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If the answer to the above question is positive, can I ask a followup, is the slope / relationship linear or more curved?

Regards,

Noel.

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If the answer to the above question is positive, can I ask a followup, is the slope / relationship linear or more curved?

Regards,

Noel.

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marcus

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It's a reasonable question and if you are going to talk about slope it is already a bit mathematical in nature.

If the answer to the above question is positive, can I ask a followup, is the slope / relationship linear or more curved?

Regards,

Noel.

So think of the function in trig called tan(x).

I think it always slopes up. The thing is though, it is occasionally not defined.

The entropy function for the U could be like that, simply not defined at the "big bang" or "big bounce" or start of the present expansion. It's something bear in mind.

An idea: just google "tangent function". You will see graphs of tan(x) which go thru a cycle over and over again without ever sloping down.

Over and over again, tan(x) starts out way negative and rises up thru zero and goes way positive, and then does that again, but never at any point is it sloping down. That is because it has no defined value at the times when it jumps down into negative territory to start a new cycle.

That is just an example to illustrate. The entropy function would not necessarily look like that, or even be cyclic! But it might have something in common, in the sense that it might not be well-defined at a certain point---might not have a definite numerical value.

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The reason that I ask is that, to me, galaxies seem more organised (and therefore I would have said less entrophic (if that's the right word)) than stars, which seem more organised than atoms, etc.

Regards,

Noel.

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marcus

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That deserves a careful answer. I have to go out now, will have to think later how to respond. It's visually unintuitive, but in the context of gravity, where everything wants to clump, clumped matter does not necessarily represent a more orderly configuration.

The reason that I ask is that, to me, galaxies seem more organised (and therefore I would have said less entrophic (if that's the right word)) than stars, which seem more organised than atoms, etc.

Regards,

Noel.

to respond I need to go into how entropy is actually defined. It does not exactly correspond to the intuitive content of an English word like "organized". Can't be equated exactly. Have to go. Hopefully I or someone else will address this question later.

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marcus

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One way to think about the entropy is that as time goes on information about the starting state becomes less and less accessible.

Or not about starting necessarily but any early U configuration that eventually led to the present. Matter was approx. evenly spread out. So there were jillions of particles and each one had a speed and direction. A huge book containing jillions of numbers

What a lot of information! If you could have recorded that setup. Now as time goes on they clump. and the individual configuration of those jillions determines exactly how they will clump. What will bump into and stick to what....

Finally say they all form galaxies and the galaxies all eventually clump into black holes and the black holes all clump into one monster black hole. How much information do you have now?

Hardly any. It takes maybe 3 or 4 numbers or perhaps a dozen, to describe all you can see about the black hole.

It is more "ORGANIZED" as you said (just taking your example to extreme of clumping). But there is very little accessible information about what the initial state was. Many different possible states have been collapsed into one highly organized state.

Theoretically a black hole has more entropy (per kilogram of mass) than anything else. It is the maximum entropy object.

So clumping into more and more organized forms actually increases entropy.

The black hole epitomized entropy, it denies access to the vast amount of information about all the different ways it could have formed and all the different things that might have fallen together to make it.

====================

I haven't given you a mathematically exact definition of entropy, only a different intuitive way to think about it. Also this way of picturing depends very much on the fact that we are dealing with GRAVITY and the universal clumping that goes with it. It is a good way to think when gravity and gravitationally bound structures are the dominant thing we are looking at.

If you were looking at a small box containing gas molecules at some temperature and pressure, then gravity would be negligible and you would need to think about it quite differently. They would not be attracting each other gravitationally (to any significant degree) and they would not be collapsing into little lumpy planets and stars. So entropy would be a different story.

Or not about starting necessarily but any early U configuration that eventually led to the present. Matter was approx. evenly spread out. So there were jillions of particles and each one had a speed and direction. A huge book containing jillions of numbers

What a lot of information! If you could have recorded that setup. Now as time goes on they clump. and the individual configuration of those jillions determines exactly how they will clump. What will bump into and stick to what....

Finally say they all form galaxies and the galaxies all eventually clump into black holes and the black holes all clump into one monster black hole. How much information do you have now?

Hardly any. It takes maybe 3 or 4 numbers or perhaps a dozen, to describe all you can see about the black hole.

It is more "ORGANIZED" as you said (just taking your example to extreme of clumping). But there is very little accessible information about what the initial state was. Many different possible states have been collapsed into one highly organized state.

Theoretically a black hole has more entropy (per kilogram of mass) than anything else. It is the maximum entropy object.

So clumping into more and more organized forms actually increases entropy.

The black hole epitomized entropy, it denies access to the vast amount of information about all the different ways it could have formed and all the different things that might have fallen together to make it.

====================

I haven't given you a mathematically exact definition of entropy, only a different intuitive way to think about it. Also this way of picturing depends very much on the fact that we are dealing with GRAVITY and the universal clumping that goes with it. It is a good way to think when gravity and gravitationally bound structures are the dominant thing we are looking at.

If you were looking at a small box containing gas molecules at some temperature and pressure, then gravity would be negligible and you would need to think about it quite differently. They would not be attracting each other gravitationally (to any significant degree) and they would not be collapsing into little lumpy planets and stars. So entropy would be a different story.

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Regards,

Noel.

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That deserves a careful answer. I have to go out now, will have to think later how to respond. It's visually unintuitive, but in the context of gravity, where everything wants to clump, clumped matter does not necessarily represent a more orderly configuration.

If matter was clumped (condensed) to the densest state possible wouldn't the (quanta particles) be as organized as possible and not moving with low to no entropy? And on the other hand if matter was diffused to the point all (quanta particles) were separated and moving wouldn’t the entropy be at its highest level? Wouldn’t entropy lower as matter condensed?

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Marcus, I'm still reading up on the information that you gave me (thanks again), but one question at this point if I may: when you refer to information about the starting point becoming less and less accessible .... how far "back" is the starting point?One way to think about the entropy is that as time goes on information about the starting state becomes less and less accessible.

For example (just because you mentioned blackholes), if a (small) blackhole evapourates and the matter within "escapes", and then gets absorbed into another blackhole, what is the "starting point"?

Thanks in advance,

Noel.

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What makes you think entropy is so low right now? Compared to what? I think space is where entropy is at its highest level and where ever matter accumulates is where entropy is getting lower. If the matter we see in the visible universe is only about 4% then the other 96% is diffused to a higher level of entropy. So high we can't even see it. I personally don't think it matters either because if the universe works in a cycle which I think it does then the entropy will always come back to where it was. There will always be a high point and low point over and over again.

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marcus

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How did I miss these two questions? Been busy with other stuff.

If you have a bunch of matter, the MOST entropy you can make with that matter is to cram it all together into a black hole. This is the "bekenstein entropy bound". It is a theoretical maximum.

Very strange because we think of having all of something in the same place as "orderly".

Like all my clean socks are in the same drawer. And all my math books are together on the shelves.**It makes them more readily accessible** and makes it easier to find what I want. That's part of what order means to me intuitively.

But having stuff so crammed together that it makes a black hole creates a HORIZON and makes the stuff LESS accessible.

My grasp of things gets shakey when you start talking about evaporation of one black holes and channeling the radiation into another black hole.

I can't picture how what you describe would happen. I think of the Hawking radiation as radiation. Most of it thermal, namely infrared light. I don't see how that would be be channeled into another black hole. Oh. OK. Some kind of optical funnel. And you need the second BH to exist already, in order to trap it. but wouldn't the second BH radiate BACK? Wouldn't they come into equilibrium instead of the first one totally evaporating? Anyway you have presented a kind of puzzle that I'd want some help with.

Also I don't see any clear "starting point" here that would be analogous to the start of expansion in cosmology.

That's the strange unintuitive thing about geometric entropy! Or, since the gravitational field is identical with the metric that defines the geometry (gravity=geometry) we can say it is the strange thing about the entropy of the gravitational field.If matter was clumped (condensed) to the densest state possible wouldn't the (quanta particles) be as organized as possible and not moving with low to no entropy? And on the other hand if matter was diffused to the point all (quanta particles) were separated and moving wouldn’t the entropy be at its highest level? Wouldn’t entropy lower as matter condensed?

If you have a bunch of matter, the MOST entropy you can make with that matter is to cram it all together into a black hole. This is the "bekenstein entropy bound". It is a theoretical maximum.

Very strange because we think of having all of something in the same place as "orderly".

Like all my clean socks are in the same drawer. And all my math books are together on the shelves.

But having stuff so crammed together that it makes a black hole creates a HORIZON and makes the stuff LESS accessible.

Lino, it goes without saying that I don't know all the answers and I think when I was talking about "starting point" it was only about the start of expansion. The initial conditions for the expansion we are witnessing....

For example (just because you mentioned blackholes), if a (small) blackhole evapourates and the matter within "escapes", and then gets absorbed into another blackhole, what is the "starting point"?

...

My grasp of things gets shakey when you start talking about evaporation of one black holes and channeling the radiation into another black hole.

I can't picture how what you describe would happen. I think of the Hawking radiation as radiation. Most of it thermal, namely infrared light. I don't see how that would be be channeled into another black hole. Oh. OK. Some kind of optical funnel. And you need the second BH to exist already, in order to trap it. but wouldn't the second BH radiate BACK? Wouldn't they come into equilibrium instead of the first one totally evaporating? Anyway you have presented a kind of puzzle that I'd want some help with.

Also I don't see any clear "starting point" here that would be analogous to the start of expansion in cosmology.

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Can I ask the same question with a different example, just to remove some of the complexity.

If I have a buket of sand (formed from worn down mountains), and refine it to make a glass statuette, which I bring on a space journey inot orbit, but gets broken, so I throw it over board, it burns up on re-entry, and ends up as sand...ish.

Working back from the present, does it matter when the "start" is? I know that this is an over simplified question, but I'm hoping that it will help get me started!

Regards,

Noel.

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Imho, and wrt my current understanding of things, entropy isn't a particularly useful way of understanding the evolution of our universe. But of course I could be quite wrong about that and am amenable to severe criticism and correction.

If the answer to the above question is positive, can I ask a followup, is the slope / relationship linear or more curved?

Regards,

Noel.

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Thanks ThomasT. I do appreciate your input & thoughts (all thoughts greatly appreciated).Imho, and wrt my current understanding of things, entropy isn't a particularly useful way of understanding the evolution of our universe. But of course I could be quite wrong about that and am amenable to severe criticism and correction.

To be clear, for anyone reading this, I'm not asking this in relation to the development / evolution of the universe, but trying to understand the nature of entropy itself. I was using the example above only as a follow on to other threads in this section. Please feel free to respond in reference to any example that you see fit (or if I should be asking such a basic question in a different section, do please let me know).

Regards,

Noel.

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marcus

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I'd say no, it doesnt matter. Not sure what further question might be bothering you. If you consider a rechargeable battery as another example, you can repeatedly charge it and use it, charge it and discharge it,...So the entropy of the battery (taken alone) can cycle. I don't see any natural "starting" state....Can I ask the same question with a different example, just to remove some of the complexity.

If I have a buket of sand (formed from worn down mountains), and refine it to make a glass statuette, which I bring on a space journey inot orbit, but gets broken, so I throw it over board, it burns up on re-entry, and ends up as sand...ish.

Working back from the present, does it matter when the "start" is? I know that this is an over simplified question, but I'm hoping that it will help get me started!...

But in that case the battery is not really isolated so the law about entropy doesn't apply to it. By itself, without outside intervention, it can only run downhill and reach a dead equilibrium.

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Questions about entropy have been asked in several different PF forums. So you might do a search on those.Thanks ThomasT. I do appreciate your input & thoughts (all thoughts greatly appreciated).

To be clear, for anyone reading this, I'm not asking this in relation to the development / evolution of the universe, but trying to understand the nature of entropy itself. I was using the example above only as a follow on to other threads in this section. Please feel free to respond in reference to any example that you see fit (or if I should be asking such a basic question in a different section, do please let me know).

Regards,

Noel.

Hopefully you're Googling also. Here's some stuff I found that might help: What is the entropy of the universe?

A Larger Estimate of the Entropy of the Universe

You can search arxiv.org for other pertinent articles.

Also, check out the Wikipedia article on it, paying special attention to the "Approaches to understanding entropy" section.

Here's some stuff from PhysLink

This article entitled Entropy and the Universe looks pretty thorough.

Here's the Wiki article on the heat death of the universe

You might find this article helpful. There are links to other discussions/explanations of entropy at the bottom of it.

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The standard cosmological model is based in the equations of GR, which are reversible and, thus, conserve thermodynamic entropy. For estimating production of entropy due to irreversible processes within universe new cosmological models based in extensions of GR are needed. Ilya Prigogine discusses an extension of GR and the production of entropy in a chapter of his book

If the answer to the above question is positive, can I ask a followup, is the slope / relationship linear or more curved?

Regards,

Noel.

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Thanks to everyone. This is great food for thought.

Regards,

Noel.

Regards,

Noel.

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Thomas, I just wanted to thank you for the reference to this article. It is pulling together a lot of threads that I had been thinking about and is a good informative read.This article entitled Entropy and the Universe looks pretty thorough.

I don't know if you wrote it yourself, or maybe you might know the person that wrote it, either way, I just wanted to say: top marks from me and lots of thanks.

Regards,

Noel.

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I didn't write that article. As far as I know it isn't the best one considering your question. I think the Wiki article is better. Either way, there's lots of stuff for you (and me) to check out and thus improve our knowledge of entropy -- what it means, how it's used in science. Your question motivated, and therefore helped, me. So I thank you.Thomas, I just wanted to thank you for the reference to this article. It is pulling together a lot of threads that I had been thinking about and is a good informative read.

I don't know if you wrote it yourself, or maybe you might know the person that wrote it, either way, I just wanted to say: top marks from me and lots of thanks.

Regards,

Noel.

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