Max Entropy: Is Infinite Chaos Possible?

[Rooster1981]

Apologies for the confusingly worded title; i was trying to keep it short.

If the universe reaches a state of maximum entropy (as in the Heat Death theory), why would that state be stable.
Wouldnt entropy be infinite and therefore any state, including the maximumly ordered state of the Big Bang, have a chance of occurring?

In fact couldn't this be thought of as a state of infinite chaos, where every configuration of the universe is possibly; including the overwhelming unlikely state that its in just at this second, where times arrow would make it appears to us that there was a big bang in the past and a heat death in the future?

Apologies if this makes no sense, i guess the key point is, why doesn't maximum entrop imply maximum chaos?

 

[I like Serena]

Apologies for the confusingly worded title; i was trying to keep it short.

If the universe reaches a state of maximum entropy (as in the Heat Death theory), why would that state be stable.
Wouldnt entropy be infinite and therefore any state, including the maximumly ordered state of the Big Bang, have a chance of occurring?

In fact couldn't this be thought of as a state of infinite chaos, where every configuration of the universe is possibly; including the overwhelming unlikely state that its in just at this second, where times arrow would make it appears to us that there was a big bang in the past and a heat death in the future?

Apologies if this makes no sense, i guess the key point is, why doesn't maximum entrop imply maximum chaos?

As I understand it, anything that "happens" involves converting some type of energy into some other type of energy. This process requires a difference in energetic levels.
In this process some of the difference in energetic levels gets lost (increase in entropy).

In the end the whole universe will become a kind of uniform soup, with hardly any differences any more in energetic levels. This means that it's not possible any more for anything to "happen".

 

[Andrew Mason]

As I understand it, anything that "happens" involves converting some type of energy into some other type of energy. This process requires a difference in energetic levels.
In this process some of the difference in energetic levels gets lost (increase in entropy).

In the end the whole universe will become a kind of uniform soup, with hardly any differences any more in energetic levels. This means that it's not possible any more for anything to "happen".

I don't see any evidence of the universe becoming a uniform soup of any kind. So long as enough non-dark-mass exists there will be sufficient energy to make things happen.

AM

 

[apeiron]

Apologies if this makes no sense, i guess the key point is, why doesn't maximum entrop imply maximum chaos?

Maximum entropy is indeed a maximum disordering - a maximum lack of order. So the heat death would be as low as you could go, and not a state you would expect to do anything of further significance.

Order is often called negentropy - negative entropy.

And while you might reason that the universe is infinite at the heat death, so increasing the odds on some really big fluctuation, it could have been just as infinite at the big bang. (We don't know, it just seems reasonable.)

 

[Dmitry67]

Note that Dark Energy can 'recycle' heat death (Big Rip->Big bang scenario)

 

[I like Serena]

I don't see any evidence of the universe becoming a uniform soup of any kind. So long as enough non-dark-mass exists there will be sufficient energy to make things happen.

AM

It will take a **while** before the universe looks like uniform soup.
And the problem is not lack of energy, but the lack of difference in energy.

If, for instance, everything has the same temperature, heat won't flow.
And a chemical reaction (other than equilibrium) will only occur if the generated heat can be dissipated (or if there is heat that can be absorbed).

 

[bcrowell]

If the universe reaches a state of maximum entropy (as in the Heat Death theory), why would that state be stable.

It would be thermodynamically stable, because it's in thermal equilibrium.

Wouldnt entropy be infinite and therefore any state, including the maximumly ordered state of the Big Bang, have a chance of occurring?

If the universe is spatially infinite, then its total entropy is always infinite, even right now. If it's spatially finite, then its entropy is always some big number, but not infinite.

In fact couldn't this be thought of as a state of infinite chaos, where every configuration of the universe is possibly;

Only high-entropy configurations would be accessible, not every configuration.

including the overwhelming unlikely state that its in just at this second, where times arrow would make it appears to us that there was a big bang in the past and a heat death in the future?

No, because the heat-dead universe would not fluctuate into a low-entropy state like the present one; that would violate the second law of thermodynamics.

Apologies if this makes no sense, i guess the key point is, why doesn't maximum entrop imply maximum chaos?

It depends on what you mean by chaos. Chaos does have a technical definition, which is not closely related to maximuum entropy.

Doesn't a state of Maximum Entropy (Heat Death) imply a Big Bang event eventually

I don't understand how the subject line relates to the OP.

 

[bcrowell]

I don't see any evidence of the universe becoming a uniform soup of any kind. So long as enough non-dark-mass exists there will be sufficient energy to make things happen.

A maximum-entropy universe is not expected to be a uniform soup; the maximum-entropy state of a gravitating system is clumpy. But in any case there is every reason to believe that the universe will continue to increase its entropy, as required by the second law of thermodynamics.

Here is a paper on this topic: http://arxiv.org/abs/astro-ph/9902189

 

[Andrew Mason]

It will take a **while** before the universe looks like uniform soup.
And the problem is not lack of energy, but the lack of difference in energy.
If, for instance, everything has the same temperature, heat won't flow.
And a chemical reaction (other than equilibrium) will only occur if the generated heat can be dissipated (or if there is heat that can be absorbed).

I don't disagee with you that local temperature differences are required. But for that to occur, all the stars would have to burn out and die and new stars would have to stop being created. All stars that have the potential to become supernova would have to have gone supernova and all of the effects of those super novae have been exhausted. Then the universe would be dead. Not because of too much entropy. Rather it would be because the universe will have run out of all its sources of local energy. Those local energy sources are needed to create the local temperature differences that drive the universe.

AM

 

[Andrew Mason]

A maximum-entropy universe is not expected to be a uniform soup; the maximum-entropy state of a gravitating system is clumpy. But in any case there is every reason to believe that the universe will continue to increase its entropy, as required by the second law of thermodynamics.

Here is a paper on this topic: http://arxiv.org/abs/astro-ph/9902189

How can there be a limit to the amount of entropy the universe can acquire? What limits it?

AM

 

[I like Serena]

I don't disagee with you that local temperature differences are required. But for that to occur, all the stars would have to burn out and die and new stars would have to stop being created. All stars that have the potential to become supernova would have to have gone supernova and all of the effects of those super novae have been exhausted. Then the universe would be dead. Not because of too much entropy. Rather it would be because the universe will have run out of all its sources of local energy. Those local energy sources are needed to create the local temperature differences that drive the universe.

AM

Yes, all stars would have to burn out.
And note that a source of local energy is not so much about having energy, but about having *more* energy than its surroundings.
All energy differences having been exhausted makes the universe dead, which is exactly what it means that entropy is at its maximum.

 

[Andrew Mason]

Yes, all stars would have to burn out.
And note that a source of local energy is not so much about having energy, but about having *more* energy than its surroundings.
All energy differences having been exhausted makes the universe dead, which is exactly what it means that entropy is at its maximum.

But that is not achieved by elimination of all temperature differences. It is achieved when there is nothing left that can create temperature differences. Local temperature differences are created by means potential energy sources (gravitational potential energy and energy in matter). A universe that is all at the same temperature could suddenly burst into life somewhere provided all potential energy sources have not been exhausted.

AM

 

[I like Serena]

But that is not achieved by elimination of all temperature differences. It is achieved when there is nothing left that can create temperature differences. Local temperature differences are created by means potential energy sources (gravitational potential energy and energy in matter). A universe that is all at the same temperature could suddenly burst into life somewhere provided all potential energy sources have not been exhausted.

AM

That's the thing.
If there's some potential energy source somewhere, there is still a difference in energy levels.
This difference can be converted into heat and back, losing some of its potential for energy on every go.
In the end there will be no difference in potential energy, no difference in electrical energy, no difference in chemical energy and no difference in temperature.

[edit]-- I like ILSe[/edit]

 

[bcrowell]

How can there be a limit to the amount of entropy the universe can acquire? What limits it?

If the universe is infinite, then its total entropy is infinite. Similarly, the amount of mechanical energy in the entire universe that's available to be extracted will always be infinite, if the universe is infinite. I haven't read the Krauss paper carefully, but it looks to me like he's talking about the observable universe that's accessible to a single observer, which is always finite.

 

[Andrew Mason]

That's the thing.
If there's some potential energy source somewhere, there is still a difference in energy levels.
This difference can be converted into heat and back, losing some of its potential for energy on every go.
In the end there will be no difference in potential energy, no difference in electrical energy, no difference in chemical energy and no difference in temperature.

I have always had difficulty attributing entropy to energy states that do not depend upon temperature, such as gravitational or nuclear potential energy. The conversion of that energy into thermal energy results in an increase in entropy. So for a maximum entropy universe, all that potential energy has to be converted into thermal energy. Since gravitational potential energy is part of that, so long as massive bodies exist at relative distances and have gravitational attraction, one could always potentially increase the supply of thermal energy and increase the entropy of the universe.

So, perhaps the OP's original question in the title is correct. We would have to return to a state in which the universe had no size in order to have maximum possible entropy.

AM

 

[bcrowell]

I have always had difficulty attributing entropy to energy states that do not depend upon temperature, such as gravitational or nuclear potential energy. The conversion of that energy into thermal energy results in an increase in entropy. So for a maximum entropy universe, all that potential energy has to be converted into thermal energy. Since gravitational potential energy is part of that, so long as massive bodies exist at relative distances and have gravitational attraction, one could always potentially increase the supply of thermal energy and increase the entropy of the universe.

A state in which these sources of potential energy still exist in a thermodynamically exploitable form is not a maximum-entropy state. This is just ordinary thermo, and is not controversial.

Applying this to astronomy, our galaxy's entropy would be increased by making it all into one big black hole. In fact, the entropy of our galaxy is currently dominated by the entropy of its supermassive black hole. (The entropy of a black hole can be further increased by letting it evaporate into Hawking radiation.)

The time-scale for the universe to reach such an equilibrium state may be very long, and may require processes like very-low-probability quantum tunneling: http://en.wikipedia.org/wiki/Future_of_an_expanding_universe

 

[mrspeedybob]

I have always had difficulty attributing entropy to energy states that do not depend upon temperature, such as gravitational or nuclear potential energy. The conversion of that energy into thermal energy results in an increase in entropy. So for a maximum entropy universe, all that potential energy has to be converted into thermal energy. Since gravitational potential energy is part of that, so long as massive bodies exist at relative distances and have gravitational attraction, one could always potentially increase the supply of thermal energy and increase the entropy of the universe.

So, perhaps the OP's original question in the title is correct. We would have to return to a state in which the universe had no size in order to have maximum possible entropy.

AM

If the expansion of the universe eventually results in a condition where each elementary particle is alone in it's observable universe then there would be no gravitational potential energy. Since it's velocity would then be undefinable there would be no kinetic energy. Since there would be nothing to react with, ever, there would be no potential nuclear or chemical energy. I think this is the likely end state of the universe.

 

[Andrew Mason]

If the expansion of the universe eventually results in a condition where each elementary particle is alone in it's observable universe then there would be no gravitational potential energy. Since it's velocity would then be undefinable there would be no kinetic energy. Since there would be nothing to react with, ever, there would be no potential nuclear or chemical energy. I think this is the likely end state of the universe.

Why would this be likely? What would cause all the particles in even one galaxy, let alone in all 100 billion + galaxies to separate like that, let alone give each of them enough energy to escape the observable universe of all the others? I think we should stick to science here.

AM

 

[1dominator1]

Why would this be likely? What would cause all the particles in even one galaxy, let alone in all 100 billion + galaxies to separate like that, let alone give each of them enough energy to escape the observable universe of all the others? I think we should stick to science here.

AM

Doesn't the 2nd law of thermodynamics state that the energy density slowly equalizes across a system? So everything would eventually (after very long time) degrade.
Also at a state of maximum entropy, would the universe be full of matter or energy, or a mixture of both?

But as to why stuff is accelerating in every direction as opposed to decelerating I have no idea.