Low entropy in extreme tempertures?

[pivoxa15]

Is it true that at extremely hot tempertures such just after the big bang, entropy is very low?

Penrose mentioned in his lecture about 40 min in that the universe started off in a very uniform state.
http://streamer.perimeterinstitute....9d9-4be4-961b-a8085fc24e07&shouldResize=False

Is it also true that at very low tempertures approaching absolute 0, entropy is also very low?


If both are true than why is it that entropy is so low at extreme tempertures? It seems contradictory.

 

[deepak9191]

well the third law of thermodynamics states that entropy is 0 at 0kelvins. entropy is nothin but randomness, obviously at low temperatures it would be low as aloms come together. at high temperatures, it hasnt ben seen yet that entropy decreases. after bigbang, i think it wud have been very cold as all energy wud be used in setting apart the celestial bodies

 

[D H]

Is it true that at extremely hot tempertures such just after the big bang, entropy is very low?
Penrose mentioned in his lecture about 40 min in that the universe started off in a very uniform state.
http://streamer.perimeterinstitute....9d9-4be4-961b-a8085fc24e07&shouldResize=False
Is it also true that at very low tempertures approaching absolute 0, entropy is also very low?
If both are true than why is it that entropy is so low at extreme tempertures? It seems contradictory.

Entropy is high, not low, when a system is in a very uniform state. The air in your room is more-or-less evenly distributed; this is a much more random state than all of the air in the bottom half of the room (the top being in vacuum). Similarly, a shuffled deck of cards has a lot more entropy than a deck with all the cards arranged in order by suit. The initial entropy of the universe was quite high; evidence of this is the high entropy extant in the cosmic background radiation.

after bigbang, i think it wud have been very cold as all energy wud be used in setting apart the celestial bodies

The temperature of the universe at the time of the big bang was very, very high. The universe has cooled ever since the big bang, just as a gas cools when it expands.

 

[SpaceTiger]

The initial entropy of the universe was quite high; evidence of this is the high entropy extant in the cosmic background radiation.

Shouldn't we be more precise here? High relative to what? Or, to the OP, low relative to what? The entropy of the universe at recombination must have been low relative to now, as given by the second law of thermodynamics. I've not read Penrose's book, but I think he was talking about the ability of inflation to explain homogeneity. Vanesch mentioned it in a previous post:

Well, Penrose's not so enthousiastic about inflation solving this problem and I have to say that I find his argument convincing. The reason is that thermal equilibrium (high entropy) is NOT equivalent to homogeneity when gravity is taken into account. Homogeneity is a state of LOW entropy (far from thermal equilibrium) when gravity is taken into account, and as such, using a time-reversible mechanism such as inflation to explain a LOW-entropy situation does only report you to a _still more stringent_ condition before it. You cannot have "matter thermalize to give you a uniform distribution" on a small scale (unless you *switch off gravity*). If it were to "thermalize" (with gravity) it would generate lots of singularities, and that wouldn't give rise to a smooth uniform homogeneous structure after inflation. The only way inflation can give rise to a (low entropy) state of homogeneity is that there was a potentially even lower entropy state before it acted.

 

[Chronos]

It might be more productive to look at the 'temperature' of the universe in the past:
http://spaceflightnow.com/news/n0012/24vlthot/ SpaceTiger was leading you to this observation. Penrose was wrong. SpaceTiger has a better explanation.

 

[oldman]

I've been re-reading parts of Penrose's massive tome "The Road to Reality" and I'm puzzled as to the status among cosmologists of some of the things he says. His ideas are briefly discussed in this long-dormant thread. They were finally dismissed

...Penrose was wrong. SpaceTiger has a better explanation.

But I don't follow these arguments, either. Could someone please explain what
is now thought about Penrose's reasoning?

My present understanding is this:

Penrose explains (in Chapter 27) that in an ordinary gas the configuration with the highest entropy is that in which particles are uniformly distributed. So one expects the uniform early universe to have high entropy. Then he points out (by invoking the Bekenstein-Hawking formula) that a universe which has gravitationally condensed into black holes has an even higher entropy. (One must of course remember, as Space Tiger emphasizes in this thread, that high and low are relative terms.)

Penrose also argues (his Fig. 27.10) --- without seeming to provide any proof --- that any gravitational condensation (perhaps into galaxies or stars) will increase the entropy of a uniform distribution of matter, and hence conform with the Second Law of thermodynamics.

Is there a simple proof for this claim that could be better understood by one for whom the Bekenstein-Hawking formula is a step much too far? Or is this where Penrose is in error, as Chronos states?

As a sidebar, I've also been long puzzled about how the total entropy changes when surplus kinetic energy is removed from local gravitational condensations (as mandated by the Virial Theorem). This mass/energy can't escape from the universe, can it?

 

[George Jones]

This has puzzled me also. Carroll says that we don't know how to define entropy in the presence of gravity. Follow the links in https://www.physicsforums.com/showthread.php?p=1355858#post1355858" to slide 11 from a talk by Carroll.

See also

http://arxiv.org/abs/gr-qc/9811085
http://arxiv.org/abs/gr-qc/0410008

 

[oldman]

This has puzzled me also. Carroll says that we don't know how to define entropy in the presence of gravity...

Thanks for this reassurance, which was bolstered by the useful links you gave. I guess Penrose was wishfully thinking, like so many others who consider such difficult matters.

 

[Chronos]

It appears the puck is still in play. I merely fail to grasp why.

 

[oldman]

It appears the puck is still in play. I merely fail to grasp why.

Could you amplify this rather cryptic remark, please Chronos? Do you now accept Penrose's reasoning, or are you still sceptical? Or do you think folk shouldn't bother with such matters?

 

[Fra]

I'm not into the details of these constructs, but most entropy arguments strikes me as boiling down to an apparent ambigousness in the choice of measure, we like to call entropy.

I still one might need to question, not wether we have found the right measure, but how any such such measure should be constructed in the first place, and what it's purpose is.

It seems that the main desire to establish an entropy measure of a state is to gauge somehow the a priori probability for a certain state. But this begs the question on exactly how this probability measure is defined? Seeking the entropy measure is to me more or less, seeking a priori probability measure - in disguise, sometimes hidden to the point where it's not noticed. And what is the physical justification for such a measure, and how can it be constructed? If we are trying to respect the measurement ideals, how do we construct such a measure physically?

I personally wonder to what extent the concept of a priori probability of various universes are well defined? This mental construction has always been disturbing to me.

I am more leaning towards the thinking that there strictly speaking exists no such objective, universal and perfectly defined 100% confident measure. Rather my question, is to try to understand what keeps the world together in despite of this lack of objectivity, or rather how objectivity can be principally understood as emergent.

I think we may need way to view these constructions. The statistical idealisations that has been so successful so far, might not hold.

/Fredrik

 

[Naty1]

Post #6: I also had a lot of difficulty with Penrose's Chapter 27 until I remembered a discussion in THE FABRIC OF THE COSMOS, Brian Greene, Entropy and Gravity page 171-173 quotes from there. I'll address 3 post # 6 statements using Greene's logic and quote when I can:
Post #6:
(1)

Penrose explains (in Chapter 27) that in an ordinary gas the configuration with the highest entropy is that in which particles are uniformly distributed. So one expects the uniform early universe to have high entropy.

second part not so!
ordinary means low gravity. Normally a uniform gas distribution, say sitting on a table top here on earth, IS in it's highest state of entropy when equilirium is reached BECAUSE GRAVITY IS NEGLIGIBLE.
Greene:

When gravity matters as it did in the high density early universe, clumpiness - not uniformity- is the norm.

So shortly after the big bang uniformity actually means LOW entropy as gravity was huge...one DOES NOT expect uniformity under such conditions of high gravity to reflect high entropy. (I think Penrose agrees.)

(2) Post #6

Then he points out (by invoking the Bekenstein-Hawking formula) that a universe which has gravitationally condensed into black holes has an even higher entropy. (One must of course remember, as Space Tiger emphasizes in this thread, that high and low are relative terms.)

Black hole entropy IS maximum because gravity is maximum in a given region of space.
Greene:

When gravity flexes it's muscles to the limit it becomes the most efficient generator of entropy in the universe. Since we can't see inside a black hole, it's impossible for us to detect any rearrangements

..,meaning hidden information (entropy) is maximized.


(3) Post#6:

Penrose also argues (his Fig. 27.10) --- without seeming to provide any proof --- that any gravitational condensation (perhaps into galaxies or stars) will increase the entropy of a uniform distribution of matter, and hence conform with the Second Law of thermodynamics.

Greene:

In calculating entropy you need to tally up the contributions from all sources. For the initially diffuse gas cloud you find that the entropy decrease through the formation of orderly clumps is more than compensated by the heat generated as the gas compresses, and ultimately, by the enormous heat and light released when nuclear processes begin to take place...The overwhelming drive towards disorder does not mean that orderly structures like stars and planets...can't form...the entropy balance sheet is still in the black even though certain constitutents have become more ordered.