Is the 2nd Law of Thermodynamics invariant?

[Matt R.]

"When all systems taking part in a process are included, the entropy either remains constant or increases.... no process is possible in which the total entropy decreases, when all systems taking part in the process are included." This is a statement of the 2nd law of thermodynamics in terms of entropy from my physics textbook.

I am wondering if the 2nd law is invariant. If it is invariant, why is the universe in its current state, and not in a state of maximal disorder. In other words, why are there small "clusters" of low entropy in the universe (galaxies, planets, life forms, the human brain), when the state of maximal entropy would have clusters of matter and energy strewn randomly about.

Is the 2nd law of thermodynamics correct, or just an oversimplification (similar to Newton's laws of motion) that is only applicable to what we can experimentally observe? Is there an "easy" and well accepted solution to this question that I'm unaware of?

If you claim to "know" the answer, please state that it is a well accepted theory. If you have an opinion, feel free to state it as well (i.e. I would just like to know that it's an opinion, and not that 99% of physicists believe it to be true).

[Borodog]

[ QUOTE ]
"When all systems taking part in a process are included, the entropy either remains constant or increases.... no process is possible in which the total entropy decreases, when all systems taking part in the process are included." This is a statement of the 2nd law of thermodynamics in terms of entropy from my physics textbook.

I am wondering if the 2nd law is invariant. If it is invariant, why is the universe in its current state, and not in a state of maximal disorder. In other words, why are there small "clusters" of low entropy in the universe (galaxies, planets, life forms, the human brain), when the state of maximal entropy would have clusters of matter and energy strewn randomly about.

Is the 2nd law of thermodynamics correct, or just an oversimplification (similar to Newton's laws of motion) that is only applicable to what we can experimentally observe? Is there an "easy" and well accepted solution to this question that I'm unaware of?

If you claim to "know" the answer, please state that it is a well accepted theory. If you have an opinion, feel free to state it as well (i.e. I would just like to know that it's an opinion, and not that 99% of physicists believe it to be true).

[/ QUOTE ]

Some caveats: It's been a while, I never cared for thermo, and I've shot off my mouth without thinking carefully about the question and my answer and gotten put in my place on thermo issues here before.

But given that, the order we see in the Universe is not terribly surprising. The best theory is that the Universe started out in a state of extremely small volume and extremely high energy; in fact the Universe was completely filled with pure radiation. Presumably there were tiny anisotropies, as has been confirmed by observation of the Cosmic Background Radiation.

As the Universe expanded, it cooled, symmetries were broken, and matter condensed out of the radiation. Because of the anisotropies, the Universe became clumpy, and those self-gravitating clumps formed structures at all scales. Hence order (clumpiness, stars, galaxies, galactic clusters, superclusters, etc.) arises out of what seemed extremely disorded (pure radiation).

A good analogy is steam. Steam is extremely hot and disordered, but as it expands, it cools and becomes water vapor, and water vapor condenses and forms water droplets. Order from disorder. The trick of course is that while the energy of the system is constant (not really, since energy is being carried away by radiation, but we can neglect that here), the volume is not.

[slickpoppa]

If you are really interested in this subject, read "The Fabric of the Cosmos" by Brian Greene. He talks a lot about this.

[Matt R.]

Borodog,
I had a long reply typed up, but then I realized that I likely made a mistake in my assumptions for calculating entropy of a system.

Without knowing much of anything regarding anisotropies and symmetry breaking, is it safe to say that the reason for localized order in the universe is due to the nature of elementary particle physics? i.e. it's all in the force interactions. Which is why I can't fully understand the explanation at the moment. I feel like some of the stuff you speak of in your post emerges naturally from the math of quantum field theory, and I won't be able to get a grasp on it until I understand the math.

Basically (from what I can understand), the anisotropies and symmetry breaking "slows down" the rate of entropy increase in the universe. Entropy was at a minimum at the big bang, as all the matter/energy was condensed into an infinitely tiny point. Rather than the big bang randomly throwing matter and energy everywhere (which would not allow for the "clumping"), the things you speak of in your post caused differential distrubutions of entropy levels in the universe. This allows for order we can observe on a day-to-day basis, and prevented the universe from moving towards a maximal state of entropy in a relatively shorter amount of time.

If there are any glaring errors in my summarized conclusion that I tried to draw from you post, feel free to correct me -- I'd like to understand this stuff better.

Also, slickpoppa, I own the fabric of the cosmos but haven't gotten around to reading it yet. Thanks for the recommendation.

[Metric]

[ QUOTE ]
"When all systems taking part in a process are included, the entropy either remains constant or increases.... no process is possible in which the total entropy decreases, when all systems taking part in the process are included." This is a statement of the 2nd law of thermodynamics in terms of entropy from my physics textbook.

I am wondering if the 2nd law is invariant. If it is invariant, why is the universe in its current state, and not in a state of maximal disorder. In other words, why are there small "clusters" of low entropy in the universe (galaxies, planets, life forms, the human brain), when the state of maximal entropy would have clusters of matter and energy strewn randomly about.

Is the 2nd law of thermodynamics correct, or just an oversimplification (similar to Newton's laws of motion) that is only applicable to what we can experimentally observe? Is there an "easy" and well accepted solution to this question that I'm unaware of?

If you claim to "know" the answer, please state that it is a well accepted theory. If you have an opinion, feel free to state it as well (i.e. I would just like to know that it's an opinion, and not that 99% of physicists believe it to be true).

[/ QUOTE ]
This is a profound question that nobody fully understands at present. You will hear people talk about inflationary cosmology from time to time, but this does not solve the problem, and confusion on this issue is common even among physics Ph.D.'s and practicing relativists!

Basically, gravity complicates thermodynamics on several levels. First and most important, if you simply treat the thermodynamics of a simple idealized box of gas, the most probable state (the one with highest entropy) is the one in which the gas is uniformly spread throughout the box. However, if you make the box big enough and allow gravity to interact, it turns out that this is not the state of highest entropy. Matter can collapse (as it is observed to do in "star factory" nebulas -- note that this would not be possible if it violated the 2nd law!) and form stars, which eventually collapse further and form black holes -- these are states of enormous entropy. The fact that we are alive here is actually a consequence of the universe starting out in a very "special" state in which the "matter" degrees of freedom were "thermalized" but gravitational degrees of freedom were somehow not. As gravitational systems slowly move toward states of higher entropy (our sun, for example), life on earth effectively mooches off the entropy imbalance. Obviously, if the universe were in a state of maximal entropy (consisting of black holes and little else), life would not be possible. But why the universe should start out in a hugely improbable state is a truly baffling puzzle!

Here is a very recent paper on the subject by one of the world's foremost relativists:

http://xxx.lanl.gov/abs/gr-qc/0507094

[yukoncpa]

Hi Metric,
I'm not questioning you, but as a layman I'm merely curious.

[ QUOTE ]
But why the universe should start out in a hugely improbable state is a truly baffling puzzle!


[/ QUOTE ]

Suppose their are many worlds (or multiple universes), Why is it baffling that we happen to be in a rare universe that is highly improbable given that we are indeed in that universe?
Again, I hate to cross swords with you Metric because I don't know the subject matter, but I am very interested in your field and would like to learn more.

[PokerPadawan]

Don't confuse gravitational clumping with order. Just because the spatial distribution of matter has changed doesn't mean it has lower entropy. There is a theorem in astrophysics that says that gravitational collapse leads to heating. More heat leads to higher entropy, usually. So a hypothetical universe where matter was uniformly distributed would be relatively cold and low in entropy, while a clumpy one like ours will have hotspots with probably higher average entropy.

Also, when thinking about clusters of low entropy, like humans, remember that the 2nd law refers to a closed system. A human is not a closed system; neither is a galaxy. You'd need to include food, air, waste, etc., in the entropy balance for humans. Basically, a human keeps entropy low because we discard waste heat into our environment. Galaxies accrete and expel material as well, not to mention the "micro" processes, such as star formation, magnetohydrodynamic turbulence, radiation fields, etc.

[maurile]

[ QUOTE ]
"When all systems taking part in a process are included, the entropy either remains constant or increases.... no process is possible in which the total entropy decreases, when all systems taking part in the process are included." This is a statement of the 2nd law of thermodynamics in terms of entropy from my physics textbook.

[/ QUOTE ]
Not that it answers your main question, but it might be worth pointing out that the second law of thermodynamics is a statistical law, not a fundamental law. Saying that entropy will not decrease in a closed system is like saying that chips on a poker table tend to flow from worse players to better players. It is true over the long run, but there are local, temporary exceptions.

[chrisnice]

[ QUOTE ]
It is true over the long run, but there are local, temporary exceptions.

[/ QUOTE ]

Are you sure? What would these be and what do you mean by local? Inside the event horizon of a black hole entrophy decreases but the entrophy of the universe as a whole increases.

[Metric]

[ QUOTE ]
Suppose their are many worlds (or multiple universes), Why is it baffling that we happen to be in a rare universe that is highly improbable given that we are indeed in that universe?
Again, I hate to cross swords with you Metric because I don't know the subject matter, but I am very interested in your field and would like to learn more.

[/ QUOTE ]
No "crossing of swords" needed. This is something that must be taken account of in the calculation. Instead of looking at the space of all possible universes, one looks at the space of all possible universes containing, say, our galaxy (and us). Then one still finds that a universe like ours occupies a vanishingly tiny region of phase space (the space of possible states), and thus appears to be highly improbable -- the (by far) most likely universe given the constraint of "us here to observe it" would be something like our galaxy surrounded by a bunch of black holes instead of other galaxies as far as the eye can see.