# How does the formation of a solar system not break the second law of thermodynamics?

Please forgive: I am a layman when it comes to physics and cosmology, and have tried finding an answer to this that I can understand, with no luck.

As I understand it, the solar system evolved from a massive molecular cloud. To me, this seems to break the second law of thermodynamics, as I think it suggests order from disorder.

I know there must be something wrong with my logic, but am really stuck.

Can anyone explain this one in layman's terms?

(Posting to both "Astronomy" and "Physics", as it seems to overlap these subjects)

• Jun 7 '14 at 6:09
• In general cross-posting like this to multiple sites is frowned upon.
– user10851
Jun 7 '14 at 7:17
• Don't miss Baez' run-up to black hole entropy, linked from John Rennie's answer. Dec 2 '19 at 20:24

The question is dealt with in some detail in this article by John Baez.

Although the article assumes only a basic understanding of physics it's probably a bit too much for the non-physicist so I'll summarise. As a gas cloud collapses the particles within it are confined to a smaller volume of space so the entropy associated with their position (call this $S_P$) goes down - basically the system gets more ordered. However as the cloud collapses it heats up and the entropy associated with the temperature (call this $S_T$) goes up. The collapsed cloud will eventually cool down of course, but that just transfers the entropy $S_T$ to the photons radiated out into space. Anyhow, the total entropy change for the collapse will be:

$$S_{total} = S_P + S_T$$

and we know that $S_P \lt 0$ and $S_T \gt 0$ so the two terms cancel each other.

Only John Baez shows that they don't cancel completely and the total entropy still goes down and this is, as you say, a violation of the second law.

What's missing from the calculation is the entropy associated with the gravitational field. There have already been various question related to this, for example Is the flatness of space a measure of entropy?, but I suspect these will be largely incomprehensible to the layman. Suffice to say that the infalling matter increasing the strength gravitational field associated with it, and this increases the entropy. Include this term and the total entropy is positive so the second law is not violated.

The ultimate limit of this is to form a black hole. Even though a (classical) black hole is completely characterised by just three parameters, mass, spin and charge, a black hole has the maximum entropy possible for the volume of space it occupies.

• if I'm not mistakened the entropy associate with a black hole was proportional to the surface area but otherwise solid post Aug 16 '14 at 8:43
• Actually, I think what's missing is not the entropy associated with the gravitational field, but the entropy change of the environment (i.e. other than the coalescing bits). As the clump cools, its own entropy decreases, but the entropy of the rest of the universe increases more, just as when any system gives off heat to a colder one.
– pwf
Dec 13 '14 at 0:56
• the infalling matter increasing the strength gravitational field associated with it I'm confused. How does a change in the distribution of mass change the strength of a gravitational field? Why would the accumulation of the mass into a confined volume have a different gravitational field than when the mass is distributed over a larger volume?
– LDC3
Dec 13 '14 at 5:10

As I understand it, the solar system evolved from a massive molecular cloud. To me, this seems to break the second law of thermodynamics, as I think it suggests order from disorder.

There are two problems here. One is the concept of entropy as disorder. A number of thermodynamics texts have now discarded this old concept. For one thing, it doesn't help in understanding entropy. For another, it's not necessarily correct. What is "disorder"? If disorder is just a synonym for an increase in entropy, explaining entropy as a measure of disorder is a meaningless tautology. You have to be very careful if "disorder" means something more than that.

The second problem, and this is a much bigger one, is that the second law of thermodynamics doesn't apply here. The second law of thermodynamics applies to isolated systems. A collapsing gas cloud is not an isolated system. Once the gas cloud has collapsed sufficiently it becomes opaque. It radiates energy thermally. That radiated energy transports entropy from the gas cloud to the universe as a whole. The second law applies to the gas cloud plus rest of the universe system. It does not necessarily apply to the gas cloud itself.

In fact, the entropy of the gas cloud decreases as the cloud collapses. There's nothing wrong with that. Think of your air conditioner. Turning your AC on decreases the entropy of your house. Your AC transfers entropy from your house to the surrounding air. The collapsing gas cloud similarly transfers entropy to the rest of the universe.

• Thanks for this answer, it's quite informative. I'd like to know, however, what did older textbooks mean by "disorder" in the context of entropy as a measure thereof. I just considered a more disordered system as less structured wrt another, more ordered one. Jul 6 '18 at 18:15

A good, semi-technical discussion of the general problem (how the post-Big-Bang evolution of the universe, including the formation of galaxies, stars, etc., can be reconciled with the 2nd Law) can be found here: http://arxiv.org/abs/0907.0659

It's important to realize that while the ensemble of atoms in the gas cloud does indeed, as your intuition suggest, lose entropy during the formation of the Sun, the total entropy of the universe increases because the photons emitted during the collapse of the gas cloud contribute a lot more entropy. This emission is pretty close to blackbody emission, which is the maximum-entropy form of radiation. (This isn't really "transport" of entropy; the newly created blackbody photons add a significant amount of entropy to the universe, more than enough to compensate for the loss of entropy by the atoms.)

"Entropy associated with the gravitational field" (as the first answer suggests) is simply not relevant.