Low entropy early Universe and the heat death musings

[martix]

I came upon a realization recently.

The early universe is always described to have begun in a state of extremely low entropy and it's been increasing ever since.

But the same amount of stuff exists now as it did back then. Only thing that's changed is how big the universe is now vs then.

So it seems to me entropy in a given system is a function of its volume.

Take the classic gas in a closed box example. It has 2 compartments, with a barrier in between. Take the barrier out, gas spreads out to both compartments until maximum entropy is achieved. But the gas was in its maximum entropy for the smaller compartment it occupied before, we just added more space. Add even more space to the box, gas will spread out even more. You essentially increase maximum entropy.

And the universe is expanding - i.e. we get more space all the time.
So the early universe is only low entropy, because space expanded to allow for more entropy.

And if it keeps expanding, it makes me conclude the "heat death" is (kinda) nonsensical. Perhaps things would slow down until interactions happen on absurdly long timescales, but they'd still keep happening.

What am I missing here?

(One thing I could think of, don't know how logically sound, is where, for every particle in the universe, each other particle finds itself outside of its cosmological horizon, removing it from the pool of particles that could interact with anything ever again.)

There's also some other philosophical arguments I can think of based on these ideas. Like for example the idea that space has to be quantized. Because of space was continuous, well, a finite region of space would have infinite entropy, because it'd have an infinite number of possible microstates.

 

[Andrew Mason]

I came upon a realization recently.

The early universe is always described to have begun in a state of extremely low entropy and it's been increasing ever since.

But the same amount of stuff exists now as it did back then. Only thing that's changed is how big the universe is now vs then.

So it seems to me entropy in a given system is a function of its volume.

Take the classic gas in a closed box example. It has 2 compartments, with a barrier in between. Take the barrier out, gas spreads out to both compartments until maximum entropy is achieved. But the gas was in its maximum entropy for the smaller compartment it occupied before, we just added more space. Add even more space to the box, gas will spread out even more. You essentially increase maximum entropy.

And the universe is expanding - i.e. we get more space all the time.
So the early universe is only low entropy, because space expanded to allow for more entropy.

And if it keeps expanding, it makes me conclude the "heat death" is (kinda) nonsensical.

"Heat death" occurs if the universe loses all its hot spots ie. because all stars have burned out and no new stars are forming. This is not necessarily a condition of maximum entropy because, as you point out, volume can still continue to increase. But, without temperature differences to drive thermodynamic processes, the universe would be a rather dead place.

AM

 

[PeterDonis]

it seems to me entropy in a given system is a function of its volume

Not entropy itself, but something like "maximum possible entropy", yes.

There are actually two issues here.

One is that the expansion of the universe means that there are, roughly speaking, more microstates available for the universe now than there were right after the Big Bang. That means, roughly speaking, that the "maximum possible entropy" of the universe is much larger now than it was then, since the maximum possible entropy should be something like the logarithm of the number of available microstates.

The second issue is that we have to take gravity--or, more precisely, the microstates available in the spacetime geometry--into account when assessing entropy. Roughly speaking, at least a large part of the increase in available microstates due to the expansion of the universe is probably due to more microstates available in the spacetime geometry, not in the "stuff" (matter and energy). However, nobody knows precisely how to describe the microstates available in the spacetime geometry, so this is all very heuristic.

Like for example the idea that space has to be quantized. Because of space was continuous, well, a finite region of space would have infinite entropy, because it'd have an infinite number of possible microstates.

Roughly speaking, yes, this is one of the reasons we expect that the correct theory of quantum gravity, if we ever discover it, will tell us that on small enough scales, spacetime is quantized. However, nobody knows precisely how to describe what that means; it is by no means clear that it is as simple as spacetime just being made of 4-dimensional "pixels" each being roughly one Planck-length-sized 4-d volume.

 

[martix]

Oh, I think I see my problem.

In the box example, we tack on a new space to the side, so the half of the box with the gas is a hot spot in relation to the other side. But space is expanding everywhere equally. It doesn't create hot-spots... it just lowers temperature everywhere equally (I think it lowers temperature?).

More shower thoughts:
- If the arrow of time is the result of entropy and entropy is dependent on space, but space is expanding with time it creates a self-referential connection between space and time that hurts my brain...

- I was reading about time crystals, which are incredibly weird. Not even sure how to interpret this statement: a time crystal cannot exist in thermal equilibrium

- Maybe space is continuous, but all the interactions are not. An abstract example - if you take the number line, and you have a thing that jumps by +/- 2 every time, it'd only ever be able to visit the even numbers and you'd never even know the odd numbers exist.

> Not entropy itself, but something like "maximum possible entropy", yes.
Yea, that. Good spot.

> the microstates available in the spacetime geometry
Wow, I hadn't even considered the idea of spacetime itself having entropy.

> it is by no means clear that it is as simple as spacetime just being made of 4-dimensional "pixels"
Maybe not, but the idea of 4-dimensional "planxels" is neat. (Also inventing new words is fun. I checked google. It's brand new.)

 

[PeterDonis]

space is expanding everywhere equally. It doesn't create hot-spots... it just lowers temperature everywhere equally (I think it lowers temperature?).

If you are thinking in terms of "space expanding" (which actually has some serious limitations), yes, it happens everywhere equally and its effect is to lower the average temperature of matter and energy.

If the arrow of time is the result of entropy and entropy is dependent on space, but space is expanding with time it creates a self-referential connection between space and time

No, it doesn't. You need to think in terms of spacetime, not space and time. The thermodynamic "arrow of time" in spacetime just means that, along any timelike worldline, the direction of increasing entropy is also the direction in which the universe is observed to be expanding (for example, distant galaxies show a redshift and the average temperature of things like the CMBR decreases). This is perfectly well-defined in terms of spacetime and doesn't create any problems.

time crystals

If you have a valid reference for this, you can start a separate thread based on that reference. It's off topic for this thread.

Maybe space is continuous, but all the interactions are not.

Please review the PF rules on personal speculation. Again, if you have a reference for something like this, you can start a separate thread based on it. Please keep this thread focused on the original topic.

 

[martix]

> You need to think in terms of spacetime, not space and time.
Good point.

> personal speculation.
Yea, these were all late night sleepy-brain shower thoughts. Best to just ignore those. I'll keep the rule in mind.

To be fair, much of what I was going on about was abstract reasoning on my part, and I wanted to find out how much of it had any merit in physical reality, which I guess I do now.

> it's pseudo-scientific nonsense
I stumbled onto the wiki article (yes, I know wikipedia is not a valid reference). Being nonsense is useful information though.

Thanks to everyone for indulging me in any case.