Entropy and the Universe

ThomasT
I've been reading some threads about the concept of entropy and how it might be related to our universe.

Assume for a moment that the universe is finite (bounded), and that a finite quantity of kinetic energy was imparted via the Big Bang via the origin of the universe, and that this energy is dispersing and dissipating primarily via the isotropic expansion of the universe so that our universe and the medium in which it is a disturbance will eventually reach an equilibrium state (ie. the wave front and internal interacting wave structures that are our universe's boundaries and contents cease to exist).

Given the above assumptions, what definition of entropy, if any, might be applied to the universe and how might it be measured?

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If you neglect gravitation, you can consider the entropy of the matter in the universe in the same way than a for gas. Due to the cosmological principle every comoving volume (stationary wrt the expansion) will have no heat transfer on its boundaries. This means that the expansion will be adiathermal. Additionally, averaging on very large scales and neglecting local processes you can assume that the expansion is reversible. Both conditions allow you to assume that the gas within every comoving volume is expanding adiabatically and, therefore, its entropy remains always constant. However, on very large time scales local processes cannot be neglected and they will sooner or later contribute to the total increase of entropy. Still on large scales, one faces also the problem that gravitation cannot be neglected. The problem with gravitation is that we do not have a clear definition of gravitational entropy. This is a very complex topic, but if you want to do some simple calculations you may want to try the mentioned assumptions for example for a relativistic gas of phhotons such as the cosmic microwave background. The entropy of the matter in the universe is currently dominated by far by the cosmic microwave background.

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ThomasT
If you neglect gravitation, you can consider the entropy of the matter in the universe in the same way than a for gas. Due to the cosmological principle every comoving volume (stationary wrt the expansion) will have no heat transfer on its boundaries. This means that the expansion will be adiathermal. Additionally, averaging on very large scales and neglecting local processes you can assume that the expansion is reversible. Both conditions allow you to assume that the gas within every comoving volume is expanding adiabatically and, therefore, its entropy remains always constant. However, on very large time scales local processes cannot be neglected and they will sooner or later contribute to the total increase of entropy. Still on large scales, one faces also the problem that gravitation cannot be neglected. The problem with gravitation is that we do not have a clear definition of gravitational entropy. This is a very complex topic, but if you want to do some simple calculations you may want to try the mentioned assumptions for example for a relativistic gas of phhotons such as the cosmic microwave background. The entropy of the matter in the universe is currently dominated by far by the cosmic microwave background.
Is it ok to define the entropy of the universe as the CMB? If so, then the entropy of the universe would seem to be decreasing. And if it's assumed that a finite amount of energy was imparted via the Big Bang, then can it be inferred that the entropy (ie., temperature) of the universe is decreasing toward an equilibrium of absolute zero?

What makes you think that it should be decreasing? The entropy of a gas in adiabatic expansion, such as the CMB, is constant. But as mentioned before, the universe is not only the CMB.

ThomasT
What makes you think that it should be decreasing? The entropy of a gas in adiabatic expansion, such as the CMB, is constant. But as mentioned before, the universe is not only the CMB.

The way I tend to think about it, our universe is losing heat, winding down. The adiabatic system is our universe and whatever it is a part of. If a Big Bang event imparted a finite amount of energy in the creation of our universe, and our universe is expanding isotropically vis the impetus of this energy, and this energy is dispersing and decreasing vis the expansion, then the overall temperature of the universe is also decreasing. If the entropy of our universe is defined as its overall temperature, and if the CMB is directly proportional to the overall temperature, then the CMB and the entropy of the universe should, in this view of things, be decreasing.

As I said, to talk about the entropy of the universe can be quite complex. However, if we restrict ourselves to the entropy of the CMB then things become simple.

Here you can apply the very basic definitions of entropy for gases. Entropy is not defined as a temperature, but a change of entropy dS is defined as dS = dQ / T. In the comoving coordinates you can consider the CMB to be a gas that expands adiabatically. The reasons for this I have mentioned already: there is no heat transfer on the boundaries of any comoving volume. For an adiabatic process dQ = 0 and therefore S = constant. This applies also for the CMB.

On the other hand you may ask about the energy of the CMB. Again, here we can apply the usual thermodynamics of gases asuming comoving coordinates. For an adiabatic process we have $dQ = 0$, which in turn means $dU + p dV = 0$. For a general equation of state $p = w u$ (with $u = U/V$) it is easy to show that is must hold:

$$\frac{U}{U_0} = \left( \frac{V}{V_0} \right)^{-w}$$

For w > 0, as for the CMB with w = 1/3, the energy U within a comoving volume V decreases as the comoving volume increases. This is due to the fact that the CMB is doing work against the expansion of the universe. This is not a work on any boundary as for gases, but somehow on every point in space, and it is reflected in the increase of wavelength of every single photon.

ThomasT
As I said, to talk about the entropy of the universe can be quite complex. However, if we restrict ourselves to the entropy of the CMB then things become simple.

Here you can apply the very basic definitions of entropy for gases. Entropy is not defined as a temperature, but a change of entropy dS is defined as dS = dQ / T. In the comoving coordinates you can consider the CMB to be a gas that expands adiabatically. The reasons for this I have mentioned already: there is no heat transfer on the boundaries of any comoving volume. For an adiabatic process dQ = 0 and therefore S = constant. This applies also for the CMB.

On the other hand you may ask about the energy of the CMB. Again, here we can apply the usual thermodynamics of gases asuming comoving coordinates. For an adiabatic process we have $dQ = 0$, which in turn means $dU + p dV = 0$. For a general equation of state $p = w u$ (with $u = U/V$) it is easy to show that is must hold:

$$\frac{U}{U_0} = \left( \frac{V}{V_0} \right)^{-w}$$

For w > 0, as for the CMB with w = 1/3, the energy U within a comoving volume V decreases as the comoving volume increases. This is due to the fact that the CMB is doing work against the expansion of the universe. This is not a work on any boundary as for gases, but somehow on every point in space, and it is reflected in the increase of wavelength of every single photon.
OK, thanks hellfire. I have a few more questions.

Can our universe be modeled as part of something larger, and as transferring heat to it as it expands? I don't see why not, but then I don't know much about this stuff.

Is it necessary to think of the CMB as doing work against the expansion of our universe? I don't think I have an idea how the CMB might be doing this.

Is it ok to think of wave interaction inside our universe (gravitational, electrical, magnetic, etc.) as doing work against the expansion?

Is it ok to think of the energy of the expansion as the dominant energy, and that it will continue to expand until an equilibrium with whatever it's a part of is reached?

Can our universe be modeled as part of something larger, and as transferring heat to it as it expands? I don't see why not, but then I don't know much about this stuff.
I don't think this agrees with standard cosmology. There may be thermodynamical analogies between gases expanding in boxes and matter and radiation expanding with space in the universe, however the mechanisms that apply are very different. The standard cosmological models that are based on general relativity do not assume that the universe is part of anything larger.

Is it necessary to think of the CMB as doing work against the expansion of our universe?
Not necessary. This view arises from the thermodynamical analogy with gases.

ThomasT
I don't think this agrees with standard cosmology. There may be thermodynamical analogies between gases expanding in boxes and matter and radiation expanding with space in the universe, however the mechanisms that apply are very different. The standard cosmological models that are based on general relativity do not assume that the universe is part of anything larger.

Would a model of our universe that assumes that our universe is part of something larger, and that our universe is evolving toward equilibrium with its parent, imply that the evolution of our universe is an irreversible process? If so, wouldn't this help to explain the irreversibility that we observe in everyday (as well as lab experimental) experience?

I'm tentatively thinking that the notion of the entropy of the universe is either superfluous or simply inapplicable.

If the entropy is proportional to the temperature of the CMB, then why not just talk about the CMB?

If the entropy is something that we can't possibly measure, then ...

And/or, if the universe is not an isolated system, then the concept of entropy would be inapplicable to that scale, wouldn't it?

If large scale isotropic expansion of our universe is a fact, and if the temperature of the CMB is decreasing, then doesn't this seem to imply that the energy of our universe is finite, dispersing, and decreasing (so, on a universal scale, conservation laws wouldn't apply)?

I'm sorry if my thoughts seem a bit scattered, but this is fascinating stuff and I don't really know how to organize all the questions that I have about it.

I have some ulterior motivation behind my considerations.

1) I don't think the statistical interpretation of entropy should be applied to cosmological scale phenomena.

2) I don't think that backward time travel is a sensible idea.

3) I think that the irreversibility of our sensory experience can be understood as a byproduct of universal scale irreversibility.

4) It doesn't make any sense to me to think of our universe as an isolated system.