Entropy and contracting universe

[Schnellmann]

My somewhat ropey understanding of entropy is that it is a measure of order/disorder and that in a closed system entropy always increases. Was discussing it with my teenage daughter. Whilst trying to convey my limited understanding it struck me that if the universe is contracting (we had also been discussing the Red Dwarf episode backwards and what it would be like to live in such a world) then is everything is being squeezed into a smaller universe then wouldn’t entropy be decreasing? Got to be something wrong with that logic but what?

 

[Andrew Mason]

My somewhat ropey understanding of entropy is that it is a measure of order/disorder and that in a closed system entropy always increases. Was discussing it with my teenage daughter. Whilst trying to convey my limited understanding it struck me that if the universe is contracting (we had also been discussing the Red Dwarf episode backwards and what it would be like to live in such a world) then is everything is being squeezed into a smaller universe then wouldn’t entropy be decreasing? Got to be something wrong with that logic but what?

What makes you think the universe is contracting?

AM

 

[windy miller]

What makes you think the universe is contracting?

AM

I think the question was hypothetical .

 

[kimbyd]

My somewhat ropey understanding of entropy is that it is a measure of order/disorder and that in a closed system entropy always increases. Was discussing it with my teenage daughter. Whilst trying to convey my limited understanding it struck me that if the universe is contracting (we had also been discussing the Red Dwarf episode backwards and what it would be like to live in such a world) then is everything is being squeezed into a smaller universe then wouldn’t entropy be decreasing? Got to be something wrong with that logic but what?

In the situation where the universe was contracting, one of the primary initial impacts of the contraction would be to cause the universe to become lumpier.

In our universe, the formation of many large structures was prevented due to the rapidity of the expansion. If the universe was collapsing instead, you'd get the development of large superstructures, which would then collide with one another more frequently creating more and more massive objects. You'd probably get much more mass contained in black holes before too long, and black holes are the highest-entropy configurations of a finite amount of matter.

We can't really model what would happen as the universe approaches the singularity that appears in a collapsing universe (there are attempts, but they're not yet proven). But the lumpier universe the universe gets, the higher its entropy. And a collapsing universe would get lumpier quite rapidly.

 

[Schnellmann]

The universe is currently expanding but I understand it might contract in the future (towards a Big Crunch). Question relates to that scenario.

 

[Bandersnatch]

The universe is currently expanding but I understand it might contract in the future (towards a Big Crunch). Question relates to that scenario.

kimbyd's answer works for the contracting phase regardless of when its onset would be. Structures currently at distances too large to interact would begin to collapse into denser concentrations.

However, Big Crunch is not going to happen if the current model of the universe - with dark energy - is correct. And there's no good reason to think it isn't. A dark energy-dominated universe expands forever.

 

[Buzz Bloom]

everything is being squeezed into a smaller universe then wouldn’t entropy be decreasing?

Hi Schnellmann:

I think the other responders have misunderstood what you are trying to find out with your question.

A dark energy-dominated universe expands forever.

This is correct, but as I understand your question it is hypothetical rather than about the behavior of the current best model of our universe. Suppose, hypothetically, that a much older model of the universe was correct (even though the current model seems to be much more likely to be correct). The earliest GR models, before the acceleration of the expansion of the scale factor of our universe became the standard, had the possibility of expanding and then later contracting. I believe your question is:

In that old model what are the implications regarding entropy during the contracting stage?​

We can't really model what would happen as the universe approaches the singularity that appears in a collapsing universe (there are attempts, but they're not yet proven). But the lumpier universe the universe gets, the higher its entropy. And a collapsing universe would get lumpier quite rapidly.

Regarding this observation I think your question relates to an earlier period of contraction.

During the long period of contraction, is there ever any era in which the entropy decrease?​

This seems like a reasonable question since new structures will gravitationally form during this period, and that should reflect a reduction in entropy, as I naively understand it, since more structure seems to imply less disorder. I do not understand the logic of the underlined concept.

Regards,
Buzz

 

[kimbyd]

During the long period of contraction, is there ever any era in which the entropy decrease?

An overall entropy decrease isn't really a thing that can happen in a closed system. To get an entropy decrease, you have to have some sort of input of energy (and the source of that energy will necessarily have its entropy increase by more than the decrease it causes).

One way to understand why this is is to consider the statistical mechanics background of thermodynamics. In that case, the entropy is defined as follows:
1. Distinguish between a "macrostate" and a "microstate". The "macrostate" is the large-scale behavior: properties like temperature and pressure of a gas. The "microstate" is the precise state of all of the individual particles that make up the system. So the gas around you has something like a thousand billion billion molecules that make it up, but can be described with its pressure, temperature, and motion as its macrostate. The microstate would be all of the positions and motions of each and every one of those thousand billion billion molecules.
2. Entropy is a measure of how many different ways you can mix up the individual components (the microstate) while leaving the large-scale behavior (the macrostate) unchanged. Higher entropy = more ways you can mix up the parts of the system to give the same behavior.

From this definition, it immediately follows that states which can be mixed up in more different ways and still remain the same are higher-probability states. All closed systems will, as time progresses, naturally progress to higher-probability (and thus higher-entropy) states. And by "higher probability" I don't mean 20% higher chance either: for large systems, increasing the entropy by only a little bit increases the probability to such an obscene degree that you can safely assume the entropy won't drop again. As in, a small increase in entropy might have billions of times more ways to mix the microstates, leading to billions of times the probability.

So in practice, drops in entropy just can't realistically happen.

 

[Buzz Bloom]

So in practice, drops in entropy just can't realistically happen.

Hi kimbyd:

I believe you, but the I find it difficult to get my head around the concept of how entropy is theoretically calculated for an assumed finite universe as a whole during contraction.

Assume a small enclosed room say, 2 m x 2m x 2m. Compare the entropy in the room between (1) a gas uniformly distributed throughout the room, and (2) all the gas molecules bunched into one corner, say 1m x 1m x 1m. Which has more entropy? My naive thought is that (1) has more entropy than (2), and that since (2) is unstable, after a while the (2) gas will gain entropy as the gas fills the whole room like (1). Is this correct?

Now, consider (1) if we add the assumption that there is a black hole (BH) just outside of the room at one corner. Since the gas cannot get into the BH, the dynamics would have the gas move from state (1) towards state (2). So the presence of gravity changes something about the entropy.

BTW, I have read somewhere that Hawking's idea about Hawking radiation (HR) was motivated for seeking a resolution of the problem that entropy was decreased as stuff fell into a black hole, and the only way he could think of to restore the reduced entropy was for the BH to evaporate. That is, without HR there would be a permanent reduction of entropy.

Regards,
Buzz

 

[kimbyd]

Hi kimbyd:

I believe you, but the I find it difficult to get my head around the concept of how entropy is theoretically calculated for an assumed finite universe as a whole during contraction.

The finiteness is not necessary. Rather, it's the assumption of large-scale homogeneity that matters. The idea is that you break up the universe into large boxes which are each close to identical in their large-scale properties, and observe how those boxes evolve over time. These finite-size boxes won't exchange entropy with the neighboring boxes, because the neighboring boxes have the same properties (i.e., they'll expel just as much heat as they absorb).

Assume a small enclosed room say, 2 m x 2m x 2m. Compare the entropy in the room between (1) a gas uniformly distributed throughout the room, and (2) all the gas molecules bunched into one corner, say 1m x 1m x 1m. Which has more entropy? My naive thought is that (1) has more entropy than (2), and that since (2) is unstable, after a while the (2) gas will gain entropy as the gas fills the whole room like (1). Is this correct?

Yes, this is correct.

Now, consider (1) if we add the assumption that there is a black hole (BH) just outside of the room at one corner. Since the gas cannot get into the BH, the dynamics would have the gas move from state (1) towards state (2). So the presence of gravity changes something about the entropy.

Yes. Gravity changes entropy dramatically. In fact, nobody knows how to actually calculate the entropy for a generic gravitational system. We know a few extreme cases (like black holes), but that's about it.

But the underlying theory of how entropy works is independent of how entropy is calculated. We know that entropy must increase over time (or stay the same, if it's in equilibrium already) because of how entropy works, no matter the physical system. So when we know that our theories of gravity predict that the universe will get more lumpy in a collapsing universe as time goes on, then that means that that must represent an increase in entropy, because that's how entropy works.

This does lead to an interesting puzzle: how did entropy get so low in the early universe? There are lots of ideas, but so far no good answers to that question.

For example, a number of years ago Sean Carroll and Jennifer Chen proposed an idea where in the far future of an expanding universe with a cosmological constant, there would be rare events which would kick off a new inflating region. This is caused by a small local drop in entropy (which do happen, though are quite rare), followed by a rapid increase as the new pocket universe expands. The paper describing it is here.

Sean Carroll later showed that this particular model doesn't actually work because those local drops in entropy are far more rare than the original model proposed.

BTW, I have read somewhere that Hawking's idea about Hawking radiation (HR) was motivated for seeking a resolution of the problem that entropy was decreased as stuff fell into a black hole, and the only way he could think of to restore the reduced entropy was for the BH to evaporate. That is, without HR there would be a permanent reduction of entropy.

Not quite.

The first issue was that it was noticed that the behavior of a black hole could be described with thermodynamics-like laws. Just as entropy doesn't decrease in a closed system, the area of a black hole's event horizon couldn't decrease (so far as anybody knew). And the mathematical way of describing that looked suspiciously liked entropy. Jacob Beckenstein came up with the idea that maybe this apparent similarity was real: that the properties that mathematically looked similar to thermodynamics were genuinely thermodynamics. This meant that the non-decreasing nature of the area meant that the area of the horizon was proportional to the entropy of the black hole. Hawking took that idea and worked out the mathematical consequences of it, eventually concluding that if the black hole had an entropy, then it also had to have a temperature. And if it has a temperature, then it will radiate based upon that temperature. He made use of some quantum field theory to show physically how that could occur without violating the notion that nothing can escape a black hole, in particular showing that the quantum field theory prediction of radiation was exactly the radiation that would be expected from the black hole being a thermodynamic body at a specific temperature.

The information stuff came later, where there was a concern that because black holes evaporate, their entropy drops. It was shown that the entropy of the outgoing radiation is even higher, so entropy continues to increase throughout this whole process.

 

[Buzz Bloom]

My somewhat ropey understanding of entropy is that it is a measure of order/disorder and that in a closed system entropy always increases.

Hi @Schnellmann:

I think the thread cited below (especially my post #33 on page 2)

https://www.physicsforums.com/threads/some-confusion-re-entropy.949595/page-2#post-6017380​

provides a bit more detail about the question I think you were asking in the OP. So far no one has questioned my final conclusion there:

So, maybe the apparent violation of the second law really does not really happen because of the assumed hypothetical universe system has a definite gravitational component.​

This is intended to take into account the quote from the post above.

Gravity changes entropy dramatically. In fact, nobody knows how to actually calculate the entropy for a generic gravitational system. We know a few extreme cases (like black holes), but that's about it.

Regards,
Buzz