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.

[madnak]

What if there are infinite universes? Or just a really really really big number?

[Metric]

[ QUOTE ]
What if there are infinite universes? Or just a really really really big number?

[/ QUOTE ]
It is possible -- in fact, one often imagines this to be true in formulating the problem. But it certainly does not get rid of the problem: Why do we find ourselves in such a special one, when the vast, vast, vast majority of intelligent beings in this "multiverse" should find themselves sitting in a little localized "oasis" of low entropy, surrounded by black holes? So the problem is effectively the same -- what makes us so fantastically special to be in a universe like this?

[madnak]

Well, with an infinite number of universes, there is certain to be one with the configuration of our universe. And of course, the people in such a universe are likely to consider themselves special in any case.

I don't mean to suggest that there is no reason to question. In that scenario the evidence we have isn't representative. So of course the likelihood of something "strange" behind the scenes is more likely. But our universe isn't inconsistent with the infinite universe idea, either.

Think about this. Maybe within infinite universes, most universes are unique in some way. Maybe a perfectly normal universe is quite rare. Maybe every universe is a bit quirky, so it's no surprise ours is. After all, if we are trying to evaluate our universe as "special," we have to take the full range of variation into account. Who knows what kinds of variables are very "normal" in our universe? We focus on that which stands out, but maybe only a few of a very large number of elements are out of place.

Wouldn't we need to know the range and extent of variability between universes in order to evaluate the likelihood of ours?

[Metric]

[ QUOTE ]
Well, with an infinite number of universes, there is certain to be one with the configuration of our universe. And of course, the people in such a universe are likely to consider themselves special in any case.

[/ QUOTE ]
No doubt. However, in cosmology, one is typically guided by the "copernican principle" -- that we don't occupy any particularly special place in the universe (or universe of universes). It's always possible that we really ARE the richest beings (entropy-wise) in 10^10^123 universes and we are simply destined to marvel forever at our extreme luck, but that's not a terribly satisfying answer from a scientific point of view...

[ QUOTE ]
Think about this. Maybe within infinite universes, most universes are unique in some way. Maybe a perfectly normal universe is quite rare. Maybe every universe is a bit quirky, so it's no surprise ours is. After all, if we are trying to evaluate our universe as "special," we have to take the full range of variation into account. Who knows what kinds of variables are very "normal" in our universe? We focus on that which stands out, but maybe only a few of a very large number of elements are out of place.

[/ QUOTE ]
But quantifying the kind of strangeness or "specialness" we see is what stat-mech was designed to do. Maybe (in fact, most probably) it just is not up to the task without some subtle revision to take into account general relativity.

[ QUOTE ]
Wouldn't we need to know the range and extent of variability between universes in order to evaluate the likelihood of ours?

[/ QUOTE ]
If we're considering universes that have the same raw materials as ours, and we simply look at the number of ways those materials can be ordered -- this is what stat mech is for. If the other universes are just completely different with utterly different physical laws, etc. then there really isn't much one can say statistically at all -- all bets are off.

[madnak]

Well, I don't see any reason to believe that all universes have the <i>same</i> materials or laws. Maybe most of our physical laws are similar with the laws of most other universes. But 100%? I don't know, that actually seems far-fetched to me considering other universes.

Maybe the laws of thermodynamics don't apply at all in some universes, and we aren't really very "lucky" in terms of entropy at all.

But even if we are special, I'm not sure how we would go about drawing conclusions from that.

[Metric]

[ QUOTE ]
Well, I don't see any reason to believe that all universes have the <i>same</i> materials or laws. Maybe most of our physical laws are similar with the laws of most other universes. But 100%? I don't know, that actually seems far-fetched to me considering other universes.

Maybe the laws of thermodynamics don't apply at all in some universes, and we aren't really very "lucky" in terms of entropy at all.

But even if we are special, I'm not sure how we would go about drawing conclusions from that.

[/ QUOTE ]
This is the danger of taking the "other universes" too literally. Usually, multiple copies of a system are simply used as a mathematical tool (called a "statistical ensemble") to make probabilistic predictions about a single, given system. For example, you can make correct thermodynamic predictions about a single cylinder of gas by considering a large collection of identical systems (without actually having to consult billions of identical cylinders of gas).

[madnak]

So when you say all "possible" universes, you mean all universes that might have been derived from the same big bang? Are you trying to suggest that the current configuration of the universe doesn't follow from the big bang?

[Metric]

[ QUOTE ]
So when you say all "possible" universes, you mean all universes that might have been derived from the same big bang? Are you trying to suggest that the current configuration of the universe doesn't follow from the big bang?

[/ QUOTE ]
Yes, I'm using "all possible universes" and "all possible configurations of our universe" more or less interchangably (see wikipedia's entry on "statistical ensemble" for details). As for the big bang, I'm simply saying that it implies something very puzzling about thermodynamics and statistical mechanics.

[maurile]

[ QUOTE ]
[ 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.

[/ QUOTE ]
When it was new, in the 1800's, the law was believed to be absolute and fundamental. Philosophers agonized over the "inevitable heat-death" of the universe, when it would have a uniform temperature and everything interesting would be over forever. This cultural fad has carried over to a lot of people's attitudes today, even though it's obsolete. Heat-death is never going to happen.

The 2nd Law is now recognized as an artifact of the way we describe the world, and it only applies probabilistically. That is, violations of the law are unlikely, not impossible, but the bigger the violation, the more unlikely it is. Imagine an evacuated box with a permeable partition and only four gas molecules in it.
<font class="small">Code:</font><hr /><pre>
--------------- ---------------
| mmmm : | | m m : m m |
--------------- ---------------
Low Entropy High Entropy
</pre><hr />
The reason entropy tends to increase is simply that if the molecules are bouncing around at random, the high entropy state is more probable. But it's perfectly possible for the system to spontaneously change from the high entropy state to the low entropy state, and if you wait long enough it will happen. It's just that the more molecules there are, the longer you'd have to wait on average.

You can watch the 2nd Law being violated any time you like with a microscope and a drop of water. According to the 2nd Law, an object moving through a viscous fluid should slow down and stop and stay stopped. But if you watch tiny dust particles in the water, they jump around erratically. Stopped particles start moving. It's perpetual motion. The particles are just getting shoved around by random water molecules.

[Metric]

[ QUOTE ]
You can watch the 2nd Law being violated any time you like with a microscope and a drop of water.

[/ QUOTE ]
Whoa -- that is a huge statement!
[ QUOTE ]
According to the 2nd Law, an object moving through a viscous fluid should slow down and stop and stay stopped.

[/ QUOTE ]
Actually, the 2nd law says that the entropy of the combined system can only increase. What is breaking down here is the concept of a "viscous fluid" -- we are seeing that the fluid is actually made of individual molecules.

[ QUOTE ]
But if you watch tiny dust particles in the water, they jump around erratically. Stopped particles start moving. It's perpetual motion. The particles are just getting shoved around by random water molecules.

[/ QUOTE ]
Yes, but this is actually a prediction of the 2nd law -- not a violation of it! One can see this as follows: The 2nd law predicts that if two systems are in thermal contact, their temperatures will tend to become equal -- i.e. the combined system will move toward a state of equilibrium. Let's model the "dust particle" as a simplified, two state system. It can either be "at rest" (and have no kinetic energy) or it can be "moving" (with some kinetic energy E). Let's say we start the dust particle out "at rest". This represents the energy probability distribution if the dust was at absolute zero. However -- now the 2nd law says that it will move into equilibrium with the "fluid" system and end up at temperature T. The Boltzmann distribution (which maximizes the entropy of a given system), then tells us that the probability to find the dust "moving" will be proportional to exp(-E/kT) where k is Boltzmann's constant and T is the equilibrium temperature. Thus, the probability to find the dust "moving" is now non-zero! (similarly, if you started out in a state of "moving" you would find that the particle moves to the same distribuition with non-zero probability to find the particle "at rest" -- effectively "slowing down" in the fluid as your intuition tells you)

Thus, the 2nd law holds up -- in fact, the 2nd law would have been in deep trouble if the opposite had happened -- if we had started the dust particle out in the "moving" state and then it ended up with 100% probability in the "at rest" state!

[PokerPadawan]

You should listen to Metric. This is all spot on.