite unscientific media science fiction show somehow happen in real life.

For a more in-depth analysis of the impact of thermodynamics on your science-fictional universe, obtain and read Ken Burnside's The Hot Equations: Thermodynamics and Military SF.

Now in some subsequent pages in this website, there will be unpalatable scientific truths. But of them all, there are two in particular that give me more hate mail than all the rest put together. The fact that there ain't no stealth in space, and the heat radiator "Achilles Heel".

Both problems are caused by heat. In one case, it is the waste heat of a spacecraft that becomes a stealth-destroying beacon. In the other, it is the fragile nature of heat radiators.

About once a month, I get an email from some eager fan who believes they have the miracle solution to both problems. "Eureka! I've got it! All you have to do is use the Peltier-Seebeck effect to convert the heat into electricity! Then you can store it or use it as is convenient. A simple thermocouple and the problem is gone!"

This solution is elegant, marvelous — and totally wrong. People who come up with this are to be congratulated on their brainpower, but they need to study their physics a bit closer.

What's the problem? Well, the general problem is that pesky Second Law of Thermodynamics. In this context, it tells you that it is impossible to destroy heat, the best you can do is move it around. So using a thermocouple to convert heat into electricity is impossible.

The specific problem is that a thermocouple does NOT convert heat into electricity. It converts a heat gradient into electricity. The original heat is still there. In fact, the conversion process adds even more waste heat to the original total.

As an analogy, think about a hydroelectric dam. The water in the reservoir is at a higher gravity gradient than the water downstream. The hydroelectric dam converts the gravity gradient into electricity. But the water is still there after passing through. The dam does not convert water into electricity, if it did the water would disappear. In the same way a thermocouple does not convert heat into electricity, the heat is still there.

But don't take just my word for it:

Using useful energy creates heat. You can't get rid of this heat; you can only move it around. You can in some cases use differences in temperature (i.e., heat) to generate useful energy, but it also generates even more heat. That can be helpful if you have somewhere to dump the heat, but if your problem is that you have a lot of heat and need to get rid of it, that doesn't fix your problem; it only makes it worse.

Erik Max Francis

Peltier devices only make electricity by using a heat gradient. They get power by moving heat from an area of high heat to an area of low heat. They don't get rid of heat, they just move it around. Once the gradient is collapsed, no more electricty can be generated.

Michael Simon

The thermoelectric effect converts a temperature difference into electricity; like all heat engines, it does not work if no temperature difference exists. In addition, like all heat engines, only a portion of the heat is converted into energy; the remaining heat is conducted from the heat source to the heat sink; specifically, like all heat engines, the upper limit on conversion efficiency is equal to the temperature change divided by the initial temperature.

In order to keep producing power, you must keep the heat sink cooler than the heat source. To keep the heat sink cooler, you must either refrigerate it (which consumes more power than is generated by the thermoelectric effect) or you must run a radiator at the temperature of the heat sink. If the heat sink is reasonably cool, this radiator will be extremely large.

Anthony Jackson

Heat, by definition, is energy that comes with associated entropy. It is a well verified physical law that entropy cannot be destroyed, it can be created but the only way to decrease your amount of entropy is to move it somewhere else. To avoid having entropy build up on your spacecraft until something breaks, you need to get rid of it by moving it off the craft. The thermoelectric effect (Seebeck effect, Peltier effect, Thompson effect) moves heat through a device -- meaning it moves both energy and entropy. Some of the energy is shunted aside as entropy-free electric work that you can use for doing other things, but the remaining energy still has at least as much (and probably more) entropy with it. You have just moved the problem around, not gotten rid of any of it. In fact, in doing this, you made it harder to get rid of that entropy.

To explain why requires a bit of simple math. If you transfer an amount of heat Q at constant temperature T, the entropy S that moves along with the heat is S=Q/T. If you take in the heat energy Q_h and entropy S at a high temperature T_h, you can get rid of the entropy at low temperature T_l with less associated heat energy Q_l = S * T_l < S * T_h = Q_h. All the remaining energy Q_h - Q_l is entropy free, and you can use it for other things. To get rid of the entropy now at T_l, however, you can only discharge it into something even colder (or do work to move it someplace warmer). This is how all heat engines work, from gas turbines to automotive piston engines to Peltier or Seebeck thermocouples.

On a spacecraft, the only way you can move energy and entropy off the spacecraft is by putting it in something else and ejecting that something else, or radiating it away as electromagnetic waves. Since trying to put all your entropy in matter and dumping it is wasteful for your mass budget, radiation is the usual trick. However, the required radiator area scales as 1/temperature to the fourth power. The colder you are storing your entropy, the larger the radiator you need to get rid of it, and the size increases very rapidly with decreasing temperature. Using a thermocouple to extract electricity means you end up with lower temperature entropy and thus need even larger radiators to get rid of it.

Luke Campbell

(ed note: Luis Wu and company have been recruited by the Puppeteer species. They travel to the Puppeteer homeworld, and are startled to discover that it is a Klemperer Rosette.)

      “Of course not,” said the puppeteer. “Doubtless you have been wondering about —”
     “Flying worlds,” the kzin interrupted.
     “And Kemplerer rosettes,” said Louis. “Okay, speak to us. Why flying worlds? Somehow it doesn’t seem safe to throw habitable worlds about with such gay abandon.”
     “Oh, but it is, Louis!” The puppeteer was terribly earnest. “Much safer than this craft, for instance; and this craft is very safe compared to most human-designed craft. We have had much practice in the moving of worlds.”
     “Practice! How did that happen?”
     “To explain this, I must speak of heat … and of population control. You will not be embarrassed or offended?”…

     …“But it does relate, Speaker. Half a trillion civilized beings produce a good deal of heat as a byproduct of their civilization. We had long since run out of farming land, and had been forced to terraform two worlds of our system for agriculture. For this it was necessary to move them closer to our sun.”
     “Your first experience in moving worlds. You used robot ships, of course.”
     “Of course … After that, food was not a problem. Living space was not a problem. We built high even then, and we like each other’s company.”…
     …“Our sole and only problem, at the time of which I speak, was heat.”
     “Heat is produced as a waste product of civilization.”
     “I fail to understand,” said Speaker-To-Animals.
     “An example. You would wish a light source at night, would you not, Speaker? Without a light source you must sleep, whether or not you have better things to do.”
     “This is elementary.”
     “Assume that your light source is perfect, that is, it gives off radiation only in the spectra visible to kzinti. Nonetheless, all light which does not escape through the window will be absorbed by walls and furniture. It will become randomized heat.
     “Another example. Earth produces too little natural fresh water for its eighteen billions. Salt water must be distilled through fusion. This produces heat. But our world, so much more crowded, would die in a day without the distilling plants.
     “A third example. Transportation involving changes in velocity always produces heat. Spacecraft filled with grain from the agricultural worlds produce heat on reentry and distribute it through our atmosphere. They produce more heat on takeoff.”
     “But cooling systems —”
     Most kinds of cooling systems only pump heat around, and produce more heat for power.”
     “U-u-urr. I begin to understand. The more puppeteers, the more heat is produced.”
     “Do you understand, then, that the heat of our civilization was making our world uninhabitable?”

     “Incredible,” said Speaker-To-Animals. “Why didn’t you leave?”
     “Who would trust his life to the many deaths of space? Only such a one as me. Should we settle worlds with our insane?”…
     …They were of equal size: perhaps twice the angular diameter of the full Moon as seen from Earth. They formed a pentagram. Four of the worlds were circled by strings of tiny, glaring lights: orbital suns giving off artificial yellow-white sunlight. These four were alike in brightness and appearance: misty blue spheres, their continental outlines invisible at this distance. But the fifth …
     The fifth world had no orbital lights. It glowed by its own light, in patches the shapes of continents and the colors of sunlight. Between the patches was a black that matched the black of surrounding space; and this black, too, was filled with stars. The black of space seemed to encroach on continents of sunlight.
     “Incredible,” said Speaker-To-Animals. “I hardly dared believe it. You took your worlds with you.”
     “Puppeteers don’t trust spacecraft,” Louis said absently.…

     “But how?”
     “I had explained,” said Nessus, “that our civilization was dying in its own waste heat. Total conversion of energy had rid us of all waste products of civilization, save that one. We had no choice but to move our world outward from its primary.”
     “Was that not dangerous?”
     “Very. Then was much madness that year. For that reason it is famous in our history. But we had purchased a reactionless, inertialess drive from the Outsiders. You may guess their price. We are still paying in installments. We had moved two agricultural worlds; we had experimented with other, useless worlds of our system, using the Outsider drive. In any case, we did it. We moved our world.
     “In later millenia our numbers reached a full trillion. The dearth of natural sunlight had made it necessary to light our streets during the day, producing more heat. Our sun was misbehaving.
     “In short, we found that a sun was a liability rather than an asset. We moved our world to a tenth of a light year’s distance, keeping the primary only as an anchor. We needed the farming worlds and it would have been dangerous to let our world wander randomly through space. Otherwise we would not have needed a sun at all.”…
     …“Yes. Shortly after we finished moving our world, our sun began the process of expansion. Your fathers were still using the upper thigh bone of an antelope to crack skulls. When you began to wonder where our world was, you were searching the wrong orbits, about the wrong Suns.
     “We had brought suitable worlds from nearby systems, increasing our agricultural worlds to four and setting them in a Kemplerer rosette. It was necessary to move them all when the sun began to expand, and to supply them with sources of ultraviolet to compensate for the reddened radiation. You will understand that when the time came to abandon galaxy (when Beowulf Shaeffer discovered the galactic core was undergoing an explosion that would eventually sterilize the entire Milky Way), two hundred years ago, we were well prepared. We had had practice in moving worlds.”

RINGWORLD by Larry Niven (1970)



      What a pleasure it is to be young, and hopeful, and unsophisticated. All things are possible and we are ready, in our heart of hearts, to believe that a fairy godmother might just come and wave her wand and turn our rags into a lavish costume and our hovel into a mansion. Why shouldn’t an enchanted ring exist somewhere which will, at a rub, load our pockets with gold and jewels?
     If this has not happened, we might wistfully imagine, it is because we just haven’t been lucky enough to find the fairy godmother, or the enchanted ring, or the jinn. All we need is that incredible stroke of luck and we will have something for nothing.

     But never mind fairies, rings, and jinn; in the real World it is energy that is the prime mover of all.

     We can define energy as anything that makes it possible to do work; anything capable of bringing about movement against resistance. In that case, we see at once that there must be various forms of energy.
     Heat will make a thread of mercury rise against the pull of gravity; light will turn the vanes of a radiometer against the slowing effect of friction; electricity will turn a motor; magnetism raise a pin; a moving bat hurl a baseball over the fence; exploding dynamite lift a boulder; a hydrogen bomb in action heave a mountain.
     Heat, light, electricity, magnetism, motion, sound, chemical bonds, nuclear forces—all represent forms of energy, and all are different forms of essentially the same thing, for one form can be freely turned into another.
     Electricity moving through a wire can produce light, and a paddle rotating rapidly in water can produce heat. Magnetism can be turned into electricity; chemical explosions into motion; nuclear reactions into sound; and so on.

     We have now sharpened the problem of getting something for nothing, and can consider it realistically. Whatever we want costs us energy, for it is only energy (by definition) that will allow work to be done. To be sure, we may need other things as well, for to build a palace we need not only the energy to lift materials but also a certain architectural knowledge—but we need energy at least. Without energy, all the architectural knowledge in the world won’t budge one grain of sand.

     To get something for nothing, then, is just another way of saying that we want to create energy.

     But alas, this apparently can't be done. In the 1840s, as a result of careful experimentation and measuring, several physicists came more or less simultaneously to the conclusion that energy cannot be created (see the earlier article, Fire). One form of energy can be converted into another, or transported from one place to another, but that is as far as it can go.
     But wait, that isn’t all. If energy cannot be created, neither can it be destroyed. When energy is used, it doesn’t disappear; it merely goes elsewhere or is changed into another form. The light that streams out of a candle does not vanish; it heats up the air and surroundings about itself. The hot water in a kettle may cool down but the heat does not disappear; it is transferred to the outside world.

     To express all this, we can say: “Energy can be transferred from one place to another, or transformed from one form to another, but it can neither be created nor destroyed.”
     Or we can put it another way: “The total quantity of energy in the Universe is constant.”
     When the total quantity of something does not change, we say that it is conserved. The two statements given above, then, are two ways of expressing “the law of conservation of energy.” This law is sometimes considered the most powerful and the most fundamental generalization about the Universe that scientists have ever been able to make.
     No one knows why energy is conserved and no one can be completely sure it is truly conserved everywhere in the Universe and under all conditions. All that anyone can say is that in over a century and a quarter of careful measurement, scientists have never been able to point to a definite violation of energy conservation either in the familiar everyday surroundings about us, or in the heavens above, or in the atoms within.

     The study of changes of energy from one form to another, or the transport of energy from one place to another, is called “thermodynamics” (from Greek words meaning “heat-motion”) because the earliest studies of the sort were made on the manner in which heat flowed from one part of a system to another.
     For that reason the law of conservation of energy is sometimes called the “First Law of Thermodynamics.” It is first because it is the starting point for all else in the study. Before you can come to any useful conclusions in thermodynamics you must accept the fact that energy can neither be created nor destroyed.

     Once that is accepted, we might decide that even so we have not entirely lost. In the great game of the Universe, maybe we can still win. If we can’t get something for nothing, maybe the First Law will allow us to get something for almost nothing.
     For instance, heat is a form of energy and we can make it do work. Suppose we take a quantity of heat and change it into work. In doing so, we haven’t destroyed the heat, we have only transferred it to another place or perhaps changed it into another energy form. Why can’t we then simply gather it up wherever it is and in whatever form, and use it again, and then again, and then still again?
     If that is so, then even if we can’t create energy out of nothing, we can at least start with just a little energy and make it do any amount of work. By using the energy of a burning candle over and over we could move the world; and it would be a greedy man indeed who wouldn’t be satisfied with that or who would complain he wasn’t really getting something for nothing.

     Alas, it sounds good, but it can’t be done. The trouble is that once energy is used, it still exists, yes, but it is spread out thinner. The heat of the burning candle spreads out into the air all about and into all the things the warmed air comes into contact with.
     To put that heat back to work again, it has to be collected from the surroundings and concentrated again so that the candle flame is re-created. Heat can be concentrated, energy can be collected—but it takes energy to do so, invariably more energy than the energy you are concentrating and collecting.
     What is the sense in using fresh energy to collect dissipated old energy, and using more to get less? You might as well use the fresh to begin with. It would be more economical.
     In short, in your attempt to use the same old energy over and over again, you would be using up more energy than if you made up your mind to use each bit of energy just once.
     You can’t get round it. What the First Law of Thermodynamics really means is that in the great game of the Universe, you can't win! You can’t get something for nothing, or even for nearly nothing.

     This is a hard thing to accept and the indomitable human spirit is bound to fall back to the next line of defense. If it is true that you can’t win, then perhaps you can at least break even. In other words, given a certain supply of energy, perhaps you can at least turn it all into work.
     This problem came up when the steam engine was first developed in the eighteenth century. To begin with, the early engines were extremely inefficient. Great quantities of fuel were burned but most of the energy was wasted in heating up the world generally; very little ended in such useful work as pumping water.
     Naturally, one assumes that if one could only cut down on friction, prevent the flow of heat in unwanted directions, make the general design more efficient, one could eventually build a machine that would turn all the energy into work.

     The first person to point out that this was not so, that even a perfect steam engine could not turn all energy into work, was a French physicist named Nicolas Léonard Sadi Carnot.
     He demonstrated, in 1824, that the steam engine did work because part of its system was quite hot (the part that consisted of steam) and part was quite cold (the part that consisted of the cold water that condensed the steam). The heat energy present was, in other words, in greater-than-average concentration in one place and in less-than-average concentration in another. We can quite easily measure the heat-concentration, which we usually call “temperature.” The fraction of the energy that can be turned into work by a steam engine depends, then, upon the difference in temperature between the hot part of the system and the cold part.
     The greater the difference in temperature between two parts of the same system, the greater the fraction of the heat energy we can tum into work. This difference in temperature becomes a maximum when all the heat in the system is concentrated in one part and none is concentrated in another.
     The trouble is that physicists have shown it is impossible to concentrate all the heat in a system in one particular part of it. Even to approach total concentration takes an enormous effort.
     If a steam engine uses ordinary steam for its hot part and ice water for its cold, the difference in heat concentration or temperature is such that only 27 per cent of the total heat energy can be converted into work, even if the steam engine were perfect in every other respect: if it lost no heat to the outside world, if there were no friction, and so on.
     This is true for any system which uses energy of any kind. To make any system useful, to allow it to turn energy into work, there must always be a difference in energy concentration in different parts of the system. There must be a high energy concentration here and a low energy concentration there, and the work to be gotten out of the system depends not on the total energy, but on the difference in energy concentration within the system.

     We can say: “No device can deliver work unless there is a difference in energy concentration within the system, no matter how much total energy is used.”
     That is one way of stating what is called the Second Law of Thermodynamics.

     Since there is never any way of reaching an ultimate difference in energy concentration, never any way of putting all the energy into one part of the system, and none into another, we can never turn every bit of the energy of a system into work. Some of the energy always manages to get away from us without being turned into work.
     What the Second Law tells us, then, is that in the great game of the Universe, we not only cannot win, we cannot even break even!

     Given energy at two different levels of concentration, we will note as part of the common experience of mankind that there is always a spontaneous transfer of energy from the place of higher concentration to the place of lower concentration; and never vice versa.
     For instance, heat will flow, of itself, from a hot body into a cold body, but not vice versa. Water will spontaneously flow from hilltop to hill bottom, but not vice versa.

     We can say: “Energy will always flow spontaneously from a point of high concentration to one of low concentration.”

     Physicists can show that it is because this statement is true that devices will convert energy into work when there is a difference in energy concentration within the system. It is the spontaneous energy flow from high to low that produces the work.
     The statement about spontaneous energy-flow is therefore another way of expressing the Second Law.

     But work is never done instantaneously. It invariably occupies time. What happens during that time?
     Suppose we consider a steam engine with a portion of itself that is at high heat-concentration and another portion that is at low heat-concentration. By the Second Law, the heat flows from high to low and that heat flow is turned into work. If the heat flow happened all at once and was converted into work in zero time, then we would at least get all the work out of the energy flow that we could.
     But it takes time, and as time passes, some of the heat in the high-concentration portion is pouring out into other parts of the Universe. Meanwhile heat from other parts of the Universe is pouring into the low-concentration portion. In other words, the hot part of the steam engine is cooling faster than you would expect just from its transfer of heat to the cold portion. The cold portion, on the other hand, is warming faster than you would think just from its receipt of heat from the hot portion.

     The difference in temperature is dropping faster than you would expect from the work done.

     Since the amount of work you can get out of any device depends upon the difference in temperature, it would seem that the quantity of energy capable of conversion into work decreases with time. The quantity of energy not capable of conversion into work increases with time.
     A German physicist, Rudolf Clausius, pointed this out in 1865. He invented a quantity consisting of the change in heat with time, divided by temperature, and called it “entropy.” He showed that entropy was a measure of the quantity of energy not capable of conversion into work.

     In any physical change that takes place by itself the entropy always increases.

     In the case of the steam engine this comes about because there is heat flow to and from the Universe. If a boulder rolls down the mountainside there is increase of entropy because of friction and air resistance. An electric current flowing from one pole of a battery to another encounters resistance from whatever it passes through and hence experiences increase in entropy.
     To be sure, we can imagine ideal cases. A hot and cold area might be perfectly insulated so that heat flows only from one to the other; a rock may fall through a perfect vacuum; an electric current may flow through a perfect conductor. In all cases. there is no entropy increase.

     Approximations to such ideals (a planet moving through outer space; an electric current moving through a superconducting metal) are highly special. If we consider the ordinary systems we work with, we can say: “In any energy transfer, there is an increase in entropy.”
     This, too, is a way of expressing the Second Law.
     In fact, a good brief way of stating the First and Second Laws of Thermodynamics is: “The total energy content of the Universe is constant and the total entropy is continually increasing.”
     This means that although the Universe never loses any energy, less and less of that energy can be converted into work as time goes on.

     The Second Law can be interpreted in terms of atomic theory, and the Scottish mathematician and physicist, James Clerk Maxwell did so in the 1860s.
     Heat can be viewed, for instance, as being represented by the random movements of the separate particles (either atoms or molecules) making up some body of matter. The greater the average velocity of particle motion, the higher the temperature.
     When two particles collide, they bounce apart and some momentum (mass multiplied by velocity) is transferred from one to the other. The transfer can take place in any fashion, but the most likely result is that the particle with more momentum will lose, and the particle with less momentum will gain. If all the particles are the same size, we can say that the faster particle will slow down after collision, the slower particle speed up. It is possible, of course, that the fast particle may just happen to bounce off faster, and the slow one slower, but it is unlikely.

     (If a rich man and a poor man put all their money in a single pile and each grabbed what he could, the chances are the rich man would end up with less money than he started and the poor man with more.)

     Where more and more particles are involved, it becomes less and less likely that a large proportion of the fast particles will all bounce off slow particles and end by moving still faster.
     Let us suppose there is a one-in-ten chance that a fast particle will bounce off a slow particle and become faster in the process. The chance of six fast particles all bouncing off faster from six slow particles will be one in ten times ten times ten times ten times ten times ten, or one in a million. The chance of ninety-six fast particles all bouncing off faster at the same time from ninety-six slow particles would be only one in a trillion-trillion-trillion-trillion-trillion-trillion-trillion-trillion.
     Suppose you took a kettle of water containing uncounted trillions of particles and put it over a fire. It might be that more than half the hot, very fast-moving particles in the hot gases of the fire might strike the kettle and bounce off still faster-moving. In that case, the water in the kettle would get cooler while the fire would get hotter. This is possible, but the chance of its happening is so small that there is no way of writing it in ordinary figures. If you tried to write: one chance in such-and-such a number, the surface of the earth wouldn’t be large enough to hold all the zeros you would have to write down for “such-and-such a number.”

     That is why the entropy of the Universe constantly increases—because the collisions of atoms and molecules tend always to chop off energy extremes. Wherever energy is more concentrated than usual, that concentration drops; where it is less concentrated than usual, that concentration rises.

     It is also possible to think of entropy in terms of “order” and “disorder.” Something is orderly when its individual parts are arranged according to some simple rule we can quickly grasp. We can then predict from each part something about the next part. The simpler the rule, the easier the prediction, and the greater the order.

     Consider a deck of cards. You might have it arranged as follows: ace of spades, two of spades, three of spades, and so on, followed by hearts, clubs, and diamonds, each suit arranged from ace to king. That is very orderly, for if you show me any card (the seven of clubs, for instance), I will instantly tell you the next card (the eight of clubs).
     Or you might arrange the suits in another order; or each suit might run from king down to ace; or you might have the four aces in a certain order of suits, then the four twos, then the four threes, and so on. These all represent order.
     We might also arrange the cards so that they are alternately red and black without any consideration for numbers or suits. We can then still make some prediction. If I am shown the seven of clubs, I know the next card must be a red one. That is some information, but not much, so that the red and black in alternation still represents some order, but not much.

     It should be obvious, though, that if you consider all the possible arrangements of the cards in a deck, the number of arrangements that allow you to make predictions about each card from the one before is a very small, a very small, portion of the whole.

     Suppose you shuffle a deck in such a way that it can take on any arrangement. The chances that the arrangement will be one of the few that will allow even a small amount of prediction and will therefore have at least a small amount of order is not great. There are so many utterly disorderly arrangements possible that one of those is just about sure to be obtained.
     That is why, when you shuffle cards thoroughly, you would be most astonished to find, when you were through, that the cards have ended up arranged ace of spades, two of spades, three of spades, and so on—or even red-black-red-black-red-black and so on.

     Let us take another example from the world of life. When a platoon of soldiers marches by four abreast and in perfect step, that represents a high degree of order. When we see one group of four soldiers move by, we can predict exactly when the next group will pass by, how many will be in the group, whether they will be moving their right foot or left at the moment of passing, and so on.
     Other examples of order would have soldiers moving two abreast; or in single file; or one row marching and the next skipping, in alternation; and so on.
     But suppose you considered all the different possible ways in which the individual soldiers of a platoon could pass by if each consulted his own tastes only and paid no attention to the others. Some might be strolling, some walking, some running, some hopping perhaps, some in this direction, some in that. The number of ways of passing without any perceptible order is much, much higher than the number of ways with order.
     Consequently, if you told the soldiers of a platoon to move from one point to another at will, you would be utterly surprised if, when each did exactly as he pleased, they just all happened to move four abreast and in step. In fact, if they were already moving four abreast and in step and were suddenly told to do as they pleased, you would expect the entire platoon to break formation and become disorderly.
     In short, in every possible situation you can think of, the number of ways of being disorderly is much, much, much, much greater than the number of ways of being orderly.

     This is exactly comparable to the fact that the number of ways in which extremes get chopped off in the random collisions of particles is much, much, much, much greater than the number of ways in which extremes get more extreme.

     Another way of stating Second Law, then, is: “The Universe is constantly getting more disorderly.”

     Viewed that way, we can see Second Law all about us. We have to work hard to straighten a room, but left to itself, it becomes a mess again very quickly and very easily. Even if we never enter it, it becomes dusty and musty. How difficult to maintain houses, and machinery, and our own bodies in perfect working order; how easy to let them deteriorate.
     In fact, all we have to do is nothing, and everything deteriorates, collapses, breaks down, wears out, all by itself—and that is What Second Law is all about.
     You can argue, of course, that the phenomenon of life may be an exception. Life on earth has steadily grown more complex, more versatile, more elaborate, mom orderly, over the billions of years of the planet’s existence. From no life at all, living molecules were developed, then living cells, then living conglomerates of cells, then worms, vertebrates, mammals, finally man. And in man is a three-pound brain which, as far as We know, is the most complex and orderly arrangement of matter in the Universe. How could the human brain develop out of the primeval slime? How could that vast increase in order (and therefore that vast decrease in entropy) have taken place?
     The answer is it could not have taken place without a tremendous source of energy constantly bathing the Earth, for it is on that energy that life subsists. Remove the Sun and the human brain would not have developed —or the primeval slime, either. And in the billions of years that it took for the human brain to develop, the increase in entropy that took place in the Sun was far greater—far, far greater—than the decrease represented by the evolution of the brain.

     But where did it all start? If the Universe is running down into utter disorder, what made it orderly to begin with? Where did the order come from that it is steadily losing? What set up the extremes that are steadily being chipped away?
     Scientists are still arguing the point. Some think the Universe originally had its matter and energy all smashed together into one huge “cosmic egg”—a situation something like a tremendous deck of cards all arranged in order. The cosmic egg exploded and ever since, for billions of years, the Universe has been running down; the deck of cards is being shuffled and shuffled and shuffled.
     Others think that there are some processes in the Universe that spontaneously decrease entropy; some natural process which unshuffles and re-orders the cards. We don’t know what it can be, perhaps because it takes place under conditions we cannot observe and cannot duplicate in the laboratory—say, in the center of exploding galaxies. Perhaps, in that case, as some parts of the Universe run down, others build up.
     Then again, it may be that once the Universe runs down, the random collisions of particles may—after umpty-ump years—just happen to bring about an at least partial unshuffling. After all, if you shuffle cards and shuffle cards and shuffle cards ceaselessly for a trillion years, you may end up with an arrangement possessing at least some order, just by the laws of chance.
     Once that happens, the Universe begins to run down again at once. Perhaps, then, we live in a Universe that was partially unshuffles after a quadrillion years of having been run-down. We are now running down again and after the Universe is all run-down, another quadrillion years or another quadrillion quadrillion years may see a section of it unshuffled once more.
     Stars and galaxies will then re-form, and life may be established here and there, and finally some science writer will sit down and begin to wonder again where it all came from and where it will all end.

From YOU CAN'T EVEN BREAK EVEN by Isaac Asimov (1970)

If someone points out to you that your pet theory of the universe is in disagreement with Maxwell’s equations—then so much the worse for Maxwell’s equations. If it is found to be contradicted by observation—well these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation.

Sir Arthur Stanley Eddington Gifford Lectures (1929)

A good many times I have been present at gatherings of people who, by the standards of the traditional culture, are thought highly educated and who have with considerable gusto been expressing their incredulity at the illiteracy of scientists. Once or twice I have been provoked and have asked the company how many of them could describe the Second Law of Thermodynamics. The response was cold: it was also negative. Yet I was asking something which is about the scientific equivalent of: Have you read a work of Shakespeare's?

Baron C.P. Snow The Two Cultures: The Rede Lecture (1959)

It is a remarkable fact that the second law of thermodynamics has played in the history of science a fundamental role far beyond its original scope. Suffice it to mention Boltzmann’s work on kinetic theory, Planck’s discovery of quantum theory or Einstein’s theory of spontaneous emission, which were all based on the second law of thermodynamics.

From Ilya Prigogine Nobel lecture 'Time, Structure and Fluctuations'

Nature prefers the more probable states to the less probable because in nature processes take place in the direction of greater probability. Heat goes from a body at higher temperature to a body at lower temperature because the state of equal temperature distribution is more probable than a state of unequal temperature distribution.

Max Planck Eight Lectures on Theoretical Physics (1915)

Since a given system can never of its own accord go over into another equally probable state but into a more probable one, it is likewise impossible to construct a system of bodies that after traversing various states returns periodically to its original state, that is a perpetual motion machine.

Ludwig Eduard Boltzmann 'The Second Law of Thermodynamics', Populäre Schriften (1886)

There is only one law of Nature—the second law of thermodynamics—which recognises a distinction between past and future more profound than the difference of plus and minus. It stands aloof from all the rest. ... It opens up a new province of knowledge, namely, the study of organisation; and it is in connection with organisation that a direction of time-flow and a distinction between doing and undoing appears for the first time.

Sir Arthur Stanley Eddington The Nature of the Physical World (1928)

It will be noticed that the fundamental theorem proved above bears some remarkable resemblances to the second law of thermodynamics.

Both are properties of populations, or aggregates, true irrespective of the nature of the units which compose them; both are statistical laws; each requires the constant increase of a measurable quantity, in the one case the entropy of a physical system and in the other the fitness, measured by m, of a biological population. As in the physical world we can conceive the theoretical systems in which dissipative forces are wholly absent, and in which the entropy consequently remains constant, so we can conceive, though we need not expect to find, biological populations in which the genetic variance is absolutely zero, and in which fitness does not increase.

Professor Eddington has recently remarked that “The law that entropy always increases—the second law of thermodynamics—holds, I think, the supreme position among the laws of nature.” It is not a little instructive that so similar a law should hold the supreme position among the biological sciences.

While it is possible that both may ultimately be absorbed by some more general principle, for the present we should note that the laws as they stand present profound differences—-(1) The systems considered in thermodynamics are permanent; species on the contrary are liable to extinction, although biological improvement must be expected to occur up to the end of their existence. (2) Fitness, although measured by a uniform method, is qualitatively different for every different organism, whereas entropy, like temperature, is taken to have the same meaning for all physical systems. (3) Fitness may be increased or decreased by changes in the environment, without reacting quantitatively upon that environment. (4) Entropy changes are exceptional in the physical world in being irreversible, while irreversible evolutionary changes form no exception among biological phenomena. Finally, (5) entropy changes lead to a progressive disorganization of the physical world, at least from the human standpoint of the utilization of energy, while evolutionary changes are generally recognized as producing progressively higher organization in the organic world.

Sir Ronald Aylmer Fisher The Genetical Theory of Natural Selection (1930)

Joke Laws

The joke version of the Three Laws of Thermodynamics are:

  1. You can't win, you can only break even.
  2. You can only break even at absolute zero.
  3. You can never reach absolute zero.

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