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April 22, 1904: Birthday of Robert Oppenheimer more: Today in Physics  





Entropy and Evolution

This is an old "world wide cobweb" page, one of the first pages I wrote. Way back when I was young(ish). It was moved to this location September, 2008. To learn more about it read this article: End of an Era.

by Doug Craigen, PhD (physics)

revision 1.02, Oct. 29, 1996


The theory of evolution presents many mechanistic and philosophical questions for those of us who believe in Divine creation. Among the many approaches to answering these questions, there are varying levels of questioning the existence of evolution and whether it could happen without Divine intervention to assist it. One argument that is commonly raised in this context that since entropy is disorder, and since evolution represents a greater state of order, therefore, evolution violates the second law of theromodynamics (that entropy is always increasing). In turn, this argument has led to the mocking reply that we believe in the "Sun God". The purpose of this present writing is to explain the relevant issues in this argument in a way that does not presume a high level of education in any of the subjects of physics, mathematics, biology, or chemistry.

Order, Disorder and Design

Consider the following three possible arrangements for 16 marbles in a box:
+----------------+     +----------------+     +----------------+ 
|                |     | *         *    |     |                |
|                |     |      *         |     |                |
|    * * * *     |     |            *   |     |   *   *        |
|    * * * *     |     |       * *      |     |   *   *        |
|    * * * *     |     | **         *   |     |   *****  *     |
|    * * * *     |     |   *       *    |     |   *   *  *     |
|                |     |          *     |     |   *   *  *     |
|                |     |              * |     |                |
|                |     |*    *       *  |     |                |
+----------------+     +----------------+     +----------------+               
     1 - ordered         2 - disordered          3 - designed
  1. to call something 'ordered' is to imply the existence of an ordering rule. In a geometrical situation like the positions of marbles in a box an ordering rule would permit you to start at one marble and then using the rule predict the positions of the others. So for example, one could have the rule "from any marble you can find another one an inch to the left, or an inch to the right, or an inch up, or an inch down". Together with a rule to tell you where the edge was, this ordering rule could describe marbles as shown in #1. Geometric ordering rules could produce a wide number of resulting shapes (spirals, triangles, diamonds ...), the unifying thing that makes them all 'ordered' is the ability to use the rule to predict where to find 'the marbles'.
  2. if we cannot find an ordering rule to describe something, then we call it disordered. If we have limited success describing something with an ordering rule then we can defined the amount of disorder mathematically by how much deviation there is from the ordering rule.
  3. when we say that something has design, it is as much a matter of how we perceive it as of what is actually there. To someone who reads english, box 3 reads "Hi", but to someone who only reads Japanese it may simply look like a case of partial ordering. If it appears to us that there was some intelligence behind how something occured, or if it conveys meaning to us, then we say there is design. There may or may not be order in something that we consider to be designed (for example, abstract art). The problem with trying to talk about design in a quantitative fashion is that the human mind seems to have endless capacity to see design in something which is disordered (animal shapes in clouds, constellations in the sky etc).


Suppose that the marbles were simply dropped into the box. Which one of the arrangements 1, 2, or 3 would be the most likely to occur? A critical thing to understand is that they are all equally likely. From a mathematical point of view you should be no more surprised to see 1 or 3 than to see 2. And yet we are, and we should be.

Confused yet? The solution is that while any single outcome is equally likely, the number of outcomes that are just plain disordered far outnumbers the number of outcomes that show either order or design. So while no single disordered outcome is any more likely than any single ordered outcome, the net probability of having the outcome disordered is much higher than the probability of having the outcome ordered. There are simply so many more ways of having the outcome disordered than there are of having it ordered.


In a Thermodynamics or Statistical Mechanics class, the preceeding ideas would be usually brought together somewhat like this:

Consider the gas molecules that make up the air of the room you are in. They are scattered somewhat evenly throughout the room. There are many possible arrangements where the gas molecules would all be on the other side of the room, but we could spend our entire life in the room without fear that we would ever see it happen. The reason is that there is such an immensely larger number of possibilities where the gas fills the room, that the probability of seeing it all in one half of the room is for all practical purposes zero. Clearly the number of ways of achieving each possibility is a very important number for predicting what will happen. We give this number a special name, entropy (I will not bother with the complete mathematical definition of entropy here as it doesn't make any difference to the understanding of principles that I'm driving at).

The Second Law of Thermodynamics

If we have a physical system that is free to change between various states, we have the question of which state we expect to find it in (or if you have are watching it change, which state it will drive towards). From the point of view of , the state which is the most likely to occur is the state which has the most ways of occuring, and this is the state of highest entropy. We don't expect to see a system move from a state of high entropy to a state of lower entropy. This is the Second Law of Thermodynamics.

So, for example, if you have a cup of water and carefully place a spoonful of milk on top of the water, you will expect to see the milk mix into the water. It will maximize its entropy by spreading out, because there are so many more ways of being spread throughout the cup than there are of being all together. We expect the milk to mix into the water, and we don't expect it to later separate itself from the water.

When Does the Second Law Apply?

In the milk example above, if you were to leave the mixture uncovered long enough, the water would evaporate and you would have the milk left over. Does this violate the second law? No it doesn't. By taking the water molecules and spreading them through the room as a vapor, the total entropy of the water and milk together is much higher (even though the entropy of the milk has decreased again). One can have a decrease in the entropy of a part of the system, provided the entropy of the entire system still increases. What if you were to have a condenser that put the water back into a second cup as it evaporated from the first one? In this case, you have included something that is not part of the system. The second law does not apply to open systems where material or energy is being traded with some outside system, it only applies to self-contained, or closed systems. To have a closed system, you would have to make the condenser a part of it. In this case the operation of the refrigeration system creates enough additional entropy to account for the decrease in entropy when the milk and water separate.

From a chemical point of view of life, the thing that keeps our world going is the continual receiving of energy from the sun and the re-radiating of heat that keeps out planet from over heating. The earth is not a closed system, the reception of energy from the sun provides the possibility of process which locally decrease entropy (even though on a large scale entropy still increases). This is why you may find yourself mocked with "believing in the Sun God" if you say that God is the creator and sustainer of life.

Other Expressions of the Second Law

With some advanced calculus it is possible to take the mathematical expressions that underlie the description above, and find other equivalent principles that apply to situations other than closed systems. The second law can be seen as a fundamental principle behind why many processes occur in the direction that they do. For example, according to the first law of thermodynamics, a ball on a hill side could either stay where it is and maintain a high potential energy, or it could roll down the hill lowering its potential energy but gaining kinetic energy (as speed and rotation). The thing that tells you that it is the second one of these that will happen is the general form of the second law.

A Question of Scale

Two common logical fallacies are the Fallacy of Composition (arguing that what is true of the parts must be true of the whole - such as "pennies are light, so a million pennies are light") and the Fallacy of Division (arguing that what is true of the whole must be true of the parts - such as "computers are changing the world, therefore my computer is changing the world"). In thermodynamics we divide properties up into how they behave with respect to scale or division. Intrinsic properties are ones which are the same for the whole system and for any part of it. For example, temperature is an intrinsic property. If you pour half a cup of water into a second cup, both half cups of water have the same temperature which is the temperature they had when they were together in one cup. Extrinsic properties are proportional to the size of the system. Weight is one example. The two half cups may be at the same temperature as the initial full cup, but they are each only half the weight.

Entropy and energy are extrinsic properties. We can find the energy of the earth by adding up all the energies of everything in it. Similarly, we can find the entropy of the earth by adding up all the entropies of everything in it. We can also find entropy changes by subdivision, so that we can look at what is happening on an individual basis (plant by plant, leaf by leaf, cell by cell, molecule by molecule) regarding absorption of sunlight and the resulting chemical changes.

Entropy is NOT Disorder

As an aid for conceptualizing entropy, it is often described as a measurement of disorder. This is not intended as a definition of either entropy or disorder. Entropy is determined by the number of ways you could achieve a state, disorder is defined by the amount of violation of an ordering rule. The assignment "entropy is disorder" is intended to describe situations such as "the more space a gas takes up, the higher its entropy is, and the less you know about where all the molecules are (which in a casual sense means more disorder)". This conceptual link between entropy and disorder should not be interpreted as saying that increased disorder is increased entropy. An example of how entropy isn't disorder is that if you take a piece of glass, which is an amorphous material (one whose atoms are disordered), and place it in a fridge to cool it down, you will not change the atom locations. The glass remains just as disordered, but its entropy decreases as its temperature drops. In fact, in a very good fridge, the closer you brought it to absolute zero (-273.15 C or -459.67 F) to closer its entropy would become to zero. This would all happen without changing its structural disorder.

Entropy and Life

To argue that evolution is inconsistent with the second law of thermodynamics it is usually stated that evolution is a continual process of achieving higher order and design, which is against the second law. This is an argument based on casual definition of terms, rather than on quantification of order, design, and entropy. I hope that by this point it is reasonably clear that this argument actually has little if anything to do with the second law of thermodynamics. How would one propose to measure the relative order or design increase that would accompany any evolutionary step? What number represents the difference between standing erect and walking on all fours, between having only day vision and between having also developed night vision...? If we cannot answer such questions, then arguments about order and design will fall outside the realm of science.

To determine whether anything about the chemical processes of life violates the second law of thermodynamics requires looking at all the process on an individual basis. If there is no violation in the absorption of sunlight, or in any subsequent reactions, then there cannot be any violation of the second law as the net sum of such reactions (see the previous section on scaling). I am not personally aware of any such individual spots where the second law is violated. In fact, the second law is about as close as science comes to having sacrosanct laws. Any violations of this law that were discovered anywhere, no matter how small they were, would be very big news... I'm sure I would have heard of it.

Closing Remarks

Though I believe that we should stop arguing that the process of life (e.g. evolution) violates the second law of thermodynamics, this is not to say that there are no big unanswered questions for those who would use evolution to argue philosophically against religious belief. How and why it is that we see so much orderliness and design in the world around us remain big questions. However, the second law says nothing about design (which is a matter of perception of what is there) and does not appear to contradict anything about the order we observe. Actually, it should strike us as odd if God had set up the universe to operate under inconsistent laws.

In fact, many experts on the philosophy and history of science and technology believe that it was no accident that it was in Christian (and perhaps in particular, Protestant) areas where science advanced so quickly and had such a revolutionary effect on society. Rather it was the Christian belief that God created an ordered and rational universe working by predictable rules that enabled a scientific view of the world to develope. While the Bible records instances of the miraculous, it is perhaps remarkable what a small fraction of its content is involved in these cases. The vast majority of the Bible is about God's Providence guiding the world in ways that we would never see, except perhaps by inferal from the final result, where the miraculous is the exception. Whereas events like the parting of the Red Sea are spectacular, most of the Bible suggests a God who orchestrates events behind the scenes, planning hundred or thousands of years in advance through the smallest details in life for thousands of miles around. It would be arrogant to believe that now that we are a "scientific" people, that if we cannot detect God's working in our microscopes, then He isn't there. The church has gotten sidetracked on this point many times, with horrible results. The Bible is not a text book of Science. It is a mistake either to classify scientific theories as Biblical and non-Biblical, or to believe that the proof of God's existence will be found in the failure of science to explain something. We believe that God set the universe in motion with consistent and sufficient mechanical rules. Science studies those rules.

The larger questions such as why should we observe any order anywhere at all (rather than the smaller question I've addressed here of whether there are contradictions within the order we see) take us into whole new questions, such as the Anthropic Principle. That would be a whole other (and much bigger) paper than this one.

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