Evolution and the Second Law

By Sean Carroll | May 7, 2009 5:45 pm

Since no one is blogging around here, and I’m still working on my book, I will cheat and just post an excerpt from the manuscript. Not an especially original one, either; in this section I steal shamelessly from the nice paper that Ted Bunn wrote last year about evolution and entropy (inspired by an previous paper by Daniel Styer).


Without even addressing the question of how “life” should be defined, we can ask what sounds like a subsequent question: does life make thermodynamic sense? The answer, before you get too excited, is “yes.” But the opposite has been claimed – not by any respectable scientists, but by creationists looking to discredit Darwinian natural selection as the correct explanation for the evolution of life on Earth. One of their arguments relies on a misunderstanding of the Second Law, which they read as “entropy always increases,” and then interpret as a universal tendency toward decay and disorder in all natural processes. Whatever life is, it’s pretty clear that life is complicated and orderly – how, then, can it be reconciled with the natural tendency toward disorder?

There is, of course, no contradiction whatsoever. The creationist argument would equally well imply that refrigerators are impossible, so it’s clearly not correct. The Second Law doesn’t say that entropy always increases. It says that entropy always increases (or stays constant) in a closed system, one that doesn’t interact noticeably with the external world. But it’s pretty obvious that life is not like that; living organisms interact very strongly with the external world. They are the quintessential examples of open systems. And that is pretty much that; we can wash our hands of the issue and get on with our lives.

But there’s a more sophisticated version of the argument, which you could imagine being true – although it still isn’t – and it’s illuminating (and fun) to see exactly how it fails. The more sophisticated argument is quantitative: sure, living beings are open systems, so in principle they can decrease entropy somewhere as long as it increases somewhere else. How do you know that the increase in entropy in the outside world is really enough to account for the low entropy of living beings?

As we mentioned way back in Chapter Two, the Earth and its biosphere are systems that are very far away from thermal equilibrium. In equilibrium, the temperature is the same everywhere, whereas when we look up we see a very hot Sun in an otherwise very cold sky. There is plenty of room for entropy to increase, and that’s exactly what’s happening. But it’s instructive to run the numbers.

The energy budget of the Earth, considered as a single system, is pretty simple. We get energy from the Sun, via radiation; we lose the same amount of energy to empty space, also via radiation. (Not exactly the same; processes such as nuclear decays also heat up the Earth and leak energy into space, and the rate at which energy is radiated is not strictly constant. Still, it’s an excellent approximation.) But while the amount is the same, there is a big difference in the quality of the energy we get and the energy we give back. Remember back in the pre-Boltzmann days, entropy was understood as a measurement of the uselessness of a certain amount of energy; low-entropy forms of energy could be put to useful work, such as powering an engine or grinding flour, while high-entropy forms of energy just sat there.


The energy we get from the Sun is of a low-entropy, useful form, while the energy we radiate back out into space has a much higher entropy. The temperature of the Sun is about twenty times the average temperature of the Earth. The temperature of radiation is just the average energy of the photons of which it is made, so the Earth needs to radiate twenty low-energy (long-wavelength, infrared) photons for every one high-energy (short-wavelength, visible) photon it receives. It turns out, after a bit of math, that twenty times as many photons directly translates into twenty times the entropy. The Earth emits the same amount of energy as it receives, but with twenty times higher entropy.

The hard part is figuring out just what we mean when we say that the life forms here on Earth are “low-entropy.” How exactly do we do the coarse-graining? It is possible to come up with reasonable answers to that question, but it’s complicated. Fortunately, there is a dramatic shortcut we can take. Consider the entire biomass of the Earth – all of the molecules that are found in living organisms of any type. We can easily calculate the maximum entropy that collection of molecules could have, if it were in thermal equilibrium; plugging in the numbers (the biomass is 1015 kilograms, the temperature of the Earth is 255 Kelvin), we find that its maximum entropy is 1044. And we can compare that to the absolute minimum entropy it could have – if it were in an exactly unique state, the entropy would be precisely zero.

So the largest conceivable change in entropy that would be required to take a completely disordered collection of molecules the size of our biomass and turn them into absolutely any configuration at all – including the actual ecosystem we currently have – is 1044. If the evolution of life is consistent with the Second Law, it must be the case that the Earth has generated more entropy over the course of life’s evolution by converting high-energy photons into low-energy ones than it has decreased entropy by creating life. The number 1044 is certainly an overly generous estimate – we don’t have to generate nearly that much entropy, but if we can generate that much, the Second Law is in good shape.

How long does it take to generate that much entropy by converting useful solar energy into useless radiated heat? The answer, once again plugging in the temperature of the Sun and so forth, is: about one year. Every year, if we were really efficient, we could take an undifferentiated mass as large as the entire biosphere and arrange it in a configuration with as small an entropy as we can imagine. In reality, life has evolved over billions of years, and the total entropy of the “Sun + Earth (including life) + escaping radiation” system has increased by quite a bit. So the Second Law is perfectly consistent with life as we know it; not that you were ever in doubt.

  • Andrew from Chicago

    As a former student of yours, it is always a pleasure to tune into your interesting and multitudinous thoughts. I like to think of you (and blogging buddies here) as the part of the broader internet intelligentsia! Keep it up!

    Any how, I was pondering these things myself the other day and found this great little site:



  • Richard Schwartz

    At the end of the paragraph by the diagram you say: “It turns out, after a bit of math, that twenty times as many photons directly translates into twenty times the entropy. The Earth emits the same amount of entropy as it receives, but with twenty times higher entropy.”

    Should the last sentence read: “The Earth emits the same amount of ENERGY as it receives, but with twenty times higher entropy.”?

  • http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean

    Andrew– Thanks! One of the wonders of the internets.

    Richard– Oops, you’re obviously right. I’ll fix it.

  • http://brokensymmetry.typepad.com Michael F. Martin

    I thought this paper on Natural Selection for Least Action was pretty interesting:


  • http://desuchan.net/ Suiseiseki

    ” The Second Law doesn’t say that entropy always increases. It says that entropy always increases (or stays constant) in a closed system, one that doesn’t interact noticeably with the external world.”

    I think you meant “isolated system”, not “closed system”. Closed systems are allowed to exchange energy with their surroundings, and the second law obviously doesn’t apply if the amount of energy entering the system is nonzero.

  • http://sneerreview.blogspot.com/ Sigmunf

    When I’ve spoken to actual creationists I find the level of scientific understanding they possess is unfortunately far below what is needed to comprehend the well written explanation provided above. When you have someone who thinks evolution can be refuted by the claim that its statistically impossible for a male and female to evolve to the same species and then stop (like evolution from a fish to a mammal happens in a manner of minutes just like a morphing cartoon model of evolution) its going to be hard to use thermodynamics as a way to convince them. I think it was Richard Feynman that coined the term ‘cargo cult science’ for people who use the appearance of science or sciencey words to convince themselves that their ideas were backed up by science. That is what we are dealing with rather than a simple misunderstanding of part of the second law.

  • http://www.astro.multivax.de:8000/helbig/helbig.html Phillip Helbig

    “I think it was Richard Feynman that coined the term ‘cargo cult science’ for people who use the appearance of science or sciencey words to convince themselves that their ideas were backed up by science.”

    Right, that was Feynman. However, what he referred to actually existed, reminding
    me of some of the contraptions the castaways put together on Gilligan’s Island:


    According to the article above, some cargo cults still exist.

  • Xul

    I think you’re over-complicating things here… Surely the argument is much simpler:

    Entropy, in mathematical terms is more accurately stated as the rate of change of configuration of a system. The whole definition in terms of order and disorder is misleading and is responsible for the many misinterpretations by creationists who haven’t bothered to study thermodynamics.

    The argument, more simply put:
    A pile of lifeless dirt over a hunded years has little change in it’s configuration, and it’s entropy measurement should be low since only the micro-vibrations of the dirt molecules and maybe wind erosion has any impact in changing it’s physical configuration. When you add life to this system, the system will have it’s configuration drastically altered; the taking up nutrients from the dirt, moving around, disturbing the order of everything, you actually have a drastic increase in entropy.

    Life causes an increase in entropy, not the other way round… Negative entropy has no place in thermodynamics, and the negative results one can get from differences between systems to say one system as more and one less, is also misleading, since the individual systems can only have positive(molecules are moving) or zero(no change in molecular configuration, theoretical only) entropy.

  • Chris

    So if the Earth were emitting the same amount of energy as it receives and thus remaining somewhat inert, how would you describe global warming?

    Often I find this website has a high amount of pro-atheistic writing or writers. But I find it odd that the scientifically inclined seem most bent towards the idea. One would think that the scientifically uneducated would use the following logical fallacy:

    “If I don’t see god, he must not exist.”

    Where as a scientific mind might think:

    “I cannot currently percieve and Nth deminsional super beings, but that doesn’t mean there aren’t any.”

    My $.02 and attempt to stir up the pot :).

  • http://sneerreview.blogspot.com/ Sigmunf

    “So if the Earth were emitting the same amount of energy as it receives and thus remaining somewhat inert, how would you describe global warming?”
    If by “somewhat inert” you mean the temperature doesn’t change and the climate stays stable then I would describe global warming as something that is not happening.
    That, however is not what we actually see when we look at the data.
    The Earth can receive and radiate the same amount of energy overall but still have dramatic changes in climate. What’s your point got to do with evolution or religion?
    Is anyone here suggesting the logical impossibility of the existence of this super being of yours?

  • Chris

    My question had nothing to do with evolution, religion, or much to do with the main topic aside from a question about the use of entropy. I would however only understand global warming as a state of increase infared radiation that does not leave the planet, not in terms of, “climate.”

    My point about the super being was more just to add a new dimension to a tired arguement, also an obvious reference to a Supreme Being which is the foundation.

    I do find the entropic discussion an odd way to go about disproving creationism.

    However if you really want to get to the meat of the problem with this blog’s arguement, I’d say that it states the oppositions platform without a reference.

  • dg

    @ Xul

    Entropy is k*log(w). The w (really an omega) deals with the configuration of the system. It’s not a rate of change of anything. Please clarify what the hell you’re talking about.

    @ Chris

    I’m surprised you’ve never heard the entropy argument Sean is talking about. I can’t give you a specific reference, but here’s something that can help: http://www.google.com. Please educate yourself.

  • Xerxes

    Nicely explained. One note: I think the phrase “do the coarse-graining”, although perfectly good physics jargon, might not mean very much to the lay reader. Unless it’s explained earlier in the book, you might consider rephrasing or defining exactly what you mean by it.

  • will

    It’s hardly stating the “opposition’s platform” (giving _all_ creationists credit for even a rudimentary understanding of thermodynamics is rather generous). Nor is it using the second law to disprove creationism. Both of these tasks are actually unreasonable.

    Rather, it is clarifying what is said and meant by a well founded and widely believed scientific discovery – and showing how it is not at all _inconsistent_ with evolution, as the argument by _some but not all_ evolution deniers goes.

    To overextend the argument is to do precisely what Chris is attempting to accuse Sean of doing, however Chris is the only one who is _actually_ doing this. This is frequently referred to as irony.

    Critical reading skillz ftw.

  • http://mogmich.blogspot.com/ mogmich

    As I understand thermodynamics, the total entropy of an isolated system always increase. There can be fluctuations, where parts of the system decrease in entropy, but this results in a higher increase of the overall entropy.

    But such spontaneous fluctuations in local entropy normally disappear again, if there is nothing to “fix and amplify” it. Gravity probably plays such a role in our universe, I guess?

    The biosphere here on Earth also amplify this. The biological system itself represents a decrease in entropy, but the net-effect of the biological processes is an increase in entropy.

    I think you can say the same about civilisation: the products of human intelligence represents in itself a decrease in entropy, but there is a serious consequence of this, which we are only becoming aware of today. Example: building a coal-based power plant represents “human intelligent design” but affects the climate negatively.

    Since the entropy of the observable universe has always been relatively low, I think this indicates, that the observable universe is actually only a part of a much larger universe (in which the entropy is increasing). But isn’t it hard to imagine, that this should be the result of a random fluctuation?

    I don’t believe in ID, but I think that “someone” must have deliberately made it that way. Not a supernatural being outside the universe, but rather that the universe itself has some kind of consciousness.

  • Count Iblis

    This can also be explained to lay people without invoking entropy. You assume that the laws of physics only allow for unitary time evolution, so information is conserved. We want to implement a process that leads to initial states of matter that can be in any one of some large number of states to end up in some specific state. Clearly processes that would evolve two different states to the same initial state are forbidden as the information about the initial state would be lost.

    Any such process must therefore dump the information present in the initial state in external degrees of freedom.

  • Count Iblis

    About Global warming: CO2 absorbs infrared radiation. So, the higher the CO2 concentration, the less the mean free path the infrared radiation that the Earth is emitting will be. Equilibrium means that the Earth will be losing the same amount of infrared radiation per unit time as the energy it is receiving from the Sun. But with higher CO2 concentrations, that escaping infrared radiation is on average coming from higher up in the atmosphere.

    Since the emitted infrared radiaton depends on the local temperature, this means that the temperature higher up in the atmposphere nust have increased which means that at the surface it must have become warmer.

  • weichi

    Surely the biomass itself is warmer than 255 K? Not that using a more realistic value will change the argument.

  • Neal J. King

    Chris, Signmunf:

    Currently, the increase in CO2 concentration has resulted in a radiative imbalance such that, in fact, more radiation is being absorbed on Earth than is being radiated away. So there IS a net increase in energy.

    If we should ever stop increasing the amount of CO2, the increase will continue, but its rate will decline until the temperature of the upper atmosphere has increased to the situation that Count Iblis described has been reached: the point in the atmosphere where the 15-micron optical depth = 1 has local temperature equal to the equivalent point prior to all the extra CO2 having been added.

    Over the next thousand years or so, the “excess” CO2 will be taken out of the atmosphere, and the planet’s radiative energy budget will go into deficit.

  • Steven Davies

    “the temperature of the Earth is 255 Kelvin”

    Isn’t more like 285 K?

  • incognegro

    This seems like it all still boils down to an anthropic argument to me. Life creates entropy, so the local drop in entropy in a single biological system increases it somewhere else. Still doesn’t answer any questions as to why or how.

    We already know the odds of spontaneous genesis occurring are about as good as the LHC creating a black hole, so why or how did this statistical anomaly occur?

    You guys are forgetting about the almost nil probability of a particular configuration creating life. Sure it could happen, but how the heck did it actually happen?

    I’m not a weird creationist or bible thumper or anything but there are serious unanswered questions as to why it works the way it does that have nothing to do with any deity or Supreme Being. That’s where I think the argument mucks up the science: keeping people from doing research into why.

    We, as scientists (I’m an engineer) need to see that order-producing processes AKA evolution drives not just biological systems but all kinds of things, even computer programs, traffic congestion, fluid dynamics, etc. It’s almost like it’s built into the universe! The problem is that we barely understand how or why it works the way it does, and the Creationists (and some of you die-hard atheists) are holding up science from asking the right questions.

  • Neal J. King


    The question Sean was addressing was, Is there a contradiction between the evolution of life and the second law of thermodynamics? The answer at which he arrived was, No.

    This answer does not stop you or anyone else from trying to find a plausible mechanism by which life did or could have evolved. Freeman Dyson, among others, has speculated on some mechanisms. (http://www.complete-review.com/reviews/dysonf/origins.htm)

    Someone else (name beginning with M) did some work a few decades ago that showed that when you have an energy source, a natural consequence would be closed cycles of material flow that dissipate that energy, which sounds like a good starting point for life, from a purely thermodynamic point of view. I vaguely remember that he also wrote a more popular book about the physics of pizza, or something like that. I never studied this, but maybe this will ring someone else’s bell.

  • Neal J. King


    You might also check out a collection of papers:
    Non-equilibrium Thermodynamics and the Production of Entropy: Life, Earth, and Beyond (Understanding Complex Systems)


  • Count Iblis

    I’ve read that the low temperatures inside comets could have provided the perfect place for complex molecules to form.

    Due to the low temperatures, a molecule in a comet will react with whatever molecule happens to be sitting next to it. So, it is possible to get large molecules that would be unstable at room temperature. You can then form large molecules that happen to be stable but that can only be made ot of smaller parts that are unstable.

    One then needs a selection mechanism that from time to time destroys the unstable molecules. Also you need to mix up everthing a bit so that new combinations can form. This can happen if the comet is kicked out of the Oort cloud and perodically comes close to the Sun.

    When the comet is close to the Sun, the more stable molecules can now start to react with molecules that are a bit further away due to the higher temperatures, forming more complex molecules. As the orbit of the comet’s orbit is perturbed more and the comet spends more time closer to the Sun, these more complex molcules are again selected for stability.

    If the comet crashes into the Earth at a very oblique angle, then the contents of the comet can survive the collision. Some of the complex molecules that have been cooked up in the comet may have been able to survive the environment on Earth.

  • Ahmed

    “There is, of course, no contradiction whatsoever. The creationist argument would equally well imply that refrigerators are impossible, so it’s clearly not correct.”

    You’re giving the creationists too easy a time.

    None of these crazies will argue that simple Darwinian evolution is impossible, only extremely unlikely. Just like your fridge. Your fridge is very unlikely. Try scouring the universe for one, you will not find many. They all happen to be here, on this tiny little planet. Energy doesn’t explain much. There are no refrigerators on the Sun.

  • karthik

    Ever since I first learned about the Second Law, I’ve always wondered how to go about this quantitative analysis; thanks for the illuminating explanation!

    “It turns out, after a bit of math, that twenty times as many photons directly translates into twenty times the entropy.”

    I think I can handle a bit of math- can anyone point me to a reference (online or otherwise) that contains this derivation?

  • Jimbo

    Am I missing something: Does’nt one need to specify a number for the heat capacity of the 10^15 kg biomass…So many Joules per kg ? Or is it assumed to be some specific hydrocarbon with a known Cv ?

  • http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean

    Sure, you have to specify some numbers for the biomass. Some details are in Ted Bunn’s paper, linked to above; some more are in a recent paper by Lineweaver and Egan.

    Xerxes– Trust me, if they’ve read this far in the book, they’ve learned a lot about coarse-graining!

  • Neal J. King


    blackbody entropy = (4b/3)T^3 = 3.6 Nk , where N = number of photons

    equation (8)

  • Ahmed


    Just look up definitions of entropy, the math is very simple. The definitions involving information (i.e from the information perspective) are a little easier to read than the physical ones.

    For photons, imagine the following: a photon can exist in a fixed number of configurations, or ‘states’. If you have more photons, the state space expands. How it expands depends on how you look at things. This is because for every possible state in the first photon, there are a similar number of possibilities for the next photon and so on, so the increase is exponential if you look carefully. If you look through a dusty lens, you don’t see that, you just see more photons (as many as you added). This number – the volume of the state space, is what entropy tries to measure.

    The author said ’20 times’ because that is the coarse grained view that physicists see. If you pack 20 times the particles you get 20 times the density. The fine grained view is that you get 2^20 times the entropy, if each particle can be in 2 states. Happy Mothers Day! :)

  • Maxwell

    This argument for the second law vs evolution tension is correct in its generality.

    But there is a more interesting comparison to make — by making the distinction between preparing a low entropy state (what Sean was really talking about) and maintaining a low entropy state.

    The 2nd law applies to the former. The latter is quite different and the calculation of entropy production per UNIT TIME using T_{sun} and T_{earth} is really related to the latter.

    As Sean notes, the existence of life (say at a steady state) is a low entropy state — lower than thermal equilibrium by some amount Delta S. To prepare such a state, of course, some entropy must have been produced elsewhere.

    To maintain a system in a non-equilibrium steady state such as this, it turns out that one needs a constant RATE of entropy production elsewhere. The T_{Sun} and T_{earth} argument really answer this question of rate.

    Crucially, the RATE of entropy production to maintain a system in a low entropy state is NOT simply directly related to the low entropy of that system — it depends on the kinetic constants between states of that system in a sense. For example, that required RATE of entropy production can be made as high as one wishes by scaling all kinetic constants without affecting the low entropy state one is able to maintain.

    It would be a very interesting and perhaps difficult generalization of Sean’s post here to estimate what RATE of entropy production is needed to maintain life of given entropy on earth and compare that RATE to the Q (1/T_{sun} – 1/T{earth}) quantity..

  • Maxwell

    In case, I wasn’t clear in my last post, the relation between the rate of entropy production to maintain a certain low entropy state and that low entropy of that state is NOT related to the 2nd law..

    In a sense, it can be called a much stronger version of the 2nd law but this relationship is not really universal as far as I know. It depends on the details of the system like the overall scale of the kinetic constants and is usually studied in a limited context such as the Boltzman master equation etc (i.e a Markov process)

    But it would be interesting nonetheless..

  • http://www.users.bigpond.com/pmurray Paul Murray

    So if the Earth were emitting the same amount of energy as it receives and thus remaining somewhat inert, how would you describe global warming?

    Mind-boggling. Here’s another little excersise: given the rate of energy that the earth gets from the sun, how many seconds of solar input would be needed to raise the temperature of the seas/atmosphere by the amount that global warming predicts?

    Here’s a hint, Chris: every morning the sun manages to raise the temperature of the earth by several degrees. Even in a global warming scenario, the energy in and out is almost exactly balanced. Or we’d all be either toast or icicles.

  • Gabe Feliciano

    Snce the Universe is a closed system, did the Universe begin in high entropy or low entropy?

  • http://scientificphilosophy.com Glenn Borchardt

    In an infinite universe, entropy increases and decreases are equivalent:

    A finite universe would have low entropy at the beginning with continuing increases marked by divergence (expansion). As you can see from the link, I prefer the infinite universe model, as it explains the development of ordered systems through convergence as well as their destruction through divergence.


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Cosmic Variance

Random samplings from a universe of ideas.

About Sean Carroll

Sean Carroll is a Senior Research Associate in the Department of Physics at the California Institute of Technology. His research interests include theoretical aspects of cosmology, field theory, and gravitation. His most recent book is The Particle at the End of the Universe, about the Large Hadron Collider and the search for the Higgs boson. Here are some of his favorite blog posts, home page, and email: carroll [at] cosmicvariance.com .


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