# 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?

• There are multiple definitions of entropy, the Gibbs entropy is usually defined for a subsystem which is in thermodynamic contact (exchanging energy and perhaps other variables) with a larger heat bath, where you assume the combined system (consisting of subsystem + heat bath) is equally likely to be in any of its possible microstates (it's at equilibrium), and using that to get probabilities for different microstates of the subsystem which then define the entropy of those microstates. I don't see how this would work for the Earth, I think you instead need to use the Boltzmann entropy, Commented Nov 7, 2021 at 22:45
• (cont.) which seems to make more sense for defining the entropy of an arbitrary out-of-equilibrium system, but the Boltzmann entropy depends on how you divide the total set of possible microstates for the system into macrostates, see this paper for some comments on the problem of arbitrariness when it comes to defining macrostates. Commented Nov 7, 2021 at 22:48
• Yes, it is not clear to me what's the best way for defining entropy of a nonequilibrium system. Boltzmann entropy is just log of phase space volume, right? Thanks for the reference...I will read as much of it as I can follow :) Commented Nov 8, 2021 at 3:27

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.

• The difference between your first and second sentences is exactly what my question is getting at. I'd like to find out which it is. Most people don't even notice there is a difference. So far nobody has convinced me that the entropy of a living thing ever needs to decrease in time, apart from losing weight or cooling off. I don't think the "orderliness" of living things contributes much to their overall entropy, when compared to the effect of properties they share with inanimate matter, like temperature. Also, I agree with your point in the last couple sentences. Commented Nov 8, 2021 at 2:57
• @ether That question can't be answered in general. There is no unique definition of entropy that says how to count macrostates. Whether a subset of a system's entropy increases or decreases depends on how you decide to count macrostates. The laws of entropy only says that no matter how you're counting your macrostates (so long as it meets a couple basic properties), entropy of a closed system will always increase on average. So whether a living thing's local entropy decreases or only increases less than its surroundings can depend entirely on how you decide to measure the entropy of the system Commented Nov 8, 2021 at 15:11

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.

• What is your opinion on whether the entropy of the earth itself has been decreasing? I understand that that would not constitute a second law violation by itself. I included those other paraphrases to provide the context in which I had encountered such claims about the earth's entropy. Commented Nov 7, 2021 at 6:14
• The total entropy of the earth has decreased due to the fact that the earth is now much cooler. This though has nothing to do with the increase in complexity of life and a violation of the second law of thermodynamics. Cheers. Commented Nov 7, 2021 at 6:18

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.

• Re "...because it's much colder now...", I think you have to specify just what you mean by "the Earth". All of it, including the heat generated by radioactive decay in the mantle & core? The thin layer that constitutes the biosphere? But then we have various "Snowball Earth" periods, and opposing "hothouse Earth" periods like the Permian-Triassic extinction. Commented Nov 7, 2021 at 17:20
• After a little reading, it seems that my belief that there was a temperature crash as a result of atmospheric oxygenation is less widely agreed-upon than I had thought, with some evidence pointing towards and some evidence pointing away from the hypothesis. (Although of course if you go more than a little before the first life, the earth's surface was molten.) I'll edit.
– g s
Commented Nov 8, 2021 at 4:50
• @g s: Life is chemistry, but chemical reactions can go from lower to higher entropy states, or vice versa - simplistically, endothermic vs exothermic reactions. The various warming & cooling periods are only a secondary effect of life: e.g. the oxygenation caused CO2 to fall, allowing more outgoing radiation. Likewise, today's global warming isn't caused by the heat from burning fossil fuels, but by increased CO2 blocking outgoing radiation of infrared, which is caused by incoming solar radiation. It's only an indirect effect of life. Commented Nov 9, 2021 at 18:25
• @jamesqf One direction of a formula's exothermic reaction is the other direction's endothermic reaction. The time arrow for the reaction is the direction of greater entropy. If you're not getting greater entropy after than before, you're making a mistake, perhaps allowing heat to enter or leave the system under consideration.
– g s
Commented Nov 9, 2021 at 19:22

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.

• Thanks you. Although I only got 50% of what you said, yet. But: what the sun is pumping into us is not only energy, but low-entropy energy, and the earth radiates roughly the same amount of energy but in high-entropy (global warming factors aside). Isn't that right? So wouldn't it be more accurate to say that the sun is pumping low entropy (instead of energy) into earth? Energy appears to be the vehicle, but low-entropy seems to be the creative force that conscious organisms like us can use to shape their surrounding (or even destroy it, e.g. climate change). Commented Sep 5, 2023 at 22:43