Why does entropy grow when a solar system is formed?

[Rovolvo]

TL;DR Summary

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?

 

[Bandersnatch]

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.

 

[Rovolvo]

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.

 

[Bandersnatch]

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]