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The Underlying Principle Behind the Second Law 

Photo: Photo: A tornado, near Elie, Manitoba, Canada, by Justin1569 at English Wikipedia [CC BY-SA 3.0], via Wikimedia Commons.

Note: The video “Why Evolution is Different” further expands on the ideas in this article.

1. Extremely Improbable Events

In a 2000 Mathematical Intelligencer article1 I claimed that:

The second law of thermodynamics — at least the underlying principle behind this law — simply says that natural forces do not cause extremely improbable things to happen, and it is absurd to argue that because the Earth receives energy from the Sun, this principle was not violated here when the original rearrangement of atoms into encyclopedias and computers occurred.

One reader noted in a published reply2 to my article that any particular long string of coin tosses is extremely improbable, so my statement that “natural forces do not cause extremely improbable things to happen” is not correct. This critic was right, and I have since been careful to state (for example in a 2013 BIO-Complexity article3) that the underlying principle behind the second law is that

Natural (unintelligent) forces do not do macroscopically describable things that are extremely improbable from the microscopic point of view. 

Extremely improbable events must be macroscopically (simply) describable to be forbidden; if we include extremely improbable events which can only be described by an atom-by-atom (or coin-by-coin) accounting, there are so many of these that some are sure to happen. But if we define an event to be “macroscopically describable” when it can be described in m or fewer bits, there are at most 2m macroscopically describable events. Then if we repeat an experiment 2k times and define an event to be “extremely improbable” if it has probability less than 1/2n, we can set the probability threshold for an event to be considered “extremely improbable” so low (n >> k+m) that we can be confident that no extremely improbable, macroscopically describable events will ever occur. And with 1023 molecules in a mole, most anything that is extremely improbable from the microscopic point of view will be impossibly improbable. If we flip a billion fair coins, any particular outcome we get can be said to be extremely improbable, but we are only astonished if something extremely improbable and simply (macroscopically) describable happens, such as “only prime number tosses are heads” or “the last million coins are tails.”

Temperature and diffusing carbon distribute themselves more and more randomly (more uniformly) in an isolated piece of steel because that is what the laws of probability at the microscopic level predict: it would be extremely improbable for either to distribute itself less randomly, assuming nothing is going on but heat conduction and diffusion. The laws of probability dictate that a digital computer, left to the forces of nature, will eventually degrade into scrap metal and it is extremely improbable that the reverse process would occur, because of all the arrangements atoms could take, only a very few would be able to do logical and arithmetic operations. 

This principle is very similar to William Dembski’s observation4, widely used by intelligent design proponents, that you can identify intelligent agents because they are the only ones that can do things that are “specified” (simply or macroscopically describable) and “complex” (extremely improbable). Any box full of wires and electronic gadgets could be said to be complex, but we only suspect intelligence has organized them if the box performs a complex and specifiable function, such as “receiving TV signals and displaying the pictures on a screen.”

2. Extension to Open Systems

So, does the origin and evolution of life, and the development of civilization, on a previously barren planet violate the more general statements of the second law of thermodynamics? It is (literally) hard to imagine anything that more obviously and spectacularly violates the underlying principle behind the second law than the idea that four fundamental, unintelligent forces of physics alone could rearrange the fundamental particles of physics into computers, science texts, nuclear power plants, and Apple iPhones. But of course, materialists point out that all current statements of the second law apply only to isolated systems, for example, “In an isolated system, the direction of spontaneous change is from an arrangement of lesser probability to an arrangement of greater probability” and “In an isolated system, the direction of spontaneous change is from order to disorder.”5

Although the second law is really all about probability, materialists avoid the issue of probability by saying that evolution does not technically violate the above statements of the second law because the Earth receives energy from the sun, so it is not an isolated system. But in BIO-Complexity3 and again in a 2017 Physics Essays article6 I pointed out that the basic principle underlying the second law doesapply to open systems. You just have to take into account what is crossing the boundary of an open system in deciding what is extremely improbable and what is not. In both I generalized the second statement cited above5 to:

If an increase in order is extremely improbable when a system is isolated, it is still extremely improbable when the system is open, unless something is entering which makes it not extremely improbable.

Then6 I illustrated this tautology by showing that the entropy associated with any diffusing component X (if X is heat this is just thermal entropy) can decrease in an open system, but no faster than it is exported through the boundary. Since this “X-entropy” measures disorder in the distribution of X, we can say that the “X-order” (the negative of X-entropy) can increase in an open system, but no faster than X-order is imported through the boundary. I had first published this analysis in my reply “Can ANYTHING Happen in an Open System?”7 to critics of the Mathematical Intelligencer article and again in an Appendix to a 2005 John Wiley text, The Numerical Solution of Ordinary and Partial Differential Equations8 and again in Biological Information: New Perspectives9.

Everyone agrees that, in an isolated system, natural forces will never reorganize scrap metal into digital computers, because this is extremely improbable. If the system is open, it is still extremely improbable that computers will appear, unless something is entering the system from outside that makes the appearance of computers not extremely improbable. For example, computers.

3. Application to Our Open System

Now let’s consider just one specific event that has occurred on Earth that seems to be extremely improbable: “From a rocky, lifeless planet, there arose over time spaceships capable of flying to the moon and back safely.” This is certainly macroscopically describable, but is it extremely improbable from the microscopic point of view? A materialist would have to argue that it only seems extremely improbable, but it really isn’t. He could argue that a few billion years ago a simple self-replicator formed by natural chemical processes, and that over millions of years natural selection was able to organize the duplication errors made by these self-replicators into intelligent, conscious, humans, who were able to build rockets that could reach the moon and return safely. 

I would counter that we with all our advanced technology are still not close to designing any “simple” self-replicator: that is still pure science fiction. When you add technology to such a machine, to bring it closer to the goal of reproduction, you only move the goal posts, as now you have a more complicated machine to reproduce. So how could we believe that such a machine could have arisen by pure chance? And suppose we did somehow manage to design, say, a fleet of cars with fully automated car building factories inside, able to produce new cars, and not just normal new cars, but new cars with fully automated car-building factories inside them. Who could seriously believe that if we left these cars alone for a long time, the accumulation of duplication errors made as they reproduced themselves would result in anything other than devolution, and eventually could even be organized by selective forces into more advanced automobile models? (Maybe after a few billion years, even into intelligent, conscious cars??) So we really have no idea how living things are able to pass their complex structures on to their descendants without significant degradation, generation after generation, much less how they evolve even more complex structures.

4. Conclusions

Materialists have developed creative ways to argue that what has happened on Earth does not violate the more general statements of the second law, as found in physics texts, primarily the “compensation” argument, which says that “entropy” can decrease in an open system as long as the decrease is compensated by equal or greater increases outside. Since in this context “entropy” is just used as a synonym for “disorder,” the compensation argument, as I paraphrased it in Physics Essays6, essentially says that extremely improbable things can happen in an open system as long as things are happening outside which, if reversed, would be even more improbable. (The two American Journal of Physics articles discussed in Physics Essays6 actually make this argument quite explicitly, complete with probability estimates.) The compensation argument is not valid even when applied just to thermal entropy, as the decrease in an open system is limited not by increases outside, but by the amount exported through the boundary, as I have shown6-9. Or as the video “Why Evolution Is Different brings out, since tornados derive their energy from the sun, the compensation argument could equally well be used to argue that a tornado running backward, turning rubble into houses and cars, would not violate the second law either. 

But there is really only one way to argue that what has happened on Earth does not violate the fundamental principle underlying the second law — the principle that justifies every application and every statement of this law. And that is to say that it only seems impossibly improbable, but it really is not, that, under the right conditions, the influx of stellar energy into a planet could cause atoms there to rearrange themselves into nuclear power plants and digital computers and encyclopedias and science texts, and spaceships that could travel to other planets and back safely. 

This is, of course, what materialists have to believe, because they insist that nothing but unintelligent forces could be at work in our universe. But surely a reasonable person of science should be allowed to doubt this, and argue that it really is impossibly improbable that unintelligent forces alone could have produced our civilization.


  1. Sewell, Granville. “A Mathematician’s View of Evolution,” The Mathematical Intelligencer, Vol 22, No. 4, 5-7, 2000. (available at
  2. Davis, Tom. “The Credibility of Evolution,” The Mathematical Intelligencer, Vol 23, No. 3, 2001.
  3. Sewell, Granville. “Entropy and Evolution,” BIO-Complexity, Vol 2013, No. 3, 2013. (available at
  4. Dembski, William. The Design Inference, Cambridge University Press, 2006.
  5. Ford, Kenneth. Classical and Modern Physics, Xerox College Publishing, 1973.
  6. Sewell, Granville. “On ‘Compensating’ Entropy Decreases,” Physics Essays, Vol 30, 70-74, 2017. (available at
  7. Sewell, Granville. “Can ANYTHING Happen in an Open System?” The Mathematical Intelligencer, Vol 23, No. 4, 8-10, 2001.
  8. Sewell, Granville. The Numerical Solution of Ordinary and Partial Differential Equations, second edition, John Wiley and Sons, 2005.
  9. Sewell, Granville. “Entropy, Evolution and Open Systems,” in Biological Information: New Perspectives, Robert Marks, editor, World Scientific Publishing Company, 2013 (available at