# Entropy vs Universal Expansion

• coolcalx
In summary, the laws of thermodynamics state that nothing can reach absolute zero and as the universe expands, it actually cools down due to adiabatic expansion. The concept of entropy also plays a role in the cooling of the universe. The universe will never reach absolute zero, but will continue to get colder and colder in the asymptotic limit. The increase in entropy is due to the larger volume of the universe and the background radiation from the Big Bang is now in the microwave spectrum.

#### coolcalx

hello, I am a high school student from Alabama, and I'm in a college level physics class. We have just finished fluids and thermodynamics, but my physics professor claimed something that has me a little irked.

according to my physics professor and the laws of thermodynamics, nothing can reach absolute zero, so I asked him about the fact that the universe is expanding, and whether or not this would still apply to a universe with infinite volume. his response was that the universe is continuously heating up due to entropy. he claimed that the universe would get even hotter as the universe expanded.

this seems... incorrect. everything I've ever learned has told me that the universe started as a singularity - infinitely hot, and infinitely dense. as the universe expanded, it got cooler and cooler until it reached the average 3 Kelvin it is today. as the universe expands forever, it should get colder and colder (called the Big Freeze), until proton decay, and all the end of all molecular motion, where eventually, the expansion would cause the Big Rip.

am I incorrect? if so, could you explain to me how entropy would cause the the universe to get hotter, and how come my perception of the Big Bang is so off base. if I'm correct, could you answer my original question: will the universe eventually reach 0 Kelvin (absolute zero), even though it's a theoretical asymptote?

Nothing can reach absolute zero because that would mean that the particles would have a definite position with zero velocity, according to the uncertainty principle we cannot know both position and momentum with definite precision simultaneously. The reason is the same for why an electron does not spiral into the nucleus of an atom.

that makes sense, but is the universe heating up due to entropy, as my professor states, or is it cooling down do to expansion, as the Big Bang theory states?

I'm wondering what happens to the infrared radiation (or any electro magnetic radiation) that "escapes" beyond the "outer perimeter" of the mass of the universe.

If I take a spring hanging from the ceiling and attach a mass to the bottom is it moving down like the theory of gravity would say or being pulled up like the force from the spring would say?

I don't think it is possible to escape beyond the universe, and since it is roughly homogeneous at large scales no matter where you go in the universe you are still surrounded by mass.

..the universe is defined as all space, time, matter, and energy. the "totality of reality." there is nothing beyond the universe. the existence of "parallel universes" would exist within dimensions of the universe we are familiar with.

but I'm still not getting an answer to my question :/

coolcalx said:
that makes sense, but is the universe heating up due to entropy, as my professor states, or is it cooling down do to expansion, as the Big Bang theory states?
I'm not sure what your professor is trying to say there, but the way you've quoted him/her, they couldn't be more wrong. The universe is doing something very similar to "adiabatic expansion" of a gas, which is a slow conversion of internal heat into bulk flow motion. That implies cooling of the gas, not heating. What's more, adiabatic expansion means there is no net heat transfer from place to place, which also means there is no change in entropy. So nothing is happening to entropy at all, we just have conversion of thermal forms of heat into bulk flow forms of energy, in the classical picture anyway (later you'll hear a different way of talking about it, general relativity, but the classical picture serves here fairly well). Of course, other things are happening-- galaxies are forming, stars are blowing up, etc., but if we just look at the expansion and simplify, then entropy stays fixed as the universe cools.

I would say the answer to your original question is much simpler, and you already said it-- the universe only reaches absolute zero in some kind of asymptotic limit, but that means it never really gets there, and that's what the theorems in thermodynamics are talking about: where you actually get, not what could happen in some ideal or asymptotic limit.

Ken G said:
I'm not sure what your professor is trying to say there, but the way you've quoted him/her, they couldn't be more wrong. The universe is doing something very similar to "adiabatic expansion" of a gas, which is a slow conversion of internal heat into bulk flow motion. That implies cooling of the gas, not heating. What's more, adiabatic expansion means there is no net heat transfer from place to place, which also means there is no change in entropy. So nothing is happening to entropy at all, we just have conversion of thermal forms of heat into bulk flow forms of energy, in the classical picture anyway (later you'll hear a different way of talking about it, general relativity, but the classical picture serves here fairly well). Of course, other things are happening-- galaxies are forming, stars are blowing up, etc., but if we just look at the expansion and simplify, then entropy stays fixed as the universe cools.

I would say the answer to your original question is much simpler, and you already said it-- the universe only reaches absolute zero in some kind of asymptotic limit, but that means it never really gets there, and that's what the theorems in thermodynamics are talking about: where you actually get, not what could happen in some ideal or asymptotic limit.

I'm speaking out of school here, but... the entropy of a closed system increases with volume, essentially because there are more microstates accessible in a larger volume. At least, that's what I recall from my statmech class. The entropy of the universe is increasing.

Also, because of universal expansion, the background radiation of the universe, the left-over from the phase transition from opaque hot dense plasma to transparent uncharged gas clouds, has been cooling steadily. That doesn't mean everything in the universe is cooling, but a big chunk is cooling.

BBB

bbbeard said:
I'm speaking out of school here, but... the entropy of a closed system increases with volume, essentially because there are more microstates accessible in a larger volume. At least, that's what I recall from my statmech class. The entropy of the universe is increasing.
No, you did not pay close enough attention in statmech class! It is a "good error" to make however, because it opens a teaching avenue. There is no law that connects entropy directly to volume, the law connects entropy and heat transfer. When heat is transferred, the entropy change is the heat transfer times the difference in 1/T across which the heat was transferred. This can be written dS = dQ/T. Thus, whenever dQ=0, as in adiabatic expansion of a gas in a box, there is never any entropy change if the expansion happens slowly ("reversibly") enough to remain in thermodynamic equilibrium, as it does in the Big Bang.

But you are correct that entropy has a lot to do with counting the states that are available, so doesn't increased volume increase the number of states available? Sure, but that increase in access to states is exactly canceled by the decrease in access to states owing to, you guessed it, the drop in heat content in the gas. The T drops in an adiabatic gas because the volume is increasing, which puts into perspective just how wrong those professor's comments really are (if that is really what they said).
Also, because of universal expansion, the background radiation of the universe, the left-over from the phase transition from opaque hot dense plasma to transparent uncharged gas clouds, has been cooling steadily. That doesn't mean everything in the universe is cooling, but a big chunk is cooling.
The gas cools too, and also adiabatically. So all the kinetic energy in the universe is dropping (counting photon energy as kinetic energy, i.e., zero rest energy) in just the way that the heat content of an expanding gas drops, and in just the way needed to keep the total entropy constant. The rest energy does not drop, because it does not count in the number of available states, and that is just why rest energy currently dominates the energy in the universe (except for dark energy, let's not get into that). And this does all idealize the situation as being all adiabatic expansion-- glossing over issues like star formation and nuclear burning and so on, which are irreversible and do increase the entropy of the universe but not enough to justify the professor's claim.

thank you so much. I'm glad I'm not crazy. also, I'm sorry I can't exactly quote my professor on what he said about entropy and a heating universe, but I did paraphrase the best I could. what I told you is what I understood him to say, and what others understood as well.

## 1. What is entropy and how does it relate to universal expansion?

Entropy is a measure of the disorder or randomness in a system. It is closely related to the concept of universal expansion, as the second law of thermodynamics states that the entropy of the universe always increases over time. This means that as the universe expands, the amount of disorder and randomness also increases.

## 2. How does entropy affect the expansion of the universe?

As the universe expands, the amount of available energy decreases, leading to a decrease in the rate of entropy production. This is because the increase in volume of the universe results in a decrease in the density of energy and matter. However, the overall entropy of the universe continues to increase due to the continuous production of new particles and radiation.

## 3. Is there a connection between the expansion rate of the universe and entropy?

Yes, there is a direct connection between the expansion rate of the universe and entropy. As the universe expands, the rate of entropy production decreases, leading to a slower expansion rate. Conversely, if the expansion rate were to increase, the rate of entropy production would also increase.

## 4. How does the concept of entropy vs universal expansion relate to the Big Bang theory?

The Big Bang theory states that the universe began as a singularity and has been expanding ever since. As the universe expands, the amount of disorder and randomness increases, which is in line with the second law of thermodynamics. This supports the idea that the universe started in a low-entropy state and has been increasing in entropy over time.

## 5. Can entropy ever decrease in the universe?

The second law of thermodynamics states that the overall entropy of the universe always increases, meaning that it is highly unlikely for entropy to decrease. However, in localized systems, such as a living organism or a refrigerated room, entropy can decrease temporarily. This is because these systems are able to use external energy sources to decrease entropy within their boundaries, but the overall entropy of the universe still increases.