Some comments on entropy
Definition
Since I reviewed the basic teachings concerning entropy, I see entropy everywhere. The most helpful definition of entropy is the one regarding the state of order. The highest the order, the lowest the entropy. Thus, I declare myself an enemy of entropy, in the sense that I, we, always try to create some order, to put things in order: putting the plates away in the kitchen, entangling an electric wire, etc. Why is it actually easier to put things in disorder and to create entropy than the reverse? One useful explanation to comprehend this difference is to see that a state in order is an improbable state, while a state in disorder is a probable one: the electric wire is more likely to be tangled after so many years than to stay untangled, and there are many ways to put a mess in a room, but only one to put things at their places.
Entropy and time
There is some controversy concerning the relationship between entropy and time. The problem is that the fundamental laws of classical physics (from Newton) are reversible in time; that is whatever happens in one direction (toward to the future) can very well happen in the other direction (toward the past). Thus, as we see a drop of milk in a tea cup spreading and diffusing throughout the volume, we should see all the milk particles to come back and form the initial drop of milk. This is indeed possible according to Poincaré's recurrence theorem, although, because the state of the drop is very unlikely compared to all the states where the milk is spread, the probability that this happens is tiny (but in theory, it could happen!).
On the other hand, the second law of thermodynamics says that for a closed system, the entropy has to increase: the spreading of the drop of milk within the cup is a perfect example of entropy increase. Some, such as Prigogine, argues that entropy carries with itself the so-called arrow of time: because entropy increases, we can make the difference between past and future. But the question then remained, is the second law compatible to the reversible laws of classical physics? Roger Penrose, in his book The emperor's new mind, argues that the second law is not only compatible, but also, contrary to Prigogine's view, that the entropy does not carry the arrow of time with it. Whatever the direction, toward the past or the future, the entropy has to increase within a closed system, in particular within a system where there is no constraint on the entropy. In the case of the drop of milk, although toward the future there is no constraint and the entropy increases indeed, toward the past, there is the constraint of the initial conditions saying that the entropy is low at the beginning: thus, if you run the experiment backwards, there is the constraint that at the end, the entropy is lower than at the beginning. Because of this constraint, the second law does not apply as such and in consequence, the entropy does not itself carry the arrow of time. The arrow of time exists because our system started with a state of low entropy. The remaining question is thus, why and how did we start with a state of low entropy?
Source of low entropy
Both L. Botlzmann and R. Penrose describe the struggle for life as a struggle for low entropy, with the ultimate source of low entropy being the sun. L. Botlzmann writes
"The general struggle for existence of animate beings is therefore not a struggle for raw materials [...] nor energy [...], but a struggle for entropy, which becomes available through the transition of energy from the hot sun to the cold earth."
and R. Penrose says
"We do not need to gain energy from our environment because energy is conserved. But we are continually fighting against the second law of thermodynamics. Entropy is not conserved; it is increasing all the time. To keep ourselves alive, we need to keep lowering the entropy that is within ourselves."
Thus, how do we get this low entropy? The ultimate source of entropy is the sun, and plants are the organisms which are using directly this entropy source, transforming it into molecular structures, themselves ready to be eaten. We, humans, via the food web, are eating plants or animals who themselves eat plants, to get low entropy for our body.
In this aspect, I am then wondering if we can class the food web in terms of entropy content. The plants would get a source of low entropy Si, some of it would be used such that the entropy content gained in the eaten plant would be actually larger, Si < Splant . This process would repeat in that the higher in the food web, the higher the entropy content. In that respect, I would conclude that 1) humans would be organisms with some of the highest entropy (the most disorder) and 2) we should all be vegetarians in order to efficiently get low entropy in our diet. Do you agree with these conclusions?
Why the sun?
R. Penrose also explains why the sun is a source of low entropy and I was very surprised to learn that the reason is nearly a geometrical one. The sun is a hot spot, a small disk of light compared to the entire sky. Because of this geometrical configuration, the energy we receive from the sun has a much lower entropy that the energy sent back to space by earth because this energy is sent into all directions. Thus, if I understand correctly, if the earth was surrounded by many suns so much so that they would cover the entire sky, there would not be any source of low entropy and life would be unable to exist? Of course, one still needs to explain why the sun, itself a compact star and thus a source of low entropy, exists but the explanation goes on with cosmological arguments that I understand much less.
References
Ludwig Boltzmann, The second law of thermodynamics, in Theoretical physics and philosophical problems
Jean Bricmont, Science of chaos or chaos in science?
Roger Penrose, The emperor's new mind
1 comment:
I like the idea that we have to fight against entropy increase to be able to live !
However, I do not agree with some other ideas you raised here.
For example, I do think that entropy carries the arrow of time.
As Feynman puts it in his Lectures on Physics, if one records on video the mixing of 2 disctinct gases initially separated, and then plays it backward in time, one would see it gradually become ordered, and this would be a possible physical outcome, which would then seem to violate the second law of thermodynamics. In fact, for this to happen, every molecule's velocities and positions would have to be just right to get back to the unmixed state of the 2 gases, so that there was not as much disorder as we thought in the special mixed arrangement we had, where every single atom had exactly the correct speed and direction to come out right.
Now statistically this would be higly improbable to happen, so that on average entropy is always increasing with time, which relates entropy and time evolutions.
But it is true that the reason as for why the universe started with a low entropy remains a mistery.
Another thing with which I disagree is that idea about low entropy sources and the increase of entropy through the food web.
We have to remember that living organisms are not closed physical systems, but exchange energy with their environment. Therefore by capting energy from the environment, an organism can lower its own entropy, while increasing the environment entropy through its rejections and release of heat, by an amount greater than the entropy decrease he gained, so that overall the entropy of the universe still increases. Therefore any energy source is a potential source of low entropy for the organisms, be it the sun or many suns in the sky for the plants (suppose the sky was always covered with clouds, so that the light would come diffusely from all directions, then life would still be possible), or the plants or other animals for the animals. So if we define entropy as a measure of the orderness or complexity or unlikelyhood of random outcome, then I would say that we as humans are the organisms with the lowest entropy on earth. And animals entropy is lower than plants entropy. Therefore I don't believe vegetarians have a lower entropy than carnivores. But to achieve such low entropy, a lot of entropy has to be rejected in the environment, so that we also are the less effective organisms in producing low entropy. Therefore vegetarians contribute less to the universe entropy increase than carnivores.
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