# Does the expansion of the universe also cause an increase in overall entropy?

1. Jun 14, 2009

### Entropee

If the expansion of the universe DID increase entropy, it would explain a lot of things but also leave me with a lot more questions.

2. Jun 14, 2009

### apeiron

Charlie Lineweaver in his Maximum Entropy Production Principle paper says that expansion in itself does not increase entropy.

"The entropy density s of a radiation field of temperature T is s ~ T3. The entropy S in a given comoving volume V is S = s V. Since the comoving volume V increases as the universe expands, we have V ~ R3. And since the temperature of the microwave background goes down as the universe expands: T ~ 1/R, we have the result that the entropy of a given comoving volume of space S ~ R-3 * R3 = constant. Thus the expansion of the universe by itself is not responsible for any entropy increase. There is no heat exchange between different parts of the universe. The expansion is adiabatic and isentropic: dSexpansion = 0."

So the first law applies in this view - the universe is modelled as a closed system where in effect more space is swapped for less heat. The microstates (as in number of CMB photons) stay the same in number, but grow larger and cooler. Redshifted.

I certainly do not think this is the full story. But I think he is putting his finger on something often overlooked.

Entropy is normally considered as a story about heat - an energy density that can be disordered, wasted to coldness. But the universe is born of a duality between heat and space. So a high heat (localised kinetics) can be exchanged for a large space (globalised a-kinetics) and vice versa. Small spaces are hot and large spaces are cold.

So the full gradient that rules our universe is the one from a highly located heat (the big bang) to a very spread out coolness (the heat death universe).

Therefore just focusing on expansion, and not seeing the balancing cooling, can throw off your intuitions about what is happening.

The second law is normally framed in terms of a closed system exporting entropy to a sink - a realm outside itself. But the universe is creating a sink for itself effectively. It is spreading the heat out within its ever increasing self.

So it is both a closed and open system in this sense.

3. Jun 14, 2009

### Entropee

Oh man this is confusing. I think i understand the 1st law, but I dont really get the 2nd law. Im starting community college next year, do you think any physics classes would go in depth in teaching about this kind of stuff?
cause high school physics is just complicated velocity, speed and work stuff.

4. Jun 14, 2009

### apeiron

There are tons of pop science books on entropy. The basics are really very easy to grasp.

5. Jun 14, 2009

### Entropee

Would you suggest The Universe in a Nutshell by Hawking?
Because brief history of time only covers it very briefly... hence the name I guess...

6. Jun 15, 2009

### Chalnoth

Okay, that paper is positively ancient where cosmology is concerned. And it's simply wrong for the cases that we know how to calculate accurately, namely a de Sitter universe with a black hole inside: in such a universe, the de Sitter universe (i.e., one with a positive cosmological constant) has a lower entropy if there is a black hole inside it than if there is nothing but empty space.

Furthermore, it's been shown that for a given enclosed mass, a black hole has the highest entropy possible. This makes sense given that what we know of physics today has our universe (over very long time spans) transitioning to nothing but black holes, and then just empty space as those evaporate.

While it is true that there are a number of calculations that we just don't know how to perform that are required to define the entropy of the current and past universe, a universe that is vastly more complicated than black holes and empty space, I think we have enough information available to us to state categorically that the entropy of the universe as a whole is increasing.

7. Jun 15, 2009

### Entropee

So do you disagree with what apeiron posted here?

8. Jun 15, 2009

### Chalnoth

Entirely, because it neglects dark energy.

That sort of description is valid in the early, hot phases of our universe, before dark energy was significant.

9. Jun 15, 2009

### apeiron

I deliberately left out dark energy because that is a further complication indeed. We have to agree whether it is even a constant cosmological constant or a big rip accelerating acceleration for a start.

But presuming the constant case, what are you actually saying about dark energy? That it over-cools the universe by moving things even further apart than would have been the case if it was only the kinetics of the big bang "inertially" dispersing itself, swapping heat for sink?

But then isn't there an argument that the event horizon created by accelerating expansion itself matches the entropy moved across it, exported into what is now an external sink so to speak?

So now we would have cold space being swapped for hot horizon? (Noting that in big rip scenarios, horizons would actually shrink to planck scale and thus restore a planck heat within them, showing there is this link between space and heat).

Again, it is very difficult, well I say impossible, to separate the space and heat views when accounting for what is going on. And this is where Davies/Lineweaver argue for "blackbox photons" - the radiation from event horizons - as the heat death minima. Even completely empty space must still retain the heat due to its event horizon structure.

So many questions arise in which we must keep track of both the heat and the space it seems.

10. Jun 15, 2009

### Chalnoth

Those aren't the only two possibilities. And a big rip is exceedingly unlikely.

However, the end result ends up being that regardless of whether we have a cosmological constant or something that will eventually decay away, the end result is the same: the eventual fate of our universe is empty space. Until our universe reaches that state, its entropy will be increasing.

No. I think I sufficiently explained myself in my previous post, and this is not it. The argument for how entropy is related to expansion in the presence of dark energy doesn't pay any attention to the complexity of the universe. It just shows that a universe with matter is lower entropy than one without.

11. Jun 15, 2009

### apeiron

Can you please supply references to this argument. It is new to me and I'm not following its logic at all.

I'm also unsure how you are measuring entropy here too. That in itself is a subject.

For example, in a heat death void at near absolute zero, where is the microstate variety that can scramble macro distinctions? If everything falls to a common lowest mode, it all starts to look orderly again.

12. Jun 15, 2009

### PrometteusBR

Well, if you use the formula of entropy. The answer would be yes, because it´s proportional to temparature and a bigger universe, is colder universe. So..it should increase.
However it´s no a quantical formula..its classical one.

Last edited: Jun 15, 2009
13. Jun 15, 2009

### Chalnoth

It's a pretty well-known result, but here's a recent paper that goes a bit into these calculations of entropy:
http://arxiv.org/abs/0906.1047

They can be measured in the same way one measures the microstates of a black hole. And no, by the way, you're misunderstanding entropy by assuming that if everything is the same, that is a form of order. The exact opposite is true: in an equilibrium state, everything is the same. It is in low entropy configurations that you have interesting things happening, not high entropy ones.

14. Jun 15, 2009

### Entropee

Well first off, according to the 2nd law of thermodynamics, entropy SHOULD increase, being that the universe is finite in extent. However if there is to be a 0 net increase in entropy you would need to take into account EVERYTHING that can possibly decrease or eliminate entropy. And some of which we don't know very much about, like dark energy.

Also what happens to the entropy of matter that falls into a black hole? This problem involves quantum mechanics AND gravity, not something were very good at explaining at the moment.

And does entropy prevent the big crunch?

15. Jun 15, 2009

### Chalnoth

Except if you take any individual system that we know of and isolate it, its entropy will increase with time (or, if it has reached equilibrium, stay the same). In fact, I would say this fact is guaranteed by the definition we use for entropy: an overall decrease would require a system to spontaneously transition from a highly-probable configuration to a very improbable one.

The nice thing about black holes, however, is that their properties actually make it so that we can calculate their entropy exactly, even without knowing all of the details of the underlying quantum mechanics.

Pretty much, yes. Basically when things collapse, the probability that their angular momentum is zero is vanishingly small. So basically things would start to spin around one another at high velocity instead of collapsing together.

16. Jun 16, 2009

### PrometteusBR

Well, a decrease of entropy is the oposite of said, isn´t?
I mean a smaller entropy means a system more probable, so a decrease of entropy require a system transition from a high improbable to a very probable with less internal configurations.

What you think?

17. Jun 16, 2009

### Chalnoth

No. Low entropy = less probable. High entropy = more probable. This is fundamentally why total entropy tends to increase (and large numbers of the constituent particles ensure that "tends to increase" equals "always increases" for all intents and purposes).

18. Jun 16, 2009

### apeiron

So you're not a big fan of the third law of thermodynamics I take it.

Overall, all your comments reflect orthodox thermo models applied to outlier cosmo models. The OP just wanted an intro to orthodox thermo - Boltzmann statistical mechanics. You tried to look clever throwing in black hole/de sitter cosmology.

To take the discussion to that level, you would then have to be prepared to question orthodox thermo models based on closed systems, Poincarre recurrence, avoidance of third law, avoidance of non-extensive models, etc.

So yes, we can see what cosmological mileage we can get out of simple Boltzmann entropy modelling. Not against that at all. But you mis-represent the certainty of that modelling. It makes necessary assumptions - assumptions that in thermo literature it would be normal to challenge.

19. Jun 16, 2009

### Chalnoth

That may effectively apply to electromagnetic systems, but it doesn't appear to apply to gravitational ones, in particularly not de Sitter space.

We've known for a long time now that the purely empirical laws of thermodynamics can be derived in full from statistical mechanics: by understanding the behavior of the constituents of the system, we can derive the system's thermodynamic behavior. And when we apply this to quantum mechanics, we find that entropy is proportional to the logarithm of the number of microstates that can replicate a given macrostate.

So, when we apply such a description to, say, a collection of normal matter, and ignore gravity, the description makes sense: cool a system down, the various components of the system start to settle into their ground states, and when the system is at zero temperature, every component of the system is necessarily in its ground state, which indicates that the system as a whole is perfectly specified by only one state. That indicates zero entropy, as the logarithm of one is zero.

But this argument fails to apply to gravitational systems, whose microstates we don't know how to accurately describe. I believe there are only a few specific gravitational systems that we are able to describe the entropy of: empty space with horizons (e.g. black holes, de Sitter space). And we find that despite the apparent simplicity of the states in question, as well as their (usually) low temperatures, they tend to have extremely high entropies.

20. Jun 17, 2009

### apeiron

So putting aside black holes or any other matter, what is the entropy of actually empty space in a de sitter universe?

Does the dark energy/cosmological constant supply some residual "action"?

And is this not the Davies/Lineweaver "black box photons" story?

21. Jun 17, 2009

### Chalnoth

It's given by the area of the horizon, just as with a black hole. This paper goes into a fair amount of detail on the entropy of de Sitter space: http://www.iop.org/EJ/article/0264-9381/5/10/013/cqv5i10p1349.pdf

Last edited by a moderator: Apr 24, 2017
22. Jun 17, 2009

### apeiron

OK, so you take the Davies/Lineweaver position then as I flagged a couple of times in the thread. So why not just say so?

As cited for example here.....and noting the phrase which you were so quick to dispute by taking things out of context: "The expansion of the universe by itself produces no
entropy."
http://www.mso.anu.edu.au/~charley/papers/LineweaverChap_6.pdf

6.1.4 Return of the Heat Death
Before the discovery that 3/4 of the energy density of the universe was vacuum
energy (ΩΛ ∼ 0.73), it was thought that the expansion of the universe
made the concept of classical heat death obsolete, because in an eternally expanding
universe with an eternally decreasing TCMB, thermodynamic equilibrium
is a moving unobtainable target (e.g., Frautschi 1982). However, the
presence of vacuum energy (also known as a cosmological constant) creates
a cosmological event horizon (Fig. 6.3) and this imposes a lower limit to
the temperature of the universe since the event horizon emits a blackbody
spectrum of photons whose temperature is determined by the value of the
cosmological constant:
TΛ = 1/2π Λ1/2
This is the minimum temperature that our universe will ever have if the
cosmological constant is a true constant. Current values of Λ yield TΛ ∼ 10−30 K. This new fixed temperature puts an upper bound on the maximum
entropy of the universe and therefore reintroduces a classical heat death as
the final state of the universe.
To summarize our cosmological considerations: Galaxies, stars and planets
Sommeria, this volume). The expansion of the universe by itself produces no
entropy. Stars are currently the largest producers of entropy in the universe
but all the stars in the universe will only ever be able to produce about 1%
of the entropy contained in the CMB. The newly discovered cosmological
constant limits the maximum entropy of the universe, and consequently the
universe is on its way to a heat death.

23. Jun 17, 2009

### Chalnoth

I think you missed the point where even if there is no cosmological constant, as long as the contents of the universe satisfy certain properties, the horizon area still acts as a measure of entropy: the "generalized second law" holds true regardless:

$$\frac{d}{dt} S_m + S_h \geq 0$$

...where $$S_m$$ is the entropy of the matter, and $$S_a$$ is the entropy from the cosmological horizon (given by its area). The only thing that the cosmological constant does do is produce a definite, finite final state: one with constant horizon size and no matter. The heat death of the universe would occur even without this, as long as expansion was infinite into the future.

24. Jun 17, 2009

### apeiron

Gotta laugh. First I missed the point as I didn't presume dark energy. Now I miss the point because I do. Trouble is you just won't stick to the point and only seek to score points.

To remind, the question was: Does the expansion of the universe also cause an increase in overall entropy?

Personally I believe that is a difficult question to answer as it calls into question what we really mean by entropy. Is there actually a way to define it in a dynamic and probably self-organising context?

So then I cited what I feel was a mainstream opinion on the question:

Charlie Lineweaver (who co-authors with Davies) says: "Thus the expansion of the universe by itself is not responsible for any entropy increase. There is no heat exchange between different parts of the universe. The expansion is adiabatic and isentropic: dSexpansion = 0."

Which then seems a good starting point to ask well what does he mean here?

Then in you came, firing off shots in all directions. You either can't explain yourself or don't have an explanation.

25. Jun 17, 2009

### Entropee

Weird I had thought all this time that entropy was the degree of disorder in a system, which means more disorder (entropy) means less probable, and less disorder meant higher probability...

have I been wrong all this time?