# How much entropy is in the universe?

## How much entropy, on average, is in a cubic km?

• ### 6 nanojoules per kelvin

• Total voters
3
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If entropy is a real thing, a real quantity like mass and energy, then we should have some idea how much there is of it in the average cubic kilometer of space

The standard metric unit of entropy is joules per kelvin. To get a quantitative grip on the amount of entropy in the universe lets estimate the amount contributed by all matter and radiation that has been detected so far. Arcane stuff like dark matter and undetectable unmeasurable but assumed low-energy neutrinos and dark energy which we dont know what it is we will leave out of the picture.

So think of all the matter and radiation in sight, think about its entropy. How much joules per kelvin per cubic kilometer is that?
Which of these is it closest to?

6 joules per kelvin
6 millijoules per kelvin
6 microjoules per kelvin
6 nanojoules per kelvin

It turns out the vast majority of the entropy is in the Cosmic Microwave Background so that a first order estimate is just the
CMB entropy per cubic kilometer. One of these is in fact that.

## Answers and Replies

Entropy

Some interesting points raised! I agree that the CMB probably contributes the bulk of the entropy of the visible universe, but I suspect neutrinos are also responsible for a large percentage as well.

Marts

Black hole entropy

Question: How much entropy is in a cubic kilometre of Black hole?

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Originally posted by Marts Liena
Question: How much entropy is in a cubic kilometre of Black hole?

for the ordinary black hole, I believe the entropy is proportional to the surface area (not to the volume)

I do not know off-hand how much there is in the BH per unit of surface area, but I will look it up and get back to this

BTW what you said about neutrinos sounds right to me. I think
that it depends on how many particles---and the CMB has more photons than there are particles of other stuff (except for neutrinos)

Can you estimate, per cubic kilometer, the number of CMB photons and also the number of neutrinos in the low-energy cosmic neutrino background?

I read in Lineweaver (astro-ph/0305179) that the predicted temperature of the cosmic netrino background is 1.9 kelvin. These are from the BB time and very much lower energy than those produced by stars, too low-energy to have been detected, but many more of them.

Any estimates from you would be helpful to me. Even a very rough comparison of the abundance of particles in the neutrino background versus the abundance of CMB photons. At present I have no idea of even the order of magnitude, so would appreciate any help.

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Originally posted by Marts Liena
Question: How much entropy is in a cubic kilometre of Black hole?

Here is a rough dimensional response to show the dependence of entropy on the square of mass-----or equivalently on surface area

In natural units the Schwarzschild radius RSchw = 2M

(you know the usual formula 2GM/c2
and I'm just using units where the constants like G and c are equal to 1)

The temperature of the black hole is 1/(8pi M)

the mass-energy of the black hole is Mc2 = M

So the ratio of energy to temperature is M divided by 1/(8pi M)

which is 8pi M2

this E/T ratio can stand for the entropy

the surface area is 4pi R2 which is the same
as 16 pi M2

it seems to me that (back-of-envelope) I have estimated that in natural units the entropy is half as big as the surface area---anyway proportional to it

Bekenstein discovered the proportionality in the 1970s----he has an article in the August 2003 Scientific American which I have not been able to read more than a few sentences of because it strikes me like so much Jello.

ranyart
Seems you are missing the point?...How much Universe is there?

{message deleted by Phobos - - seems that ranyart is missing the point of PF guidelines}

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*snickers softly*

Moderators?

- Warren

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Originally posted by chroot
*snickers softly*

Warren, I know you read that Lineweaver article so you saw the estimate of the temperature of the cosmic neutrino background (1.9 kelvin) there----at least there and maybe other places too.

Marts asked about how much entropy is in the neutrinos. Check out my reasoning---it should go as the square of the temp.
Both are relativistic forms of energy and in a thermal distribution so as a rough estimate the energy density goes as the cube of temp and E/T goes as square of temp

So (1.9/2.73)2 = 0.48 and that suggests to me that
the neutrinos represent half as much entropy as the CMB. Alles gut?

meteor
If entropy is a real thing, a real quantity like mass and energy, then we should have some idea how much there is of it in the average cubic kilometer of space
If you are interested in information entropy of the observable universe, perhaps you can apply the holographic principle. I mean, calculate the area of the boundary of the observable universe, and then the holographic principle says that the information entropy inside the region can't surpass 1/4 of the area of the boundary

I will be happy if someone can answer this question: the Bekenstein-Hawking formula for a black hole, what kind of entropy calculate, information or thermodynamical?

Neo
Originally posted by marcus
If entropy is a real thing, a real quantity like mass and energy, then we should have some idea how much there is of it in the average cubic kilometer of space

The problem with such a calculation is the fact that entropy is not uniform so an average of earth, for instance, could be significantly different from an average of another planet, where entropy is not so "suspended" by evolution.

shouldn't it be just
S = %int; dQ/T
with proper boundary conditions?

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