Entropy in a contracting universe?

[nicktacik]

Now we all know the 2nd law of thermodynamics says that the entropy of the universe increases in physical processes. We also all know the universe is expanding. Now suppose the \Omega value led to a big crunch situation. It would seem intuitive to me, that the moment right after the big bang, should have the same entropy value as the moment right before the 'big crunch', however the 2nd law says that the moment right before the 'big crunch' will have a higher entropy.

So the question is; does the 2nd law apply in a contracting universe?

Note that I am only familiar with the dS=\frac{dQ}{T} definition of entropy, so please explain any more advanced (ie stat mech) definitions clearly.

 

[marcus]

It would seem intuitive to me, that the moment right after the big bang, should have the same entropy value as the moment right before the 'big crunch',

it does not seem intuitive to me. but people's intuitions differ.

I picture right after bang (or right after inflation if you like it in the story) as very SMOOTH AND UNIFORM
and in the case of gravity a uniform field is the LOWEST ENTROPY.

by contrast, I picture conditions during a crunch as highly lumpy and INHOMOGENEOUS
and in the case of gravity a clumpy irregular field with all kinds of warts pimples and black holes is the HIGHEST ENTROPY

So the question is; does the 2nd law apply in a contracting universe?

Note that I am only familiar with the dS=\frac{dQ}{T} definition of entropy, so please explain any more advanced (ie stat mech) definitions clearly.

conditions at bang (lo entopy) are very different from conditions at crunch (hi entropy) and so, at least in my intuitive picture the 2nd law HOLDS for the entire history of the universe from bang to crunch

you are postulating an unrealistic case where Lambda is zero, in the usual LambdaCDM model we do not expect a crunch, even if Omega > 1 and the universe is spatial closed (as it may very well be).

Roger Penrose has given several talks about applying 2nd Law to Cosmology and if you want to have entropy explained in the context of the gravitational field then you might like to watch and listen to one of his talks, which are online.

Here is a Penrose talk that does the Stat Mech definition with pictures, in the context of cosmology:
http://www.Newton.cam.ac.uk/webseminars/pg+ws/2005/gmr/gmrw04/1107/penrose/

Here Penrose argues that a BOUNCE cosmology is theoretically impossible because entropy is very high at crunch and very low at bang---so how do you bounce from crunch to bang without violating 2nd Law and abruptly setting entropy back to zero, essentially.
This argument is flawed because you have different observers watching the crunch and watching the bang, with different macrostates mapping the phase space. However it is only his argument against bounce that I believe is flawed. The rest of what he has to say is correct, valuable, and very well presented!

 

[DaveC426913]

by contrast, I picture conditions during a crunch as highly lumpy and INHOMOGENEOUS

I'd never really given it a lot of thought before, but I can see it going both ways.

Just before the Crunch, it won't be like we have material objects such as stars and BHs bumping into each other - which might be my primitive description of what you're envisioning. It seems to me, that well before that, all the matter will have been compressed and heated first to plasma (where anything larger than subatomic particles such as protons and electons will be torn apart), but then the matter will be converted into energy.

I can see a case for a fairly uniform universe merely because no matter - let alone any granular structure - of any kind could exist.

 

[marcus]

I'd never really given it a lot of thought before, but I can see it going both ways.

Just before the Crunch, it won't be like we have material objects such as stars and BHs bumping into each other ...

I can see a case for a fairly uniform universe merely because no matter - let alone any granular structure - of any kind could exist.

what about irregular density?
that is, a highly chaotic GEOMETRY

Penrose talk teaches us that when you look at the entropy of the gravitational field (which is the same thing as the geometry) a uniform regular geometry is low entropy and a chaotic geometry---like crumpled paper except more so and at all scales---is high entropy

even if all the matter evaporates, can't there still be a bumpiness to the density causing the gravitational field to develop worse and worse inhomogeneities. At the moment I can't think of a further source for you, except possibly another Penrose lecture----or maybe his book.

I know. George Jones understands this pretty well and he will be around in a day or two. Let's keep this discussion going and hope that some others show up.

 

[Chronos]

If entropy is an emergent, rather than fundamental property, attempts to assign it a 'value' in the early universe will yield paradoxical results.

 

[nicktacik]

Thanks for the replies... that makes a lot of sense! (And the penrose talk was brilliant)

 

[Demystifier]

In one of his earlier papers, S. Hawking concluded that the entropy will start to decrease when the universe will start to contract. Later he said that this was his biggest mistake.

 

[xantox]

Just before the Crunch, it won't be like we have material objects such as stars and BHs bumping into each other - which might be my primitive description of what you're envisioning. It seems to me, that well before that, all the matter will have been compressed and heated first to plasma (where anything larger than subatomic particles such as protons and electons will be torn apart), but then the matter will be converted into energy.

I can see a case for a fairly uniform universe merely because no matter - let alone any granular structure - of any kind could exist.

Matter would be converted into energy, as well as energy would be converted into matter. This means that near the big crunch matter and radiation would be in thermal equilibrium, so that entropy would be maximal.

 

[Chronos]

Reality may not be causal. It may be a coincidence that accidently produces causality in our universe. I dislike ST, but cannot dismiss it. The mathematical contortions are useless exercises in futility, IMO.