Entropy and expanding universe

[geonat]

If I remember right, I have on several occasions read that the second law of thermodynamics is a consequence of the very unlikely initial state of the universe, and that it is this "potential" that drives the universe.

I would rather give the credit to the fact that the universe can expand, since *any* initial state (even a "maximally relaxed" one) will become less likely, or even impossible, to re-occur as the universe expands.
In a non-expanding universe on the other hand, the probability of a maximally relaxed initial condition to re-occur would be quite likely in comparison.

As the universe expands, particles without volume will have access to an increasing number of states since they can occupy a larger number of positions in space. This, from my current point of view, would be a better explanation of the second law of thermodynamics.

Are my arguments flawed, or have I just read the wrong books?

 

[Mentz114]

As the universe expands, particles without volume will have access to an increasing number of states since they can occupy a larger number of positions in space.

This thought has occurred to me and many others, I expect. Can you write this as an equation ? My own attempts have floundered.

 

[geonat]

This thought has occurred to me and many others, I expect. Can you write this as an equation ? My own attempts have floundered.

If, say, the number of available states s(t) per particle is approx. proportional to volume V(t), then s(t) = s(0) * V(t)/V(0), where t is time.

This is certainly an extreme oversimplification, but the best I could produce in a few minutes I guess.

 

[Mentz114]

So far so good, but you need to give a definition of entropy that uses s(t) to finish it.

The problem is that local, isolated systems also move towards lower entropy, and they're not affected by cosmic expansion.

 

[geonat]

So far so good, but you need to give a definition of entropy that uses s(t) to finish it.

If I carelessly assume that the total number of available states for $$N$$ particles simply is $$s^N$$, then the entropy S becomes

$$S(t)=k \ln s(t)^N = kN \ln \left[ s(0) V(t)/V(0) \right]$$ , k being Boltzmann's constant.

The problem is that local, isolated systems also move towards lower entropy, and they're not affected by cosmic expansion.

I do not understand why they aren't affected by cosmic expansion. Cosmic expansion happens everywhere, even between particles in isolated systems, doesn't it?

 

[Mentz114]

Cosmic expansion happens everywhere, even between particles in isolated systems, doesn't it?

We only have theory ( GR mostly) to go on, because no local effect would be large enough to be noticeable in our lives.
But GR shows that non-expanding 'bubbles' ( like the Schwarzshild space-time) can be embedded in expanding universes.

 

[geonat]

We only have theory ( GR mostly) to go on, because no local effect would be large enough to be noticeable in our lives.

Can't just the fact that entropy actually decreases be the noticeable effect of an expanding universe?
If I remember right, time-reversibility is a built-in feature of both Newton's and Einstein's equations. Can GR then really be used to disprove this proposition?

But GR shows that non-expanding 'bubbles' ( like the Schwarzshild space-time) can be embedded in expanding universes.

I had no idea about that - this is of course very interesting.

 

[Mentz114]

I'm getting out of my comfort level. The subject area of thermodynamics and GR is big and there a lot of papers and chapters in books. I can't find anything about expanding space and entropy though. Another problem with this hypothesis is that it doesn't seem to have any observable predictions.

Try a Google search, or hope an expert comes along.

 

[geonat]

Another problem with this hypothesis is that it doesn't seem to have any observable predictions.

Agreed - I can't directly come to think of any either.

Irrespective of this however, I find it to be a plausible explanation for entropy increase, and a better one than that of a highly improbable initial condition (for logical reasons that we have discussed).

Thank you for your comments - it has been a rewarding discussion.

 

[vanesch]

I don't know in how much this applies, but there's the Bekenstein limit
( http://en.wikipedia.org/wiki/Bekenstein_bound )
which gives an indication of the entropy of a gravitational system...

But I'm far beyond my "comfort level" here too...

 

[Mentz114]

Working out entropy in practice requires some kind of fine-graining process so one can count micro-states. Discrete energy states, for instance. Now, cosmic expansion may have no effect on the number of levels available, in this case, expansion would have no effect. If space-time is discretized ( as a means ) to get relative entropies, then your argument depends on whether more 'boxes" are created, or if existing boxes get bigger.

So it's possible to argue the case both ways, depending on the way the entropy is calculated.

Good thought, for sure.

Vanesch - that's an interesting link. Looks like a classical formula in a quantum context.

 

[Phred101.2]

"...the entropy metric is defined by the
order or disorder of topological structure[.]” -J. E. Johnson

(is the following a valid observation
The entropy of the universe is a surface that has the arrow of time against its edge. Spacetime has no 3-dimensional edge, but it has a dimensional surface. Gravity (a force due to matter/energy) provides valleys in this surface (spacetime) where matter/energy clumps together and so expands away from other clumps. Large sheets and filaments (of matter/energy) collect together, and leave expanding space behind. There is both a (local) compaction and a (distant) dispersal of the matter and energy that fill space, and of space itself. The edge of the universe is its own expansion.