# Entropy after the Big Bang

• I
• shlosmem

#### shlosmem

If the universe was very hot right after the Big Bang how come the entropy of the universe was lower at that point than now? Isn't heat a reason for higher entropy?

Temperature and entropy are not the same thing.

ohwilleke and Orodruin
If the universe was very hot right after the Big Bang how come the entropy of the universe was lower at that point than now? Isn't heat a reason for higher entropy?

Brian Greene’s 2020 video, Entropy and the Arrow of Time, might be interesting. He is an American theoretical physicist, mathematician, and string theorist at Columbia University.

ohwilleke
Temperature and entropy are not the same thing.
No. They're not.

Let's say we have in interstellar space two tanks with reflective walls. Volume of tank A is 1 cubic meter, volume of tank B is 1 cubic kilometer.

We put infrared heaters and thermometers in both tanks. We notice that the reading of the thermometer in the bigger tank rises slowly compared to the thermometer in the smaller tank.

So we conclude that bigger volume of empty space has larger heat capacity than a smaller volume of empty space.

As we know, space has stretched a lot since the big bang. So that has increased the heat capacity of said space.

What happens when you keep the heat energy thermal energy constant and increase heat capacity? Well one thing is that temperature decreases. Other thing is that entropy increases.

Does this maybe kind of answer the question? It's not a complete answer for sure.

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Does this maybe kind of answer the question?
Where are you getting all this from? Empty space does not even have a well-defined heat capacity.

What happens when you keep the thermal energy constant and increase heat capacity? Well one thing is that temperature decreases. Other thing is that entropy increases.
Let's look at the sun's formation. Some gas and dust in space compressed by gravity to form the sun. In one way the compressed particles
have less movement freedom so the system has less potential states which means lower entropy. On the other hand the high temperature means more potential states , so in total we can say that the sun state has more entropy then the dust state and the second law is not broken.
But this keeps me back to the original question, why the same rule is not applied to the universe itself?

256bits
On the other hand the high temperature means more potential states , so in total we can say that the sun state has more entropy then the dust state and the second law is not broken.
This argument is faulty. Eventually the Sun runs out of stuff to burn and cools down. The correct argument in gravitational clustering is to not ignore the entropy of the radiation that is emitted in the process.

PeroK
The OP is confused about entropy vs. temperature. Having other people post their own areas of confusion is unlikely to help.

phinds
Entropy in the presence of gravity is monstrously complicated. As I understand it, we only know how to calculate the entropy for a select few gravitational systems (such as black holes and empty space).

The expansion alone doesn't change entropy at all, as far as I'm aware. This can be concluded from the fact that it's possible for an expanding universe to become a contracting universe. I believe the entropy production in the early universe was primarily a result of increased clustering of matter as the universe expanded. Eventually all matter will be within black holes, which is the maximal-entropy configuration of matter. Those black holes will then evaporate over a long period of time, leading to empty space which has even greater entropy.

Those black holes will then evaporate over a long period of time, leading to empty space
In an idealized scenario where a single hole evaporates, after the last burst of outgoing radiation from the evaporation leaves, there is empty space inside where the hole used to be, yes. But in any real scenario, you won't have just one hole evaporating. There will already be radiation present coming from elsewhere, either from other holes evaporating or from the CMB if nothing else. So the end result for the universe as a whole would be a universe filled with nothing but radiation.

This argument is faulty.
This argument is uninformative. What exactly is faulty?

ohwilleke
This argument is uninformative. What exactly is faulty?
You would have known if you continued reading. The rise in temperature is insufficient to lead to an increase in entropy unless you also consider the radiation emitted.

You would have known if you continued reading. The rise in temperature is insufficient to lead to an increase in entropy unless you also consider the radiation emitted.

A. The radiation is a small faction of the entire sun's mass on any given moment , so it probably should be neglected in any practical measure of the sun's entropy.
B. How is even relevant. Are you suggesting that the low entropy of the hot universe after the bb is duo to the lack of radiation?

If the universe was very hot right after the Big Bang how come the entropy of the universe was lower at that point than now? Isn't heat a reason for higher entropy?

This chapter by Charles H. Lineweaver,

in "Beyond the Second Law: Entropy Production and Non-Equilibrium Systems", eds. R. Dewar, C.H. Lineweaver, R. Niven, & K. Regenaur-Lieb, Springer, pp 415-428, 2014

might be interesting.

Lord Jestocost, shlosmem and Ibix
A. The radiation is a small faction of the entire sun's mass on any given moment , so it probably should be neglected in any practical measure of the sun's entropy.
B. How is even relevant. Are you suggesting that the low entropy of the hot universe after the bb is duo to the lack of radiation?
I'm sorry, but you are entirely missing the point. The point is not a question of how to define the Sun's entropy. The point is that the material that the Sun consists of is not a closed system. Over the billions of years that the Sun has formed and radiated, its entropy has actually decreased, which is fine as it is not a closed system. The "missing" entropy has been carried away by radiation over billions of years.

Where are you getting all this from? Empty space does not even have a well-defined heat capacity.
Well I thought I kind of understood how entropy, temperature and heat capacity work. Maybe I don't.

Let's consider an universe with two black hokes, and nothing else. After the black holes have merged the universe contains cooler stuff and more entropy.

And after the merger the temperature of the stuff changes less when heat is added to it or taken away from it. IOW heat capacity is larger.

Oh yes, it was wrong to say that empty large volume has large entropy. Radiation in that volume can have lot of entropy.

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Let's look at the sun's formation. Some gas and dust in space compressed by gravity to form the sun. In one way the compressed particles
have less movement freedom so the system has less potential states which means lower entropy. On the other hand the high temperature means more potential states , so in total we can say that the sun state has more entropy then the dust state and the second law is not broken.

Yes that is an example where temperature increases and entropy increases.

And this is an example where temperature decreases and entropy increases:

Let's look at the evaporation of an ice cube in space. In one way after the evaporation the particles
have less kinetic energy so the system has less potential states which means lower entropy. On the other hand the large volume means more potential states, so in total we can say that the evaporated state has more entropy then the solid state.

The ice cube starts at 0 degrees Celsius, then part of it evaporates, using the thermal energy of the ice cube. For simplicity's sake this happens in empty space, no cosmic background radiation.

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Let's consider an universe with two black hokes, and nothing else.
If we're talking about classical black holes, there is no way to define their temperature or their entropy. Making sense of those concepts at all for black holes requires some kind of quantum gravity theory or approximation thereof.

After the black holes have merged the universe contains cooler stuff and more entropy.
If we're talking about classical black holes, this is false; the universe just contains one black hole instead of two. There is still no way to define either temperature or entropy.

If you put "stuff" in other than the holes themselves, i.e., nonzero stress-energy tensor somewhere, then you no longer have a universe with just two black holes and nothing else, so you are contradicting your initial scenario. You can of course define a temperature and entropy for the "stuff", but classically that still does not change the fact that there is no way to define temperature or entropy for black holes.

after the evaporation the particles
have less kinetic energy
No, they don't. Evaporation is a constant temperature process. The average kinetic energy of the particles does not change. The reason the ice cube at 0 C evaporates (the correct name for the process is actually "sublimation") in empty space is that the vapor pressure is zero.

I'm sorry, but you are entirely missing the point. The point is not a question of how to define the Sun's entropy. The point is that the material that the Sun consists of is not a closed system. Over the billions of years that the Sun has formed and radiated, its entropy has actually decreased, which is fine as it is not a closed system. The "missing" entropy has been carried away by radiation over billions of years.
To put this into a bit more perspective, John Baez has a (now over 20 year old) writeup with the qualitative argumentation.
https://math.ucr.edu/home/baez/entropy.html

Boiling it down, physical volume goes as ##R^3## but momentum space volume goes as ##R^{-3/2}## where ##R## is a relevant length scale. Therefore, phase space volume goes as ##R^{3/2}## and therefore decreases as the gas cloud contracts and heats up, resulting in an overall lower entropy for the gas cloud (which eventually forms the star). It follows that the gas cloud heating up as it contracts is not a correct explanation to why the second law is not broken. You need to look at the entropy carried away by radiation to save the second law.

PeterDonis
Collapsing gas clouds have negative heat capacity. That's one more confusing element. One not present in the OP. I think people's posting of other areas of confusion don't help the OP understand any better.

If the universe was very hot right after the Big Bang how come the entropy of the universe was lower at that point than now? Isn't heat a reason for higher entropy?

Ethan Siegel’s 2017 article,

might be interesting. The last paragraph of the article:

If there were no such things as black holes, the entropy of the Universe would have been almost constant for the past 13.8 billion years! That primal state actually had a considerable amount of entropy; it's just that black holes have so much more, and are so easy to make from a cosmic perspective.​

Ethan Siegel’s 2017 article,

might be interesting. The last paragraph of the article:

If there were no such things as black holes, the entropy of the Universe would have been almost constant for the past 13.8 billion years! That primal state actually had a considerable amount of entropy; it's just that black holes have so much more, and are so easy to make from a cosmic perspective.​
That almost seems to suggest that there would be no structure formation without black holes ...

That almost seems to suggest that there would be no structure formation without black holes ...

I think Siegel’s article does not suggest that. He is saying,

While we might look at galaxies, stars, planets, etc., and marvel at how ordered or disordered they appear to be, their entropy is negligible. So, what caused that tremendous entropy increase?​

The answer is black holes. If you think about all the particles that go into making a black hole, it's a tremendous number.​

This is consistent with the last paragraph of the article:

If there were no such things as black holes, the entropy of the Universe would have been almost constant for the past 13.8 billion years! That primal state actually had a considerable amount of entropy; it's just that black holes have so much more, and are so easy to make from a cosmic perspective.​

256bits
If the universe was very hot right after the Big Bang how come the entropy of the universe was lower at that point than now? Isn't heat a reason for higher entropy?
Point 1 - 2nd law states that entropy of a system can remain constant, or increase with time. If we treat the universe as a thermodynamic system. then its entropy is either the same or greater than that at the big bang.
Point 2 - high temperature could mean that to raise the temperature by value ΔT, one has to add more
Q than that at a lower temperature, but that is not a solid fast rule. ( ie negative heat capacity for instance ). See the discussions previously.
Point 3 - SBig Bang < SNow < SFuture is not the same as S_MaxBig Bang < S_MaxNow < S_MaxFuture. So while at he Big Bang the actual entropy S may been SMax, or close to it, our S at the present is very much lower than the maximum possible entropy at the present ( An entropy deficit if you will that allows you, and the universe, to do a whole bunch of thermodynamically irreversible activities ).