Entropy and evolution

One of the oldest canards in the creationists' book is the claim that evolution must be false because it violates the second law of thermodynamics, or the principle that, as they put it, everything must go from order to disorder. One of the more persistent perpetrators of this kind of sloppy thinking is Henry Morris, and few creationists today seem able to get beyond this error.

Remember this tendency from order to disorder applies to all real processes. Real processes include, of course, biological and geological processes, as well as chemical and physical processes. The interesting question is: "How does a real biological process, which goes from order to disorder, result in evolution. which goes from disorder to order?" Perhaps the evolutionist can ultimately find an answer to this question, but he at least should not ignore it, as most evolutionists do.

Especially is such a question vital, when we are thinking of evolution as a growth process on the grand scale from atom to Adam and from particle to people. This represents in absolutely gigantic increase in order and complexity, and is clearly out of place altogether in the context of the Second Law.

As most biologists get a fair amount of training in chemistry, I'm afraid he's wrong on one bit of slander there: we do not ignore entropy, and are in fact better informed on it than most creationists, as is clearly shown by their continued use of this bad argument. I usually rebut this claim about the second law in a qualitative way, and by example — it's obvious that the second law does not state that nothing can ever increase in order, but only that an decrease in one part must be accompanied by a greater increase in entropy in another. Two gametes, for instance, can fuse and begin a complicated process in development that represents a long-term local decrease in entropy, but at the same time that embryo is pumping heat out into its environment and increasing the entropy of the surrounding bit of the world.

It's a very bad argument they are making, but let's consider just the last sentence of the quote above.

This represents in absolutely gigantic increase in order and complexity, and is clearly out of place altogether in the context of the Second Law.

A "gigantic increase in order and complexity" … how interesting. How much of an increase? Can we get some numbers for that?

Daniel Styer has published an eminently useful article on "Entropy and Evolution" that does exactly that — he makes some quantitative estimates of how much entropy might be decreased by the process of evolution. I knew we kept physicists around for something; they are so useful for filling in the tricky details.

The article nicely summarizes the general problems with the creationist claim. They confuse the metaphor of 'disorder' for the actual phenomenon of entropy; they seem to have an absolutist notion that the second law prohibits all decreases in entropy; and they generally lack any quantitative notion of how entropy actually works. The cool part of this particular article, though, is that he makes an estimate of exactly how much entropy is decreased by the process of evolution.

First he estimates, very generously, how much entropy is decreased per individual. If we assume each individual is 1000 times "more improbable" than its ancestor one century ago, that is, that we are specified a thousand times more precisely than our great-grandparents (obviously a ludicrously high over-estimate, but he's trying to give every advantage to the creationists here), then we can describe the reduction in the number of microstates in the modern organism as:

Now I'm strolling into dangerous ground for us poor biologists, since this is a mathematical argument, but really, this is simple enough for me to understand. We know the statistical definition of entropy:

In the formula above, k_B is the Boltzmann constant. We can just plug in our estimated (grossly overestimated!) value for Ω, have fun with a little algebra, and presto, a measure of the change in entropy per individual per century emerges.

Centuries are awkward units, so Styer converts that to something more conventional: the entropy change per second is -3.02 x 10^-30 J/K. There are, of course, a lot of individual organisms on the planet, so that number needs to be multiplied by the total number of evolving organism, which, again, we charitably overestimate at 10³², most of which are prokaryotes, of course. The final result is a number that tells us the total change in entropy of the planet caused by evolution each second:

-302 J/K

What does that number mean? We need a context. Styer also estimates the Earth's total entropy throughput per second, that is, the total flux involved from absorption of the sun's energy and re-radiation of heat out into space. It's a slightly bigger number:

420 x 10¹² J/K

To spell it out, there's about a trillion times more entropy flux available than is required for evolution. The degree by which earth's entropy is reduced by the action of evolutionary processes is miniscule relative to the amount that the entropy of the cosmic microwave background is increased.

This is very cool and very clear. I'm folding up my copy of Styer's paper and tucking it into my copy of The Counter-Creationism Handbook, where it will come in handy.

Styer DF (2008) Entropy and evolution. Am J Phys 76(11):1031-1033.