# Finite amount of degree of freedom for entropy available in universe (?)

_heretic
The spectrum of the Cosmic Microwave Background radiation - the flash of the Big Bang, aligns almost precisely with the shape of the Black Body radiation curve. This means that the CMB radiation came from a state that was in thermal equilibrium.

Since thermal equilibrium is a state of maximum entropy, doesn't this means that there is a theoretical maximum to the entropy of our observable universe? i.e. entropy can not (overall) continue increasing forever, it must eventually reach a maximum and stop?

_heretic

Mentor
Since thermal equilibrium is a state of maximum entropy
With gravity, a uniform distribution is not a state of maximal entropy, even in thermal equilibrium.

For a discussion about the entropy of the observable universe, see here (pdf) for example. As the observable universe is finite, it should have a finite maximal entropy (and they give values for its current entropy). For the total universe, it depends on its size (finite <-> infinite).

_heretic
With gravity, a uniform distribution is not a state of maximal entropy, even in thermal equilibrium.

For a discussion about the entropy of the observable universe, see here (pdf) for example. As the observable universe is finite, it should have a finite maximal entropy (and they give values for its current entropy). For the total universe, it depends on its size (finite <-> infinite).

For gravity, what would be a state of maximum entropy? Black holes?

Mentor
For a low density, just very low-energetic photons probably - and black holes produce that as Hawking radiation.

_heretic
Thanks again,

Would maximum gravitational energy be reached once all of the black holes evaporate, then?

Mentor
"maximum gravitational energy"? Minimal absolute value of (negative) binding energy? In that case: Yes.

_heretic
I apologise, I meant to say "maximum gravitational entropy." So when all of the black holes evaporate, does that represent maximum gravitational entropy?

Mentor
What is "gravitational entropy"?

_heretic
The entropy of the gravitational field.

Mentor
What is "The entropy of the gravitational field."?
Entropy is a property of whole systems, not a property of forces.

I don't think that black holes will necessarily all evaporate. Eventually the universe could settle into a state with a single massive black hole surrounded by a background radiation field, where the temperature of the black hole and the background radiation are equal, so the black hole and radiation field are in equilibrium. Since the black hole temperature rises when the mass decreases, it's hard to figure out if this is a stable or unstable equilibrium. If the absolute value of the heat capacity of the black hole is larger than the heat capacity of the surrounding universe, then I suppose the black hole will tend to evaporate until it disappears.

I guess the fate of the universe depends on how fast it is expanding. 1 solar mass black holes have a temperature of some 60 nK according to wikipedia, which is much less than the cosmic background temperature ~2.7K, so in current conditions, black holes tend to increase in size rather than evaporate. So, it looks like black holes won't evaporate, and the maximum entropy universe seems to contain black holes. But, as the universe expands, the background temperature decreases. The question is, will the universe keep expanding past the point where background temperature is colder than all the black holes? Then the black holes will evaporate, and we are left with a, for all purposes, empty universe. Entropy will be large simply because the universe is so utterly big.

Mentor
With accelerated expansion, such an equilibrium cannot exist. All radiation coming from the black hole would be lost forever.

The question is, will the universe keep expanding past the point where background temperature is colder than all the black holes?
It is accelerating already with the current, "high" energy density. Why should it stop to do so with a lower density?