Why does entropy grow when a solar system is formed?

In summary, Sean Carroll writes that the protostellar cloud had a lower entropy than the solar system it produced.
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In "From eternity to here", Sean Carroll writes that the protostellar cloud had a lower entropy than te solar system it produced. That strikes me as odd. A solar system looks more arranged than a dust cloud. What am I missing here?
On page 50 of "From eternity to here", Sean Carroll writes that the protostellar cloud had a lower entropy than the solar system it produced. That strikes me as odd. A solar system looks more arranged than a dust cloud. When talking about entropy, someone always mentions the milk in the coffee. Milk in a drop of milk has lower entropy then milk spread in one of the billion ways it can spread between the "coffee molecules". Wouldn't you aggree, that the milk in a drop looks more like a planet and the milk all spread out looks more like the dustcloud. What am I missing here?
 
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A collapsing cloud of gas is not quite like milk in coffee. The crucial part is that there is an attractive force in the form of gravity.
On the one hand, it causes the cloud to shrink and clump up - which gives us a pause, as this reduces the entropy. But on the other hand, the gas heats up as it shrinks. And then radiates into space. And then shrinks some more. And then radiates. And so on. The key is not to forget about the radiation part.
If we want to think about this in terms of how ordered a system is, it's best to consider where the energy was when you had a cloud, and where it is when it's become a bunch of rocks. You should be able to see that a lot of the energy that was initially confined to the area of space where the cloud was, has been 'smeared' around a huge volume of space (as radiation). This wins over the decrease of entropy from matter clumping into dense balls.

John Baez has a nice write-up on the topic here: https://math.ucr.edu/home/baez/entropy.html , with more detailed treatment. He's a bit coy in not wanting to provide the final answer on a plate, though.
 
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Bandersnatch said:
A collapsing cloud of gas is not quite like milk in coffee. The crucial part is that there is an attractive force in the form of gravity.
On the one hand, it causes the cloud to shrink and clump up - which gives us a pause, as this reduces the entropy. But on the other hand, the gas heats up as it shrinks. And then radiates into space. And then shrinks some more. And then radiates. And so on. The key is not to forget about the radiation part.
If we want to think about this in terms of how ordered a system is, it's best to consider where the energy was when you had a cloud, and where it is when it's become a bunch of rocks. You should be able to see that a lot of the energy that was initially confined to the area of space where the cloud was, has been 'smeared' around a huge volume of space (as radiation). This wins over the decrease of entropy from matter clumping into dense balls.

John Baez has a nice write-up on the topic here: https://math.ucr.edu/home/baez/entropy.html , with more detailed treatment. He's a bit coy in not wanting to provide the final answer on a plate, though.
Thanks, that makes so much sense. The energy part, that was what I was missing.
 
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Oh, poo. I've just noticed. The link attribution should read John Baez. Not his arguably more musical cousin Joan.

[Typo fixed in your post above by a Mentor] :smile:
 
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1. Why does entropy increase during the formation of a solar system?

Entropy is a measure of the disorder or randomness in a system. When a solar system is formed, there is a large amount of matter and energy that is spread out and not yet organized into planets, moons, and other celestial bodies. This high level of disorder leads to an increase in entropy.

2. How does the formation of a solar system contribute to the increase in entropy?

The process of forming a solar system involves the collapse of a large cloud of gas and dust, which releases a tremendous amount of energy. This energy is then spread out and becomes more disordered as it interacts with other particles and objects in the system. As a result, the overall entropy of the system increases.

3. Is the increase in entropy during the formation of a solar system inevitable?

Yes, according to the second law of thermodynamics, the total entropy of a closed system will always increase over time. This means that the increase in entropy during the formation of a solar system is a natural and inevitable process.

4. How does the increase in entropy affect the stability of a newly formed solar system?

The increase in entropy during the formation of a solar system can actually contribute to its stability. As the system becomes more disordered, it also becomes more complex and diverse, which can lead to the emergence of stable planetary orbits and other dynamic systems within the solar system.

5. Can the increase in entropy be reversed in a solar system?

No, the second law of thermodynamics states that entropy can only increase or remain constant in a closed system. Therefore, once a solar system has formed and reached a state of maximum entropy, it cannot be reversed. However, local decreases in entropy can occur through processes such as the formation of planets and the emergence of life.

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