‘The Law of Large Numbers’ and ‘Central Limit Theorem’ are representations of Probability Theory. According to Jaynes, the behaviors of any system in question appear “random” because we are not privy to the complete composition, behavior, and influences upon that system. Given many examples of the given system’s behavior, however, certain trends stand out- characteristics more essentially of the system than others; this may be more accurately stated: “characteristics definitive of the system”.

Obviously, Probability Theory was a coping method acquired by the developing ocean beast simply to function more effectively in its unfurling World.

More strangeness radiates from the unusual, inexplicable asymmetries of Thermodynamics when ’statistical mechanics’ is regarded in light of this take on Probability. Deep quantum understanding and non-relativistic physics do a fine job of indicating the fundamental possibility or truth of bidirectional “time”. However, action in the universe proceeds unidirectionally; this is a basic tenet of Thermodynamics. How curious that this framework of understanding, to our best knowledge, is inseparable from the epistemological workings of Probability.

bene signori, buttiamo all’aria i nostri libri di fisica. ricordate quando, chini sui banchi di scuola, studiavamo le tre leggi della termodinamica? la seconda legge della termodinamica recita così: “in un sistema isolato l’entropia è una funzione non decrescente nel tempo.” (n.d.r dicesi entropia il cosidetto grado di disordine del sistema). in più, un altro principio basilare della fisica è che il tempo non è una freccia che può andare solo in avanti, ma piuttosto è un fiume che può andare avanti ed indietro. come si concilia il fatto che l’entropia aumenta (in funzione del tempo) anche nel caso in cui il tempo invece di andare avanti va indietro? in realtà le due cose non si conciliano proprio tanto bene. ecco la necessità di creare in fisica un cosidetto paradosso : il paradosso di loschmidt.

quindi prendete il vostro caforio-ferilli, fatene barchette e dopodichè mettetelo nella carta riciclata. secondo una ricerca pubblicata qualche giorno fa sul physical review letters, lorenzo maccone del qubit group (n.d.r si siori e siori… è un italiano) ha teorizzato che, se andiamo a studiare i fenomeni entropici a livello quantistico, non è vero che l’entropia aumenta in ogni trasformazione. è vero invece che aumenta nei fenomeni che lasciano traccia di se stessi, ma diminuisce nei fenomeni che avvengono senza lasciarci informazione. esistono cioè, secondo maccone, dei fenomeni non osservabili, nei quali però l’entropia è in diminuzione e non in aumento…

curiosi di saperne di più? ecco il paper originale…

When thinking of science the first scientific principle that comes to many peoples minds are the laws of thermodynamics. Just as thoughts on the existence of God are foundational to theology (see Principia Theologica), the foundational thoughts of science generally conjure up vivid imagery of scientific laws and white lab coats.

Why is it that this is the place that the public comes to first when entertaining thoughts of science? Perhaps they feel a sense of definitiveness when discussing scientific matters. Maybe science provides a place where the average person can turn to derive truth about the world around us.  Somehow, if a single piece of evidence that was scientifically found (that is found via the laws of scientific inquiry) is cited, the discussion has a new sense of authority derived from Ph.D.s in a lab somewhere. Apparently, the common man has the idea that those in the process of unaided (unaided in the sense that this is the forefront and the material cannot be gained through the written word) discovery in the lab are able to achieve such a high standard of pure fact as to not be questioned. Even when questioned these scientists work on projects that are so immense and complex that if this is what they say, who are we to really cast doubt on their conclusion. These people have spent their life (or at least a large part) studying the very principle on which the conclusion is based and must be closer to correct than my thought process can attain. This is an easy way for the average person to categorize many aspects of science and scholarship in general. Whether this is a warranted approach to take, I leave to you to question.

How does this relate to thermodynamics? Thermodynamics is often a set of scientific ideas that is brought to light when science is discussed by the common man to provide a sense of factual authority. The foundational character of these laws is obvious and indeed they have been well tested and proven correct, to the point of being granted the status of a scientific law, the laws of thermodynamics. So next time you are tempted to invoke the laws of thermodynamics to support your argument as to why the wooly mammoths of the northern hemisphere preferred to roam gregariously or your thoughts about how the future of sub-oceanic dwellings will rely on renewable resources you will have an idea as to if the laws of thermodynamics truly apply to your discussion.

What does the word thermodynamics even mean? Well you might not be acquainted with a formal definition of thermodynamics but it comes down to the mechanical action produced by heat. How does this have such wide applicability? The various fundamental laws of thermodynamics are so foundational to many scientific principles you will see how it is possible for it to creep up in discussions. While there are certainly limits on what classical thermodynamics can explain it provides a robust description of the properties of matter in bulk such as pressure, temperature, volume, electromotive force, magnetic susceptibility, heat capacity etc.[1] Most are familiar with the three laws of thermodynamics and are happy to just negate the fourth. Ok there really isn’t a fourth law just what is known as the zeroth law which makes four laws of thermodynamics.

Thermodynamics was essentially created by Carnot (you may be familiar with the Carnot engine). He laid out his formulations in his paper entitled “Reflections on the Motive Power of Heat.”[2] Much has been put forth in the field of thermodynamics since that time. Anyone who has studied statistical mechanics can tell you that there are many facets to this subject and it can be quite difficult.

The four laws of thermodynamics are seemingly broad and general. Maybe they are even self-evident. Here is what we have:

0^th law of thermodynamics: If A is in thermal equilibrium with B, and B is in thermal equilibrium with C, then A is in thermal equilibrium with C.[3] Stated another way that is if A=B and B=C then A=C. In mathematics, this is known as the property of transitivity.[4] You are probably wondering why anyone would start the numbering at zero. Well, you’re not alone. It seems that this law was more elementary than the other established laws of thermodynamics at the time and so the proper place for it was not the fourth law but the zeroth law. What does it mean to be in thermal equilibrium? It is a situation in which two objects would not exchange energy by heat or electromagnetic radiation if they were placed in thermal contact. As you may have guessed, temperature is the property that determines whether an object is in thermal equilibrium with other objects.

1^st law of thermodynamics: The internal energy of an isolated system is constant. This is also seen in the formula U=q+w. where U is the change in internal energy, w is the work done on a system, and q is the energy transferred as heat to a system.[5] Here we could get into many discussions about definitions, which I am going to skip (feel free to comment if you would like further explanation).

2^nd law of thermodynamics: The entropy of an isolated system increases in the course of a spontaneous change. That is the change in the total entropy (S) is > 0.[6] This is the law most often cited. You will hear it invoked in everything from evolution to ice crystals. It was explained to me during the course of my education that the entropy of a system relates to the amount of information that is available to the system. You can think of this in terms of possible states that something could inhabit. If there are a large number of possible states then the entropy is large. Undoubtedly, this does injustice to some aspect or area to which the second law is applied. It provides a convenient construct with which to work.

3^rd law of thermodynamics: The absolute value of the entropy of a pure solid or a pure liquid approaches zero at 0K. One could state this mathematically as lim(S)=0 at T goes to 0. This is the Planck formulation of the third law.[7] The third law is usually overlooked in most texts. By far, attention is placed on the first and second laws.

Other concepts have been put forth as candidates as fourth, fifth, and sixth laws but they remain unaccepted in general and are more controversial. I am not aware of any scientist who questions the 0 through 3^rd laws.

We have covered the laws of thermodynamics and hopefully broadened our understanding of these principles of science. Next time you are tempted to utilize a scientific law to support your argument please try to use it in context and please be prepared to demonstrate how, from the very law itself, you can rightly use it.

[2] Carnot, S.; Reflexions sur la puissance motrice du feu, Bachelier, Paris, 1824.

[3] Serway, Raymond A.; Jewett, John W. Jr.; Physics for Scientists and Engineers; 6^th ed. Thomson Brooks/Cole: Belmont, CA. 2004 p. 582

[4] Papantonopoulou, Aigli; Algebra pure and applied; Prentice Hall: Upper Saddle River, NJ. 2002 p. 8

[5] Atkins, Peter; de Paula, Julio; Physical Chemistry; 7^th ed. W. H. Freeman and Co.: New York, NY. 2002 p. 35

[6] Ibid, p. 92

[7] Planck, M. Thermodynamik, 3^rd ed., Veit & Co., Leipzig, 1911 p. 279

As I see it, the second law states that in every process the distribution of energy in the universe must move closer to the most probable distribution.  The maximum entropy of the universe is achieved when it reaches the configuration that can be achieved the greatest number of ways.  S=k ln W.  This seems to imply that the universe is fundamentally random.  That is, it is ruled by pure, raw probability.  Is there any way out of this implication? 

When I roll a pair of dice, I am much more likely to roll a seven than a two or a twelve.  This can be explained by noting that any specific configuration (die A=2, die B=3 or die A=6, die B=6) is equally likely, but the sum of seven can be achieved in a greater number of ways (6) than a sum of 12 (1).  To recognize that an outcome of seven is more likely is to imply that for all practical purposes, the system is fundamentally random.

It seems that the same must be true of the universe as a whole.  To recognize that the universe is moving toward a most probable state (of maximum energy dispersion) implies that events are fundamentally random, like rolling dice.  This randomness, it would seem, must over-rule any deterministic processes, such as macroscopic physical interactions.  The second law seems to present the universe as a great set of dice that takes billions of years to settle down and reveal its predictable, most probable sum, regardless of what happens in the interim.

BUT, we may assume that the dice are not truly random, that if we knew everything about the dice and their environment, we could predict the outcome of every roll.  Why then do the rolls follow the laws of probability?  Why do they “act” as if they were truly random?  Apparently, deterministic systems can follow the laws of probability.  

Why?  In this case, it is simply that there is no cause that would weight any one specific outcome any more than any other.  But why is that?  It seems that it has to do with the level of complexity of the system:  air currents, starting positions, variations in height of throw, etc.  all interact to change the outcome in such a way that any biases are erased.  Is the same true of the universe?

Are all specific configurations of the energy in the universe equally likely?  Does the tremendous complexity of the interactions and sequences of events shuffle the deck so well that any outcome is equally likely, and therefore the dominant configuration inexorably reveals itself? 

In other words, I might hold both dice with the 6 upright, but it doesn’t matter.  I still roll a seven.

So perhaps entropy does not imply fundamental randomness, only tremendous complexity.

But what about us?  Are we free, or are we bound to this entropic journey toward the predetermined distribution?  I suppose we could still be free, but our actions are swamped out on a universal scale.  But then what about the local scale.  There, our actions are certainly not swamped out, and yet the second law holds there as well.  We may decrease entropy in a particular system, but it will then increase elsewhere.  Perhaps we can apply the same explanation as in the larger case, that is, it has to do with the tremendous complexity of the countless interactions between the system and its surroundings–interactions that I am unable to control.

Just thinking out loud.  What do you think?

The law that entropy always increases holds, I think, the supreme position among the laws of Nature. 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, The Nature of the Physical World (1927)

This arena today sees the clash of two fundamental concepts of science, which one will emerge victorious? In the Blue corner we have the Second Law of Theeeeeeermodynamics! Weighing in at hefty 158 years old and representing a foundational view of how energy is represented and the ability of systems to do useful work it is considered unalterable and universal in it’s application. In the Red corner is the Theory of Evolution by Nnnnnnnnnnnatural Selection! Weighing in at only 150 years this theory has become a cornerstone of modern biology and allows an unprecedented ability to combine disparate fields into a unified whole, a biological theory of everything.

Evolution comes out swinging jumping straight to the thrust of the argument and serving up the whole conclusion of the theory. “Variation in species is acted upon by natural means to produce, over geological time, changes that increase the adaptation of the organism to it’s environment and can thus cause the creation of new species.”, the Second Law of Thermodynamics staggers from the blow but shakes it off quickly and returns it’s own salvo. “Entropy in a system will increase over time, order cannot come from disorder and increasing information content of a species DNA through random processes represents an increase in order.”, Evolution is down! Can this be the K.O. for the theory? Wait! The Ref is stepping in, Second Law has made an illegal move!

The Ref has made his ruling, Second Law only applies to either the Universe as a whole or energetically isolated subsystems, Evolution considered on it’s own is not an isolated system and so the argument is invalid. The Second Law of Thermodynamics is disqualified! What an humiliating development. Evolution wins by default but fans of the Second Law do not look happy, it’s clear that this ain’t over folks.

The Post-bout Wrap-up:

“Well Jim, Evolution started strong but didn’t even get a chance to follow-up. The Second Law made a good attempt to hit back but fumbled, what happened?”

“That’s right Bob, this was a case of a poor matching of opponents. Fans love to think about these two giants battling it out but they are really on the same side and it’s just not natural for them to be in conflict.”

“You’re right on the nose there Jim, like Superman vs Batman, it’s just not right. The fans are thinking too narrowly in this instance, the Second Law is very specific in the areas it can be applied to. It can apply to the entropy state of the entire Universe as this can be considered the ultimate set of all things and so by definition is a closed system with no energy input from an external source. Or it can be applied to systems that are self contained and also do not have access to an external source of energy with which to reverse it’s entropic progression. Evolution meets neither of those categories, it does not cover the entire Universe and it is not an isolated sub-system as energy external to it is able to be used to build organisms and drive variation. The majority of life on Earth owes it’s existence to the energy provided by the Sun and this is a resource that can inject more than enough energy into the system to allow all the processes we see.”

“I know, right? No doubt about it Bob, this is a fight that’s just not meant to happen. I think though that we will still see confused fans trying to force this conflict for a long time to come.”

“I have to agree with you there Jim, well next up is the fight between Astronomy and Astrology, what do you think will happen?”

“You’re kidding right Bob?”

Given the milestones reached this year, the 200^th birthday of Darwin and the 150^th anniversary of his revolutionary and unfortunately still controversial theory, expect to see a few more evolution based posts than I usually allow myself. This satirical rant was inspired by a letter I happened read in the Waikato Times dating back to December 7, 2007, old but it riled me up. The letter can be found Here and is the second from the bottom. It’s ignorance is excusable, I myself am ignorant of a great many things, but it’s the stupefying arrogance that really bugs me, in the letter the writer relates how in school he/she was taught about both thermodynamics and evolution. In his view the two were incompatible and so the teacher must have been espousing evolution in blatant disregard of science thus turning evolution into a religion. The mere possibility that the writer actually misunderstood both concepts never enters his/her head.

:: :: :: :: :: :: :: :: :: ::

Here’s something that’s in textbooks, but they tend to leave out lots of little bits and pieces, the way I used to when I made sandwiches for Arby’s one summer. Not that you’ll get the full story here, either. But you’ll get a more satisfying hunk of disgusting, gray, dampish meat clumps, and a little piece of metaphorical lettuce, too.

When two particles interact, Newton’s third law postulates

,

where means, “the force particle ‘1′ exerts on particle ‘2′.” This is useless knowledge unless you have some sort of interpretation of force. Force is defined by the second law

.

Someone once tried to tell me that Newton’s second law is not just a definition of force, but has some deeper meaning. I think they were lying because they wanted to seduce me. (No luck there, Grandpa!)

So Newton’s second law defines force, and is meaningless without some rules about what force should do. For example, if you say that a particle with absolutely nothing around to interact with must have no force on it, you’ve said something about force and now Newton’s second law can step in. In this case it says

so that a free particle does not accelerate. (That’s Newton’s first law. However, there are philosophical problems with such a conclusion. If there is nothing around for the particle to interact with, then how could you tell whether or not it’s accelerating?)

The third law, a rule about force, is lame without a definition of force. The second law, a definition of force, is lame without any rules. They were made for each other, like rabbits and lawn mowers (but with less of those annoying screaming sounds). By combining Newton’s second and third laws for two interacting particles, we get

By the transitive law

or

and assuming that mass is constant

for arbitrary times and . Using the fundamental theorem of calculus and the definition

yields

again for arbitrary times . What we’ve discovered is that if you take measure the quantity

at any two times, you will always get the same answer. That quantity is called “momentum”, and the fact that it doesn’t change is called “conservation of momentum.”

We haven’t proved it to be true. Science doesn’t prove anything to be true. What we’ve proved is that it follows from certain assumptions. If we make some measurements and find that the “law” of momentum conservation doesn’t hold, there are a few possibilities that I can think of:

1. We made a mistake with the measurements. Our apparatus is broken, or we did something dumb like converting units wrong, etc.
2. Newton’s laws are wrong. They do not accurately represent the interaction of particles.
3. We were not doing an experiment with exactly two particles. (That is the only situation for which we did the proof. Maybe the theorem failed because there was some third particle around that we didn’t see, or maybe the objects in our experiment were not particles, but instead more complicated composite things that are not bound by Newton’s laws.)
4. The mass of the particles is not constant. (Remember that this was an assumption used in the proof).

Maybe you can think of other explanations. I can’t at the moment. But it turns out that these explanations can account for a lot of situations. Item (1) comes up frequently enough – it’s just a fact that people make misteaks.

Explanation (2) is sometimes correct as well; Newton’s laws aren’t true. Special relativity modifies them. General relativity pretty much scraps them (er, don’t quote me on that). In quantum mechanics, momentum is important, but no longer has an interpretation as mass*velocity. In fact it (mathematically) no longer has any “interpretation” – instead it is its own primary quantity, equally as fundamental to the theory as the concept of “position”. It even steals “position”’s claim to the letter ‘p’. Momentum is nobody’s bitch.

Complication (3), that we aren’t using two isolated particles, arises in practice as well. There are obvious examples, such as everything. When I drop my spoon, it starts gaining momentum until it hits the floor, when it loses momentum. Then I pick it up and lick it clean, and its momentum bounces all around as I lick more and more violently. All this occurs because a spoon is not a system of two particles.

There are more interesting (but less tasty) examples where the “not-two-particles” explanation manifests. Take two charged nonrelativistic, non-quantum particles and let them interact. They won’t conserve momentum. The reason is charged bodies generate electromagnetic fields, and our assumption that the only things around are the charged bodies fails. The electromagnetic field can carry its own momentum, although technically in order to break the proof all it would have to do is exist. In another example, Wolfgang Pauli was thinking about another case in which momentum is not conserved – beta decay. He decided options (1), (2), and (4) were not for him, and instead guessed that beta decay must involve some previously-unseen stuff. That stuff is the neutrino.

Finally, explanation (4), that the mass is variable, is not something that occurs in practice to my knowledge, but it could. Of course, if a meteor shooting through space hurls off some of its rock-junk when it get near the sun and heats up, then the meteor’s mass decreases. But that doesn’t count because it’s not two particles, and also momentum actually is conserved in that situation if you consider the momentum of the space junk, the meteor, and the sun altogether. What I mean is that I’m not aware of any evidence that fundamental particles can have variable mass.

What if there are three particles? Can we prove that momentum is still conserved if we define momentum to be

No. We can’t because we could only prove anything by getting some knowledge about force from Newton’s third law. But Newton’s third law is only telling us the story for two lone particles. When there’s a third, all bets are off. However, there is another assumption that we usually take along with Newton’s laws, often implicitly. This is that forces add linearly.

Imagine conducting an experiment with particles 1 and 2, and no particle 3 around. Measure the force on particle 1. Now conduct a new experiment where particle 1 does the same thing it did before, but particle 2 is absent, and particle 3 is around doing whatever it wants. Again, measure the force on particle 1.

We assume that if we conduct a third experiment with particles 1, 2, and 3 all together, the force on particle 1 will be the sum of the forces in the first two experiments.

With this law that forces add linearly, we can prove momentum conservation for three particles. And if we assume forces continue to add in the simple manner for any number of particles, then momentum conservation also holds for any number of particles.

tomorrow: energy

Can we “save” energy? Of course not. We cannot “save” energy as the first law of thermodynamics explains: energy is conserved no matter what we do. The only thing we can do to help solve the planet’s energy problem is to reduce the speed with which we degrade the quality of the energy sources available to us. And indeed the best way to accomplish that is to “use” as less as possible of this high quality energy. Examples of high quality energy are fossil fuels, nuclear fuel, solar or PV energy, wind energy etc. The common factor in all these different sources is that the energy is concentrated in a relatively small volume. A typical example of low quality energy is heat (most of the times at least). Why? Heat is difficult to maintain and tends to leak away and thus disperses over a large volume. One joule of heat remains one joule of energy regardless whether the volume in which it is contained is one cubic cm or the entire galaxy. So where is the problem? Here is where the Second Law of thermodynamics kicks in. High quality energy conditions have a low entropy value whereas low quality energy has a high entropy value. The entropy law teaches us that with each “use” of energy the entropy increases (and thus the quality is decreasing) and that there is no recovery back from that. In other words quite a fundamental limitation and no technology can help you overcome that Second Law!

There are two ways how we can help ourselves to slow down the ever ongoing energy quality degradation.

1) The quickest one is simple: reduce the need for energy as much as you can! Let’s have a look at the energy ‘consumption” breakdown (IEA 2008):

For example, as long as the fuel “consumption” in the USA per km is still about 40% higher than that in Europe it is clear where the focus needs to be. Also, note that about 20% of the total energy needs goes into road transportation. Thus if we would start to drive energy efficient cars, it would cut 10% of the US total national energy bill! No needs for new inventions, just take what exist already today!

 Because of the high fuel prices there have been proposals from politicians and governments to reduce taxes on fuels. This is precisely the wrong measure to implement. What should be done is to lower the tax or subsidize more measures that will result in less energy needs such as home insulation, fuel efficient cars and fuel efficient heating units. The best way to solve the energy problems of the planet in short term is reducing the need for energy in the first place!

 2) The other way to mitigate the energy problems of the planet, but then more long term, is the use of renewable energy sources, basically all based on the solar energy that reaches the earth. The sun is such a rich source. Realize that the energy influx is many times higher than the world energy need. There are massive problems to overcome such as costs price and, more importantly, the capacity of our power grid that can accommodate these variable energy sources. This will ask for clever storage means that must come along with the renewable sources.

© Copyright 2009 John Schmitz

As always, check out the question.

A simple explanation for why surface brightness cannot increase is that it would violate the second law of thermodynamics. Instead of calculating, I’ll try to convince you of this with a gedankenexperiment.

Imagine a universe with one large ideal black body, one small “othello disk” (perfectly black on one side, perfectly white on the other), a parabolic reflecting mirror, and some dark matter to cause gravitational lensing. (In the picture below, the black body is orange, the mirror is gray, the disk is green, and optical paths are dotted black.)

The time scale on which the large black body comes to thermal equilibrium with its surroundings by radiation is much longer than the equivalent time scale for the disk, so throughout the course of the experiment we can consider the large black body to have a constant temperature. The disk is at the focus of the parabolic mirror. It is small enough and placed close enough to the large black body that the image of the large black body covers the surface of the disk. The mirror itself is smaller than the typical spatial scale of variations in the large black body’s radiation’s surface brightness (assuming it has some).

If there were no variations in surface brightness, the black side of the disk would be completely covered by the image of the large black body. Then the disk would come to equilibrium with the radiation coming in, and would reach the same temperature as the large black body.

Now imagine there are variations in surface brightness. Conservation of energy requires that if surface brightness decreases somewhere, it must increase somewhere else. So place the dark matter so that the mirror is at a patch of high surface brightness. Then the disk is still covered by the image of the black body, but that image is now brighter. When the disk comes to equilibrium, it must be hotter than the large black body, which was itself the source of the heat. So we have heat flowing from a cold body to a hot one, in violation of the second law. By R.A.A, the variations in surface brightness must not exist.

A sponsor company left their pamphlets at my thesis conference dinner last night.

Three times more efficient... makes efficiency 100. What happened to COP usage?

Heat pumps take in a total of 3kW, gives an output of 3kW. Even more painful is the right diagram. 1kW electricity gives 1kW hot water? Wait, am I mistaken somewhere?

What about Carnot efficiency? I mean, seriously – this is a breakthrough! 100% efficiency. Alien technology?

Wow… now I really want to work with them.

In the latest issue of PNAS, David Andrieux and Pierre Gaspard write about the nonequilibirum process involved in the copolymerization process in a paper titled Nonequilibrium generation of information in copolymerization process:

We consider general fluctuating copolymerization processes, with or without underlying templates. The dissipation associated with these nonequilibrium processes turns out to be closely related to the information generated. This shows in particular how information acquisition results from the interplay between stored patterns and dynamical evolution in nonequilibrium environments. In addition, we apply these results to the process of DNA replication.

The commentary of Christopher Jarzynski on the paper titled The thermodynamics of writing a random polymer also reads extremely well, and puts the work in perspective:

The notion that information has physical, and in particular, thermodynamic, content can be traced to the paradox of Maxwell’s demon, a sly creature who observes the microscopic motions of gas particles on both sides of a partition. By controlling a trap door the demon segregates fast particles from slow ones to create a temperature difference across the partition, seemingly without expending any work. Generations of physicists have scratched their heads over this apparent violation of the second law of thermodynamics. The resolution that has eventually emerged acknowledges that a real-life Maxwell’s demon—say, a nanoscale machine designed for the task—collects information as it operates, and work must be expended to erase this information, otherwise the demon’s memory banks fill up. The minimum work required is k _B T ln 2 per bit of information, precisely what is needed to rescue the second law from the paradox. In this issue of PNAS, Andrieux and Gaspard analyze the flip side of the thermodynamic cost of information erasure; namely, the cost of information acquisition. The setting of their analysis is not a demon and a gas, but rather a process essential to living organisms: copolymerization, in which a chain-like molecule grows by the addition of chemically distinct units (monomers). The most celebrated example is the replication of DNA, by which genetic information is copied at the molecular level, ultimately to pass down the generations of a family tree.

A very interesting piece; take a look!

Creativity comes from the discovery of patterns, and patterns are found through system thinking. The notion of the interconnectedness of all things is a fundamental concept in cultivating more mind power. Issac Newton’s Second Law (“Every action has an equal and opposite reaction”) and Law of Universal Gravitation (an algebraic equation proving a physical attraction between any two masses) supports the Butterfly Effect — the notion that a butterfly stirring the air today in Beijing can transform storm systems next month in New York. 

In his writings, Leonardo DaVinci certainly would agree with the Butterfly Effect:

“Every part is disposed to unite with the whole, that it may thereby escape from its own incompleteness.”

“The stone where it strikes the surface of the water, causes circles around it which spread out until they are lost; and in the same manner the air, struck by a voice or a noise, also has a circular motion…”

“Mountains are made by the currents of rivers. Mountains are destroyed by the currents of rivers.”

“Swimming in water teaches men how birds fly upon the air. Swimming illustrates the method of flying.”

Looking for connections — learning and understanding systems by exploring or imagining them — is a great priming technique for creativity. Taking a holistic approach in all facets of everyday life, including diet, health and fitness will focus your mind on the bigger picture.

DaVinci Exercise: Origin thinking on a meal

In his book How to Think Live Leonardo da Vinci, Michael Gelb suggests contemplating on the origin of the ingredients in the next meal you are about to eat. Pause to give thanks and reflect on the orgins of the blessing you’re about to receive. Thinking about the origins of things is a great way to enhance your understanding of system thinking.

1. It’s usually held that Mechanics belongs to the Reversibility domain and the time-symmetry of dynamics’ second law would confirm this belief. Of course, it is maintained, the solution exhibited at the time “t” must show a reversible process. Otherwise the solution at time “-t” would cause the actual inversion of an irreversible process, which cannot happen in nature. In other words, the fact that both solutions are observable would confirm beyond any doubt Mechanics’ Reversibility.
2. Unfortunately, the argument misses the point that solution “-t” might not violate any natural law simply because it exhibits the same irreversible process of solution “t”. As such, both solutions are again observable. An example will clarify that this is indeed the case.
3. In a 1D elastic collision the two bodies move, say, from left to right. In this “t” solution we always observe the faster than average body slowing down and the slower than average one accelerating. This is an irreversible process in which kinetic energy flows spontaneously (since our system is isolated) from the faster body to the slower one, just like heat flows spontaneously from a hotter body to a colder one in contact. And the same irreversible process occurs when we observe the “-t” solution: now our colliding bodies will be moving from right to left, and it’s still true that the faster body slows down while the slower one accelerates.
4. We meet the same situation with inertial forces when the motion of a material point along its path is considered. In a frame aboard the material point we detect the same inertial force for both, “t” and “-t”, solutions as stated by the dynamics’ second law. Here the classic example is the elevator in free fall: the inertial force is directed upwards compensating for “gravitational effects” of bodies inside. The “-t” solution shows a raising elevator, ascending at less rate in order to have the same inertial force still directed upwards.
5. This is what, in my opinion, establishes a deep connection between Inertia and Irreversibility. By the way, the motion of an inertial frame would be reversible. But, does it really exist in nature a frame like that?

“Why did you {them, this company, those guys, that company, this group} do this?”

Yup, that’s the first – maybe second – question any consultant or new hire in a media company asks.  The hope is to find some easily understandable, presumably correctable, explanation for how the hell on earth a product, service, experience, division, or company came to its current state.

That question is never answered easily nor accurately, though almost everyone asked responds with a flurry of justifications and musings.

There is no accurate answer possible.

When a company or product is successful, we heap praise on the executives and their innovative approaches.  We retroactively assign a grand plan. i.e. Google eyed Microsoft from the beginning.  Steve Jobs planned the destruction of the music distribution model. American Idol creators just knew they had a pop culture masterpiece.  “We stuck to our guns despite the disbelievers.”

When a company or product is awful, we blame those engaged as lacking vision or being too stupid to see the obvious.  i.e. Ford didn’t see the hybrid coming.  Yahoo! hired too many Hollywood types to see that search was the way to go. “The guy before you just didn’t get it.”

In either case, this is myth.  It is impossible to explain the current state of a product, company or service with any accuracy.  Not only is it impossible, it would be worthless if you could do it – it would take too much time and wouldn’t be all that accurate for whatever comes next.

So?  what’s yer point?

Media and business can’t avoid the second law of thermodynamics – systems never decrease in disorder. (there are lots of variants on this).  That’s right.  A company is never going to get more orderly.  A product is never going to get more orderly.  It’s just not. It’s impossible.  It is a universal law.  Media properties, websites, networks, companies behind those entities are never going to get more orderly.

Thus, any explanation of why things are at the current state doesn’t help you avoid the looming disorder.

The only way to go from a poor product, company or experience is to move completely into a new one.  Start over from a more orderly state.  Don’t spend any energy in gluing the broken coffee cup back together, just go get a new one or form one from raw materials.

Yes, it is possible to pour a huge amount of energy into something that is in disorder to restore some order but the work (real energy) require to do so is not 100% efficient -  that is, you’d be wasting a lot of energy in ever increasing amounts to battle disorder.

Now imagine your own company and situation?  can you provide an example where a project, product, campaign, division actually got more orderly without diminishing returns?  I can’t think of a single instance of this in my own experience.

I’m going to draw this out more specifically for different types of media.  There’s no way to battle disorder.  There is a way to benefit from disorder…

~R

 In previous blogs  I have explained how entropy could be calculated from the amount of heat exchanged divided by the temperature at which that heat exchange occurred ( S = Q/T, see blog of 5/6/07). Rudolf Clausius introduced this definition around 1865. His motivation was that something was missing as the First Law of thermodynamics (conservation of energy) could not explain why heat flows always from hot to cold regions and that the opposite was never observed. While he studied the properties of this new concept he came to the conclusion that in an isolated system (a system that cannot exchange energy or material with its environment) the entropy always increases for processes that change the energy distribution within that system. [i] This proved to an important conclusion, as we are about to find out. Let me elaborate a bit on this. 

As I have mentioned before, in all the processes where we say that we are consuming energy, the only thing we are really doing is that we are transforming or re-distributing energy. An example of energy transformation is when we are burning fossil fuels. Here we transform chemical energy stored in the chemical bonds between the atoms of the fuel into heat. That heat can then be used to power a car and in doing that we transform (part of ) the heat into work. The net result of this process is that the fuel is completely gone (except for some ashes or soot) and is transformed into gaseous products (such as CO₂  and water), and that we have travelled over a certain distance (that is where we used the work obtained from the heat for) and that the remaining heat that we could not convert into work is diffused into the air. Now, the question arises whether we could come up with a clever idea to get the energy back in its intial condition because then we could use it another time to power our car? If we would have to deal only with the First Law, then in principle this would be achievable since we have not “consumed” the energy, we have only transformed it into other forms (work and heat) and have distributed the energy into a larger volume (it was first contained in a condensed volume of fuel but is at the end all over the place). Unfortunately we know from experience that this idea has not yet materialized. In fact if we would be able to do this we would invent a sort of perpetual engine. So what is going on, why can we not do this?

Well folks here it is that the Second Law or entropy of thermodynamics kicks in. If we would make an entropy calculation of the situation described above we would come to the conclusion that the entropy would have been increased. The entropy law forbids that the entropy can decrease. Every time that we transform (“use”) energy it comes automatically with an increase in entropy [ii]. Of course you could argue that we could catch all the evolved molecules from burning the fuel after we completed our car ride and restore them such that we get back to our original amount of fuel. Indeed that can be done (in principle at least) but in doing so you will need to transform even more energy (and thus produce even more entropy!). So we are trapped in this viscieuze circle where we only can produce entropy and never be able to restore it.

Although we do not change at all the total amount of energy available to us, the entropy law hinders us to recycle energy so to say. Energy is only useful to us when it is in a form that it is capable of doing work. With work I mean here lifting weights, because once you can lift weights you can use that work to drive wheels, engines and so forth. Another, more popular, way to put this is to say that the quality of the energy while transforming it, degrades. Therefore, entropy can be used to determine the quality of energy. This we can summarize as:

High quality energy (capacity to do work)  has a low entropy value

Low quality energy (less or no capacity to do work) has a high entropy value

To recap this: the entropy law learns us that transforming energy from a high quality state to a low quality state can only be done once. There is absolutely no way to recycle the low quality energy back to high quality energy. During the process of energy transformation there is always an inherent production of entropy that can never be reversed. There is a fundamental reason that the entropy only can increase and, in a way, makes our life miserable. I will come back to this matter in one of the next blogs.

© Copyright 2007, John E.J. Schmitz 

Nicholas Georgescu-Roegen was born in Romania in 1906 and lived until 1994. Although he obtained a PhD in mathematical statistics, he familiarized himself with the new field of economics during a stay at Harvard University. In 1948, he fled Romania’s Communist regime and returned to the US to teach at Vanderbilt University, where he published many studies in economic science.

Georgescu-Roegen is important to our discussion, because he made a connection between the two fundamental laws of Thermodynamics (conservation of energy and increase in entropy) and the economic process. He describes all this in his seminal book,  The Entropy Law and the Economic Process, published in 1971. The book is not always easy to read, but that doesn’t detract from the power of his conclusions.  He tells us that the Second Law of Thermodynamics dictates that the world has a limited entropy budget. It’s like a bucket that holds only 10 liters of water: once it’s full, you can no longer collect water and you have to work with what you’ve got.

Georgescu-Roegen stated that the entropy law applies to everything we do, and that with every action that degrades energy (it is never really “used up”) entropy is produced, leaving a smaller entropy budget for future generations. In other words, he made us aware of the entropic constraint on all economic activity. It can be shown (see my book, Chapter 5) that even by recycling (for instance, glass bottles), we cannot go back to the original situation without lowering the quality of the natural resources that we consume. The entropy law simply prevents us from creating a kind of perpetual cycle that would miraculously restore natural resources.

Georgescu-Roegen’s main complaint about economists is that they ignore this fact, and assume that everything in the economic process is cyclic in nature, and that in any case technology will provide us with solutions. However, it can be shown that often each new technology tends to accelerate the entropy production even more.

Here’s a simple example: More and more people hop on a plane to go on vacation or  make a quick weekend visit to friends and relatives 1000 km away. Well, the burning of the aircraft’s fuel causes a tremendous increase in entropy, and that will never be reversed. Another example: cars allow us to live further away from work, but force us to spend lots of time in traffic jams while burning huge amounts of fossil fuels.

The message here is that if we want to save our planet for future generations, then we must be very responsible in the way we exploit non-renewable natural resources. There is simply no escape from the Second Law!