• Quick note - the problem with Youtube videos not embedding on the forum appears to have been fixed, thanks to ZiprHead. If you do still see problems let me know.

Entropy and the Big Bang

Roboramma

Penultimate Amazing
R
Joined
Feb 22, 2005
Messages
16,747
Location
Shanghai
It seems that an important question in physics is "why did the universe start in a state of low entropy?".

I'd like to ask a related question: given an expanding universe, is there a relationship between density and entropy?

The early universe was in a state of high density and high temperature. What I'm asking is, given expansion doesn't that necessarily imply low entropy?

As the universe expands it will necessarily cool off. That's very similar, as I see it, to a state where there is a high temperature region with a low temperature region near-by, such that energy can flow from the region of high to low temperature.

In this case we have a high temperature system that will evolve into a low temperature system over time (due to expansion). Without expansion that wouldn't happen: the average temperature would just remain the same.

So, my question is, does that evolution from high to low temperature imply an evolution from low to high entropy?

If so it seems odd, but entropy becomes dependent not just on the current state of the system but on possible future states.


To make my point perhaps more clear: isn't it necessarily the case the there are more possible states for a system to take post-expansion than pre-expansion?

Or to take another tack: say I have a model universe that's finite in size. I start it in a low entropy state and let it evolve for a while until it reaches thermal equilibrium. It's now in a high entropy state. Then we turn on expansion. It seems to me that I've just opened up the possibility for higher entropy and my system can go on evolving in interesting ways (rather than just having random thermal fluctuations).

But maybe I'm just rambling incoherently here.
 
How are you thinking about gravity?

Does your expansion pull things farther apart and add gravitational potential energy (less entropy) or is this compensated for? Remember, the farther things are apart, the more work I can get out of them by allowing gravity to pull them together again.
 
The problem is that entropy depends on the number of available states (and these concepts get pretty diffuse once you move away from particles in a box, ideal Einstein solid, etc). If a non-expanding universe is sufficiently hot then low-temperature states will never become available unless there is some mechanism for energy fluctuation.

But the "entropy of the universe" is a very diffuse concepts. If the universe is infinity but unbounded, how many de Broglie wavelengths of a particle fit into it?
 
Roboramma said:
I'd like to ask a related question: given an expanding universe, is there a relationship between density and entropy?
Click to expand...

Yes. This is a classic component to the ideal gas problem. If you have a container with a divider in the middle, and fill it with gas on one side and nothing on the other, what happens when you remove the divider? The gas won't lose any energy in the process, and it won't change temperature either, but it will expand into the entire chamber. Furthermore, that change is irreversible: the gas won't spontaneously return to one half of the container. Why? Because the expansion increased the entropy of the system.

HOWEVER...

If you don't expand the gas by removing the divider, but instead by allowing the gas to do work against the divider (ie, move it like a piston), then the change is reversible: the gas loses energy and lowers in temperature as it expands. The momentum contribution to entropy lowers, compensating the increase in the positional entropy. This process is reversible: get the gas back on one side by moving the divider back.

So, in regards to the universe as a whole: which expansion does it more resemble?
 
Ziggurat said:
If you don't expand the gas by removing the divider, but instead by allowing the gas to do work against the divider (ie, move it like a piston), then the change is reversible: the gas loses energy and lowers in temperature as it expands. The momentum contribution to entropy lowers, compensating the increase in the positional entropy. This process is reversible: get the gas back on one side by moving the divider back.
Click to expand...

This to me is one of the most counterintuitive concepts of elementary thermodynamics - when you expand a gas container mechanically, its contents do work.
 
Ziggurat said:
Yes. This is a classic component to the ideal gas problem. If you have a container with a divider in the middle, and fill it with gas on one side and nothing on the other, what happens when you remove the divider? The gas won't lose any energy in the process, and it won't change temperature either, but it will expand into the entire chamber. Furthermore, that change is irreversible: the gas won't spontaneously return to one half of the container. Why? Because the expansion increased the entropy of the system.

HOWEVER...

If you don't expand the gas by removing the divider, but instead by allowing the gas to do work against the divider (ie, move it like a piston), then the change is reversible: the gas loses energy and lowers in temperature as it expands. The momentum contribution to entropy lowers, compensating the increase in the positional entropy. This process is reversible: get the gas back on one side by moving the divider back.

So, in regards to the universe as a whole: which expansion does it more resemble?
Click to expand...

It depends on boundary conditions. The piston is a boundary that moves adiabatically (slowly). The divider is a boundary that disappears instantaneously.

The boundary conditions for the universe are not known precisely. This is why there are so many models that scientists compare to data. Even if a scientists agrees in the validity of general relativity, he does not know the boundary conditions to the universe.

The inflation model corresponds to one boundary condition. The oscillating universe corresponds to another. Steady state cosmos corresponds to yet another boundary condition. So the physicist's cosmology research may be said to determining the boundary conditions of the universe.

I am looking at it from the standpoint of a well educated layman. I am a physicist, but cosmology is not my field. I have enough knowledge to sound erudite while making stupid remarks. However, I do see something worth considering now and again. So althoug my opinion is hardly authoritative, I conjecture that:

Sudden phase transitions are associated with increases in entropy. The universe has undergone several phase transitions that were 'sudden' compared to the current age of the universe. The cosmic bleaching event, the formation of the first stars, and the onset of negative energy are all like sudden phase transitions. So the entropy of the universe greatly increased at each phase transition.

If inflation were true, the termination of cosmic inflation was like a phase transition. The universe was in a quantum condensate type phase before inflation, and is now in a semiclassical state

I think that most of the observational data supports boundary conditions where the entropy of the universe increases over a 13.8 BY time scale. The total entropy of the universe has been increasing from the official Big Bang until today. I would expect the entropy of the universe to increase at least for another 15 BY.

The future is an extrapolation of current data, at best. I am not sure that the creation of entropy will continue forever. This 13.8 BY time span constitutes all of the observational data that we have. Extrapolations slightly beyond the observational data are probably reliable. All extrapolations past the range of observational data are going to be model dependent. I am not even sure how far the laws of thermodynamics can be plausibly extrapolated.

The concept of entropy may be ill posed for the universe because it includes everything. There is no separation of system from environment, making the second law of thermodynamics hard to express. So extrapolation past 14 BY in the future may be a matter of metaphysics rather than science. With this caveat:


Some models of cosmology lead to the prediction that the universe will be 'recreated' after it heat death. For instance, the oscillating universe model was developed soon after general relativity. The total entropy in that model is a periodic function of time, sort of like a harmonic oscillator.

The brane model of the universe assumes that the universe formed in a collision of branes. Branes are one of those really mathematical concepts which is well beyond my ability to explain. However, it appears to me that every collision in this model destroys entropy.
 
Roboramma said:
It seems that an important question in physics is "why did the universe start in a state of low entropy?".

I'd like to ask a related question: given an expanding universe, is there a relationship between density and entropy?

The early universe was in a state of high density and high temperature. What I'm asking is, given expansion doesn't that necessarily imply low entropy?

As the universe expands it will necessarily cool off. That's very similar, as I see it, to a state where there is a high temperature region with a low temperature region near-by, such that energy can flow from the region of high to low temperature.

In this case we have a high temperature system that will evolve into a low temperature system over time (due to expansion). Without expansion that wouldn't happen: the average temperature would just remain the same.

So, my question is, does that evolution from high to low temperature imply an evolution from low to high entropy?

If so it seems odd, but entropy becomes dependent not just on the current state of the system but on possible future states.


To make my point perhaps more clear: isn't it necessarily the case the there are more possible states for a system to take post-expansion than pre-expansion?

Or to take another tack: say I have a model universe that's finite in size. I start it in a low entropy state and let it evolve for a while until it reaches thermal equilibrium. It's now in a high entropy state. Then we turn on expansion. It seems to me that I've just opened up the possibility for higher entropy and my system can go on evolving in interesting ways (rather than just having random thermal fluctuations).

But maybe I'm just rambling incoherently here.
Click to expand...

Nope, seems quite coherent.

One of the things I linked in our previous discussions was the entropy gap. That as the universe approaches maximum entropy the expansion increases that maximum maintaining an entropy gap between current entropy and maximum entropy. Unfortunately I can't find any relevant articles and the end result of such a scenario might be a big rip.


Something I did find that goes more to marplots question on gravitational entropy.

https://www.researchgate.net/public..._universe's_low_initial_gravitational_entropy
 
Everyone: thanks for the replies! I haven't had time to give them the necessary thought to give the kind of reply I'd like to, hopefully later today. But you've all given me a lot to think about. :)
 
The Man said:
Nope, seems quite coherent.

One of the things I linked in our previous discussions was the entropy gap. That as the universe approaches maximum entropy the expansion increases that maximum maintaining an entropy gap between current entropy and maximum entropy. Unfortunately I can't find any relevant articles and the end result of such a scenario might be a big rip.


Something I did find that goes more to marplots question on gravitational entropy.

https://www.researchgate.net/public..._universe's_low_initial_gravitational_entropy
Click to expand...

Hey, cool, that sounds a lot like the sort of ideas that I was talking about in the OP. :D
 
The Man said:
Nope, seems quite coherent.

One of the things I linked in our previous discussions was the entropy gap. That as the universe approaches maximum entropy the expansion increases that maximum maintaining an entropy gap between current entropy and maximum entropy. Unfortunately I can't find any relevant articles and the end result of such a scenario might be a big rip.


Something I did find that goes more to marplots question on gravitational entropy.

https://www.researchgate.net/public..._universe's_low_initial_gravitational_entropy
Click to expand...

AFAIK The Big Rip scenario will only come in to play if Dark Energy isn't a constant and the vacuum energy keeps increasing over time.
 
Ziggurat said:
So, in regards to the universe as a whole: which expansion does it more resemble?
Click to expand...


In the first case of the gas expanding outwards from one partition to the next
corresponds to a preexisting spacetime. The Big Bang in creates matter but not
space. Initial entropy is high at the center of the expansion and low everywhere
else. Entropy increases and energy remains constant.

In the second case, the expansion of the gas pressing against the divider
resembles the expansion of spacetime. The gas does work pushing the divider
outwards and the entropy decreases. One can divide the universe into a series
dividers with pockets of hot gas between them. The expansion of the universe
cools the gas exactly as expected.

The problem, for an observer at any one of the dividers sees the other
dividers move away with the expansion and work being performed by
the gas, but no work being done at his divider. The energy of the universe
disappears as total entropy decreases.

This fits the universe better than the fixed spacetime model.
 
Ziggurat said:
Yes. This is a classic component to the ideal gas problem. If you have a container with a divider in the middle, and fill it with gas on one side and nothing on the other, what happens when you remove the divider? The gas won't lose any energy in the process, and it won't change temperature either, but it will expand into the entire chamber. Furthermore, that change is irreversible: the gas won't spontaneously return to one half of the container. Why? Because the expansion increased the entropy of the system.

HOWEVER...

If you don't expand the gas by removing the divider, but instead by allowing the gas to do work against the divider (ie, move it like a piston), then the change is reversible: the gas loses energy and lowers in temperature as it expands. The momentum contribution to entropy lowers, compensating the increase in the positional entropy. This process is reversible: get the gas back on one side by moving the divider back.

So, in regards to the universe as a whole: which expansion does it more resemble?
Click to expand...

I never thought that I would say this, but please check your math 'Ziggurat'.

In the first case you outline if the barrier is removed, then the gas pressure will be reduced and there will be a reduction in the temperature as well due to the increase in volume.

In the case of the Ideal Gas Law:

PV = nRT

Therefore if the volume is doubled, then the pressure and temperature must be reduced by one-half in order to keep the equation in balance.
 
Crossbow said:
I never thought that I would say this, but please check your math 'Ziggurat'.

In the first case you outline if the barrier is removed, then the gas pressure will be reduced and there will be a reduction in the temperature as well due to the increase in volume.

In the case of the Ideal Gas Law:

PV = nRT

Therefore if the volume is doubled, then the pressure and temperature must be reduced by one-half in order to keep the equation in balance.
Click to expand...

What? No. If the volume doubles in this particular case the pressure halves, as you say. So the RHS stays the same. 2 × 1/2 = 1.
 
Crossbow said:
I never thought that I would say this, but please check your math 'Ziggurat'.
Click to expand...

I occasionally make mistakes, but this isn't one of those times. :o

In the first case you outline if the barrier is removed, then the gas pressure will be reduced and there will be a reduction in the temperature as well due to the increase in volume.
Click to expand...

In the case of free expansion of an ideal gas, there is no drop in temperature, because there's no loss of energy (the gas did no work against the barrier). This is a canonical thermodynamics problem, the kind basically every thermo textbook covers.

In the case of the Ideal Gas Law:

PV = nRT

Therefore if the volume is doubled, then the pressure and temperature must be reduced by one-half in order to keep the equation in balance.
Click to expand...

In the case of free expansion, the temperature will remain the same, so the right side of the equation remains unchanged. To balance the left side, the pressure must drop to 1/2 if the volume increases by a factor of 2, and that balances everything.

For expansion to double the volume where the gas does work but exchanges no heat, the temperature drops so the pressure must drop by MORE than a factor of 2 to keep the equation balanced.
 
To 'TubbaBlubba' and 'Ziggurat':

Sorry about that! My mistake.

You all are quite correct and I was mistaken.

My apologies for the error.
 
Hercules Rockefeller said:
AFAIK The Big Rip scenario will only come in to play if Dark Energy isn't a constant and the vacuum energy keeps increasing over time.
Click to expand...


As far as I know the relevant factor is the ratio of pressure to energy density of the universe. That ratio (w) being less than -1 indicates the domination of the hypothetical dark energy referred to as "phantom energy".


https://en.wikipedia.org/wiki/Equation_of_state_(cosmology)


https://en.wikipedia.org/wiki/Phantom_energy

Indeed though, a big rip is only the result of a particular hypothetical state (w < -1) of the universe. A positive pressure and negative energy density or a negative pressure and positive energy density (a negative ratio). Where the absolute value of the energy density is less than that of the pressure (a ratio with an absolute value greater than 1).
 
Last edited:
TubbaBlubba said:
This to me is one of the most counterintuitive concepts of elementary thermodynamics - when you expand a gas container mechanically, its contents do work.
Click to expand...

Why is this counterintuitive? Have you tried not thinking of it as an expanding gas but as a set of discrete particles which either do or don't exchange energy and momentum with a diviser?
 
Last edited:
caveman1917 said:
Why is this counterintuitive? Have you tried not thinking of it as an expanding gas but as a set of discrete particles which either do or don't exchange energy and momentum with a diviser?
Click to expand...

Yeah, once you break it down it makes sense in any model, but it is still not inmediately obvious to me. The issue being that I forget to consider the equilibrium between atmosphere and cylinder, I suppose.
 
You must log in or register to reply here.

Back
Top Bottom