There are some things in science that are just so complicated that they cannot be explained to the uninitiated—things like quantum mechanics, the second law of thermodynamics, how a geek thinks, etc. To understand these things, it takes years of sleeping though dull lectures and late nights carous…. Oops, let’s start that again. It takes years of sitting in rapt attention at scintillating lectures, late nights studying (I have it right this time) and the secret initiation ritess. Don’t forget the secret initiation rites. But in this post, I am going to attempt the impossible and explain the second law of thermodynamics in a way that can be understood by the uninitiated. Fools rush in where angels fear to tread and all that. Now the second law is so complicated that there are several alternate but equivalent formulations. One is due to Rudolf Clausius (1822 – 1888). Now, this is very complicated, so take a very deep breath:
The second law of thermodynamics (Clausius): If you want your fridge to work you must plug it in.
See I told you it was complicated. There is an equally complicated version due to Lord Kelvin (1824 – 1907):
The second law of thermodynamics (Kelvin): The exhaust from your car motor will be hot.
Now you may think I am being facetious but I am not (OK, maybe about the scintillating lectures). What a fridge does is cool things down by taking heat from the inside and depositing it outside, ie it takes heat from where it is cooler (the inside) and deposits it where it is hotter (the outside). An exact statement of the second law is that no process can simply do that: transfer heat from where it is colder to where it is hotter and have no other effect. In the case of the refrigerator, the other effect is turning electricity into heat. No fridge can be 100% efficient. Hence, you must plug your fridge in. Similarly, the Lord Kelvin statement is that no heat engine (e.g. your car motor, assuming it is not electric) can be 100% efficient and simply turn heat (the burning fuel) into mechanical energy (moving the car). Part of the heat energy must be wasted. In this case, the waste heat is in the hot exhaust.
The second law of thermodynamics, as these two examples illustrate, has significant implications for engineering and was derived in that context. It limits what even the best engineers can do and rules out a large class of second-law violating perpetual motion machines (Not to be confused with perpetual motion machines of the first kind which violate energy conservation, the first law of thermodynamics).
You may notice, that so far, this discussion has nothing to do with order, disorder or spontaneous creation or destruction that are so frequently associated with the second law (and used to create confusion and disorder). But there is yet another statement of the second law that does involve order and the concept of entropy. Entropy is simply a way of counting the number of microscopic states that correspond to given macroscopic state. Think of the air in a room: macroscopically it can be described by the temperature, pressure, and volume. Microscopically, it can be described by the location and motion of all the gazillions of particles that make up the air. Many different locations and motions of the air molecules correspond to the same set of temperature, pressure, and volume. Entropy is related to the number of different locations and motions (technically, the natural logarithm of the number) that correspond to the same temperature, pressure and volume.
One can crudely think of entropy as being the information content of a system—the information needed to specify the location and motions of the gazillions of air molecules in the example above. The lower the entropy, the less information content. Also note that ordered systems have less information content than disordered ones. Consider the strings: 1111111111111111 and 1907214836589457. The first is highly ordered and has low information content: it is just all ones. The second needs much more information to describe; each digit must be specified individually. It is less ordered and hence higher information content and entropy.
A third equivalent statement of the second law is that the entropy of a closed system (ie one that does not interact with the outside world) can never decrease. Now the earth’s atmosphere and biosphere are not closed systems. They get energy from the sun and radiate it back out into space as thermal energy. The atmosphere and the biosphere together act like a giant heat engine using the sun as a source of energy and outer space as a sink for the exhaust heat (like the hot gas from the car engine). This heat engine lifts water from the oceans and puts it on mountaintops. It drives all weather systems including hurricanes and blizzards, evolution, and life itself. It is this heat engine and the lack of thermal equilibrium that generates local regions of low entropy like the sheet of ice on the pond I skated on as child or the alligator in the southern bijou. The alligator, like all living things, has a high degree of order, hence low entropy and information content. Waste heat produced by living things is a side effect of maintaining that order. It might seem strange that I say living things have low information content but it would take much more information to describe in detail the location and motion of the atoms in an homogenized (think blender) alligator[1] than in a living one. There are simply many more ways to arrange the atoms in the homogenized version.
The second law of thermodynamics, being obscure when expressed in terms of entropy, is used to justify all kinds of nonsense. For example, evolution is sometimes claimed to be inconsistent with the second law of thermodynamics. But the second law of thermodynamics is not that obscure: it simply says you must plug your fridge in order for it to work. What’s obscure about that? Now, what evolution has to do with plugging in refrigerators is beyond me. After all, the earth’s biosphere is plugged directly into solar energy, bypassing the need for the electrical grid and cutting out the middleman. I guess I will have to sleep through some more dull lectures to sort this all out. Zzzzz.
Additional posts in this series will appear most Friday afternoons at 3:30 pm Vancouver time. To receive a reminder follow me on Twitter: @musquod
[1] Relax, I am a theorist and have not homogenized any alligators.
Tags: evolution, Philosophy of science, second law of thermodynamics
The revolutionary ideas in Evolution are the notions of primary cause and growing complexity. This contrasts with the idea of growing disorder and the arrow of time. The paradox may be resolved by employing two distinct time concepts in definitions of measurement. This is unsurprising from an arealist’s view of quantum mechanics, the difficulty being in the gravitational consequences.
Nothing particularly strange about the increasing order in evolution. It is just driven by the biosphere acting as a heat engine.
Try not to assume that 20th century physics has the final answers to everything. You work in Physics admin, right?
[...] Byron’s terrific post here. One word I did recognize, [...]
Good post.
It also avoids tying thermodynamics to order, which is one of my pet peeves.
Microscopically one finds that entropy is simply a measure of the available energy states. The as entropy increases towards an equilibrium order is as often decreased as it is increased, depending on your definition of it. For example, a steady state system can have more macrostates than an equilibrium system. Biological organisms with their many functional traits is a good example of that.
However, the post uses another one of my pet peeves, the idea that there is an absolute measure of information.
Again biology serves as a good example. A population’s genome has information content as measured by Kolmogorov complexity described in the post. Variation will lead to more alleles, i.e. increased information content. Selection will channel Shannon information from the environment to the genome and pare down a preexisting set of alleles. That can be realized by noting that set of alleles under selection is a model of bayesian learning, a probabilistic selection on pre set vs post set of alleles constitutes a bayesian likelihood algorithm.
In other words environmental information is used to decrease the information content of the population’s genome (and increase the set of useful traits and/or surviving biomass, the macro order). The article avoids that trap, but this goes to show that information is always relative a system and a chosen measure.
The tie between entropy and information is merely that both uses logarithmic measures. That is why Shannon used the term in his theory of channels in the first place.
As for evolution, it is orthogonal to entropy and information both. If thermodynamics allows organisms to grow and procreate, we are good. Evolution is simply a process of inheritance on genomes.
[If you go really physical on this, there are a few arxiv papers that tries to estimate the entropy out of the process. It is orders of magnitude less than produced by biomass at large (no surprise there), and that in turn is many orders of magnitude much less than produced by the Sun-Earth system (again, no surprise).]
“The revolutionary ideas in Evolution are the notions of primary cause and growing complexity.”
Ouch, most often only creationists says that!
Biologists are very keen on noting that there is no order direction in evolution. Most multicellulars are parasites, and they decrease in complexity as they ride along or inhabit other organisms.
Take the tape worm that has lost its stomach since it sits in a stomach and can absorb nutrients through the skin, and all its moveability since the host moves. The loss of traits correspond to a loss genes over time, as variation destroys non-functional genes (and leaves so called pseudogenes, “ghosts” of once functional genes).
So evolution is known to “increase and decrease order”.
The reason it looks like an accumulation of complexity, but only superficially since mosts organisms are viruses followed by bacteria followed by archaea with tissue containing multicellulars a remote fourth, is because the first population was simple cells.
In fact, the LUCA was as complex as the average bacteria today, and the LUEA (last common eukaryote ancestor) was as complex as eukaryotes today. The largest genome today is likely no larger than the largest genomes in the Cambrian. There is a very definite limit in genome size due to the maximum energy density provided by mitochondria. (Lane’s energy theory on eukaryotes, explaining why we have ~ 10^5 more energy to produce proteins and keep a large genome.)
Same goes for functional traits such as brains, it is estimated that the largest brain for our size would be around double ours (~ 3.5 kg) purely due to energy considerations. And you would have to live on pure sugar. :-/
Finally, there is no primary cause (what is that?) in evolution.
Evolution can be defined most openly as the process that takes living populations to living populations with inheritance. If you want biological evolution, constrain to biological (biochemical) populations. What causes evolution is mechanisms such as variation and selection in some form of inheritance.
The section on the entropy definition could be shorter, if it took the history of science into account. In the late 19th century the known laws of physics were in contradiction to Darwins theory. However, a lot of evidence in biology and geology supported it. So one theoretical physicist sat down asking “What properties would a universe that allows Darwinian evolution to work have?” That physicist was Ludwig Boltzman and the 2nd law of Thermodynamics in the entropy formulation was one result.
So the notion that the 2nd law is at odds with evolution makes as much sense as the statement that c being constant in all frames of reference was fundamentally at odds with special relativity.
Evolution theory is just a stupidity. OK, The Earth isn’t a closed system, so entropy may decreasing, allowing more complex combinations. But “allowing” doesn’t necessarily mean “must”. If something is possible to happen it doesn’t at all mean that it actually happened. Evolutionist must yet prove their theory is correct and this so called evolution is actually happened.
Perhaps stupid. but then again many stupid ideas have turned out to be vailid; like a round and moving earth.
The alligator, like all living things, has a high degree of order, hence low entropy and information content. Waste heat produced by living things is a side effect of maintaining that order. It might seem strange that I say living things have low information content but it would take much more information to describe in detail the location and motion of the atoms in an homogenized (think blender) alligator[1] than in a living one. There are simply many more ways to arrange the atoms in the homogenized version.
What you describe here is coherence and order as a tool to diminish entropy, but usually decoherence is the word assigned to alligators. Decoherence is then increased entropy or negentropy? I think this would need some explanations or at least a link.
Nothing fancy here. Just the straight forward, but counter intuitive, observation that the amount of information (Kolmogorov complexity) need to specify a system goes down as the order goes up.
First off, here is a great song about thermodynamics by Flanders and Swan http://bit.ly/fHvZCO
Second off, It is interesting that people are still debating this,but you open up a can of worms with the word “Evolution”, I agree with you about energy and constraints of entropy and you explain it well, but of all those states consistent with the constraints, to me entropy is still a measure of randomness of a system. I put this idea across to students by rolling dice, as long as it is clear that the frequency of the most random outcomes in rolling is not really entropy but just a way to show that the most random state dominates as the number of dice increases. I wrote a few blogs on this http://bit.ly/sZfQE0