Entropy of the earth decreased since pre-biological times? Here is a quote from Brian Clegg's book Dice World

Think about the earth as a system. When you look at all the complex organisation not just of human technology but everything that goes into making living animals and plants, the Earth as a system clearly has much lower entropy than it had in the past when all the atoms and molecules were pretty randomly scattered about. Entropy on the Earth has decreased over time as more and more structures and patterns have been added.

Does this sound right? I would think that after the earth cooled down to roughly the temperature it is now,  from then on it would be gaining entropy as the surface of the earth got better at capturing sunlight.  Until it reaches a steady state, in which case entropy stays the same on average.
I've read similar things in other places but it still doesn't make sense to me.  Usually they add something like, "but this decrease doesn't violate the 2nd law because the Earth isn't a closed system," or "entropy is increasing in the Sun, so it makes up for the decrease on Earth."  This sounds like quack thermodynamics to me, but I could be wrong.  Has the entropy of the Earth been decreasing apart from cooling off?  Do living things actually decrease in entropy, as opposed to merely maintaining themselves below maximum entropy?
 A: An organism (or any self-replicating arrangement of matter) is a machine that concentrates environmental negentropy in itself while increasing total system entropy.
The false belief that evolution represents a movement from higher to lower entropy because more advanced life forms seem more "ordered" is common. Earth is indeed not a closed system. Entropy is indeed increasing in the Sun. And Earth's biosphere is indeed in a lower entropy state than it was before life evolved.
But. The lower entropy state of Earth's biosphere is because it's much colder now than it was before the evolution of life. This may have a lot to do with life: early life broke down carbon dioxide, sequestering carbon and releasing oxygen gas into the atmosphere. Oxygen is a bad insulator, which may have contributed significantly to cooling. (For instance some evidence suggests ocean temperatures gradually decreased but remained in the neighborhood of 70 degrees Celsius before the oxygenation of the atmosphere (2000MYA to 3500 MYA), with a sharp drop of about 30 degrees over the next billion years.) In any case, heat transport out of the system, not the presence of the "orderly" bacteria vs the "disorderly" nutrient-rich primordial ooze, caused the entropy to fall.
In fact, the "orderly" life plus its environment had higher entropy than the pre-life environment, if we zoom in closely enough that we can ignore global cooling. Life, including evolution, is chemistry. Chemistry is the probabilistic re-arrangement of matter from lower entropy to higher entropy states.
A: Yes, the statement by Brian Clegg is absolutely correct. This is in full accordance with the "Dissipative Structures Theory" established by the Nobel laureate Ilya Prigogine. We regard the so called self-organized system of Earth as a system in a Dissipative Far Equilibrium State indeed. Such a system which has passed non-linear far equilibrium phase transitions (for instance along chemical, biochemical and then biological life formation), however, in accordance with the basic laws of thermodynamics, in order to maintain system stability and form stable structures in between such transition processes -- ensuring "LOCAL" maximum entropy in a quasi-stationary state of an at least fourth order non-linear potential (Hamiltonian) and related negative Lyapunov exponents -- such a system at macroscopic scale is very costly, requiring pumping energy as well as ongoing matter and entropy flux. That means, despite the fact that the Living Earth compared to its early days is of lower entropy, however because of its enormous dissipative structures it has consumed (and consumes ongoing) huge amounts of energy. The solution of your semi-paradox thought experiment is exactly herein: The SUN. Without the energy of Sun, pumped into Earth, life could not form and evolve, and Earth at large scale could not maintain life structures and lower its entropy over millions of years. However, that does not mean that the whole system and its processes {Earth AND Sun} have not been (are not) highly dissipative and with high Entropy production dS>>0. Indeed, if by Climate Change the Earth would get hotter and hotter, then the same sun may cause a vanishing of dissipative life structures parallel to Earth warming, and that would mean that Entropy might increase again on Earth: At a bifurcation point complex self-organizing systems may either run into a (1) catastrophe of death of all life for ever, (2) regeneration and transition to partly or complete new life structures. This bifurcation point in the phase space might be at a higher entropy level than we have today.
A: 
Entropy on the Earth has decreased over time as more and more structures and patterns have been added.

The entropy of the earth has decreased over time due to the fact that it has cooled down significantly and not due to increased complexity of life or certain structures.

...the Earth as a system clearly has much lower entropy than it had in the past...

There is already a problem with this in that the earth is not an isolated system. The second law of thermodynamics states that the total entropy of an isolated system will never decrease. Clearly, with the presence of the sun as you have stated, one can hardly call the earth an isolated system.

"but this decrease doesn't violate the 2nd law because the Earth isn't a closed system,"

Again, the earth is not an isolated system (you used the word closed), and yes it is very important to note that the earth receives energy from the sun and also radiates this energy back into space, meaning it's not an isolated system and is part of a larger system.

Has the entropy of the Earth been decreasing apart from cooling off?

This is irrelevant to the question of the second law, since the earth is not an isolated system. The entropy of the earth may have decreased as part of a system (due to a decrease in temperature), but this is certainly not an indicator that the second law has been violated. The second law of thermodynamics never makes any claims about the entropy of part of a system, and the argument above claims that part of a system (earth) decreases in entropy.

Do living things actually decrease in entropy, as opposed to merely maintaining themselves below maximum entropy?

Living things themselves receive energy from their environment to be able to form. If complex life appeared to form spontaneously (without any external interactions or sources of energy), one may then make such claims about the second law being violated. Until then, one cannot make such claims. Complex life formation on earth does not violate the second law of thermodynamics.
A: To differentiate itself from its surroundings, any living organism (no matter how simple) must decrease its entropy. Or, at least, it must ensure that its entropy increases more slowly than its surroundings. This takes energy, which creates heat. The organism must excrete this heat into its surroundings. And this means that the total entropy of the organism plus its environment increases, so the second law of thermodynamics is not broken.
We know that the presence of living organisms has significantly affected the entropy of the Earth’s atmosphere throughout its history. However, it is not clear whether all the living organisms on Earth are sufficient to significantly affect the entropy of the whole Earth. Remember the Earth is pretty big - it is roughly a billion times as massive as the global biomass. That’s an awful lot of entropy.
