All Downhill From Here!

Although I've posted previously specifically on the second law of thermodynamics, there were some features of it that I didn't discuss. This is largely due to the fact that the original iteration of the essay on this topic was written quite some years ago for a different venue. 

In that previous post, I discussed at length what the second law of thermodynamics is, what it says, and how it applies to different types of thermodynamic system. It was written to directly address the false conflation of entropy with disorder, as this is the basis for a lot of the claims against evolutionary theory.

Here, I want to explore some of the more subtle aspects of entropy as it pertains to evolution and, indeed, life. I'm going to begin with a statement that many, even some with a reasonable understanding of entropy and/or evolution, will find quite counter-intuitive. However, if I marshal my facts and arguments correctly, I'm confident that it will become clear.

So, what is this counter-intuitive statement? It's simply this:

Life and evolution, rather than being a violation of the second law of thermodynamics, are actually manifestations of it!

In a nutshell, entropy is the tendency for thermodynamic systems to move toward their lowest energy state. They do this via equalisation of differentials which, in physics, is called doing work.

Let's start from first principles, as there will be some good examples as we go of how entropy works.

As we've noted in earlier posts, one of our best current sources of information about the early universe is the cosmic microwave background radiation (CMBR), discovered serendipitously by Penzias and Wilson in 1964. What the CMBR actually represents is not, as I've seen suggested, the glow of the big bang, but the photons that come to us from the 'last scattering surface'. This is going to serve as a useful pointer to what we're discussing here, so it's worth spending a little time on.

For about the first 380,000 years or so after the Planck time - a theoretical construct dealing with the smallest useful amount of time after the 'beginning' of expansion - the cosmos was opaque to photons. The reason for this is that, after the onset of expansion, the cosmos was extremely hot and dense. So hot, in fact, that it was basically a white-hot plasma of photons and ionised hydrogen, which consists of protons and free electrons. Because of the abundance of free electrons at such temperatures, the distance that photons could travel freely was massively restricted due to Compton scattering. 

Now, anybody who likes to smell nice knows what happens when a body of particles expands, because we've all felt the deodorant can cool down as we let out the smellies. The same thing happens with the cosmos. As expansion continues, the cosmos cools. Prior to a certain low temperature, electrons remain free, not bound to protons, because of a quirk of entropy, namely that, in the environment they find themselves in, there's nowhere for energy to go to become unavailable. As the termperature gets below about 4,000 Kelvin, however, something interesting happens; there's somewhere for energy to go, so the free electrons begin to bind to protons, forming the first neutral atoms. The reason they do this is because it's energetically favourable for them to do so. This is just another way of saying that, once they can shed some energy, their lowest available energy state consists of being bound to protons. 

As an aside, this is where the CMBR comes to us from. By the time the temperature gets as low as 3,000K, most of the free electrons have become bound, and the photons from the last bit of Compton scattering are now free to travel through the cosmos, and it's these photons that we detect as the CMBR. Due to the expansion of the cosmos, these photons are hugely red-shifted, meaning that their wavelengths are stretched out, until their temperature is about 2.7K, or -270 degrees Celsius, a smidge less than three degrees above absolute zero.

So we have a cosmos filled with neutral hydrogen, along with some helium, a bit of lithium and trace amounts of beryllium. An atom has less mass than its constituent particles, and remember that m=E/c², so its mass and its energy are the same thing. What's been shed in the binding of the electrons to the protons is known, somewhat misleadingly, as 'binding energy', because from here on in you have to input energy to break them apart. 

The main point here is that, because of entropy, the tendency for things to find their way to their lowest energy state, we can end up with a situation that seems slightly counter to our cursory understanding of entropy.

How about a more complicated scenario? One of the things we covered in the earlier post was black holes, which are the highest entropy entities in the cosmos (despite also being the most highly ordered). This is because, in the context of gravity, clumping of matter constitutes an increase in entropy. Thus, after the initial period of expansion, and possibly due to quantum fluctuations in the plasma during expansion, some areas of the CMBR are slightly cooler than others. These anisotropies (lack of sameness) represent areas of slightly lower energy, which also means lower mass in a given are. As discussed before, these differences represent only a few ten-thousandths of a degree, but it's enough for clumping to begin under gravity.

So, our hydrogen et al begin to clump and, where there is enough in one place, they clump tightly enough under gravity that the temperature begins to increase again. Once again, this looks like a violation of entropy, but it's once again a manifestation of it. Once there's sufficient mass in a small enough volume, fusion begins. This is the next stage of our explanation.

It's well-understood that fusion is a pretty complex process, because it's incredibly difficult for the nuclei of two atoms to get sufficiently close together to bond under the strong nuclear force. This is due to an energy barrier arising from electrostatic interaction between nuclei. Occasionally, this barrier, known as the Coulomb barrier, after French physicist Charles-Augustin Coulomb, will be overcome as a matter of statistics, but not nearly sufficiently often for stellar fusion to be a reliable process. For that, we need our old friend quantum tunnelling, discussed in another post. Quantum tunnelling allows hydrogen nuclei to overcome the Coulomb barrier, which in turn allows hydrogen to fuse into helium much more readily. 

This particular process is extremely interesting for our purposes here because, once again, the mass of the helium atom is less than the two hydrogen atoms independently, even though they have exactly the same constituents. We can see this quite easily. We have 2 protons, at 1.673 x 10^-27 kg each, 2 neutrons at 1.675 x 10^-27 kg and 2 electrons at 9.109 x 10^-31 kg. The helium atom has a mass of 6.646 x 10^-27 kg. We don't even need to get the chalk out to see that just the four nucleons, at a total mass of 6.696 x 10^-27 kg, add up to more than the entire helium atom, without even bringing the electrons into the mix. This energy is, of course, shed as photons which, in the case of Sol, our sun, we see as sunlight.

So, here we have a process in which, locally, entropy increases by undergoing reactions. In this particular case, we're also talking about overcoming a barrier to attaining the lower-energy state. This is only a partial, short-term solution (albeit on the scale of billions of years), however, because the entropy can still increase. The point here is that the energy barrier can be overcome to find an even lower-energy state.

There's another process that overcomes energy barriers to reach short-term lower-energy states, and I'm reasonably sure that you should be able to see where this is going by now. We can follow this exact chain of reasoning all the way through the periodic table, and indeed on beyond it into chemistry. Quite often, we'll find that there's a slight energy barrier to overcome, such as when hydrogen bonds to oxygen. We've all seen, I'm sure, an example of a hydrogen explosion, whether at the hands of a maniacal physics teacher or via footage of the Hindenburg disaster. Here's a nice little video from Periodic Videos:

 

In this video, we can see a hydrogen-filled balloon being exploded. Hydrogen naturally exists in a molecular state as H₂ at the range of temperatures we think of as normal, and is highly flammable, and really wants to bond with oxygen, two atoms of hydrogen to one atom of oxygen, to make water, H₂O. There is a tiny energy barrier to overcome, and this is facilitated by inputting a little bit of energy, in this case, with an electric match. Once the first hydrogen molecule has bonded, the binding energy released will go on to give a kick to several more, and so on, so there's sufficient energy to trigger an exponential chain reaction until all the hydrogen is bonded to oxygen, leaving water. The additional energy is released as sound, heat and light.

So, we've seen that, starting from first principles, the tendency toward lower energy states appears at every point and in every process, not just in degeneration, but also in generation, in processes in which locally entropy can be increased by a small amount in lieu of greater increase in entropy later, but what about life and evolution?


Well, these are simply continuations of the self-same processes. Chemicals react to each other, seeking ways to shed a little bit of energy at a time. Over time, these processes result in something that self-replicates, entirely in line with - and a manifestation of - this exact tendency toward shedding energy, helped along by energy input from the sun, where entropy is increasing all the time as it loses energy in the form of electromagnetic radiation. Once this has begun, especially where this replication is imperfect to any degree, it's a simple matter of generations to find bigger agglomerations that locally find the lowest possible energy state. Eventually, these chemicals organise into cells, which are incredible generators of entropy, and these form colonies of ever-greater complexity, ever better at locally tying up small amounts of energy while the whole system equalises.


Ultimately, as the expansion of the cosmos continues and, in fact, accelerates, all those little bits of energy tied up will eventually be broken apart, and all that will be left is a sea of photons, cooling and expanding, asymptotically approaching absolute zero.


All of the above, the entire history of the cosmos, nucleosynthesis, gravitational accretion of stars and solar systems, life, evolution and the eventual heat-death of the cosmos, all driven by a single process, encapsulated in a single simple equation that can be written on the back of a cigarette packet:

Image courtesy Mike Drippe Sr.

 
One final note, just to clear up a common misconception about heat death that I've seen bandied about.

I've seen it said or implied that heat death will be the point at which the cosmos reaches absolute zero. This can't actually happen because, like the singularity, absolute zero is an asymptotic value, meaning that it can be approached but never reached. Heat death can occur at any temperature. As stated right at the top of this post, work is the equalisation of differentials. Heat death occurs when there are no more differentials left to equalise, because there will be no usable energy.

Hope this has been enjoyable and informative. Nits, crits and corrections, as always, extremely welcome.

Share and enjoy.