Understanding the second law of thermodynamics

[soon2bepro]

I've read a bit about the 2nd law of thermodynamics.

As I understand it, no process can happen if it's not increasing the overall entropy of a system, therefore the universe is always going towards more entropy. And as I understand that, in a system with total entropy, there's no time.

Now my question is, is this change towards entropy slowing, accelerating, or neither? Put another way, does the 2nd law imply that the universe will at a certain point reach total entropy, or could it be the case that even though it has more entropy as time progresses, it can never reach a state of total entropy since this change is being slowed by orders of magnitude?

A second question - if we can choose what process to let happen (say use an engine vs using horsepower, etc), does that mean we get to choose to some extent the speed at which the entropy of a system progresses to?

And a third, related one: If a system has an X "level" of entropy, does that mean that in average, all processes will yield Y progress in entropy? In other words, given a set amount of entropy, is the average speed at which processes produce entropy fixed, or can it vary?



Thanks a lot for taking the time to read (and hopefully answer!) these questions. If you want to add any additional information that you consider relevant, I'll be grateful for that aswell

[Drag]

"As I understand it, no process can happen if it's not increasing the overall entropy of a system, therefore the universe is always going towards more entropy."

Not exactly, this law is of statistical nature and it is generalized on the basis of experiments that we can observe on Earth. Some people argue that on a bigger scale entropy can decrease, i.e. in the stars/galaxy formation, etc.

'And as I understand that, in a system with total entropy, there's no time.'

I've never heard about that, source? As far as I know time has no connection with entropy.

'Now my question is, is this change towards entropy slowing, accelerating, or neither?'

I doubt that anyone can tell. I don't know.


'Put another way, does the 2nd law imply that the universe will at a certain point reach total entropy, or could it be the case that even though it has more entropy as time progresses, it can never reach a state of total entropy since this change is being slowed by orders of magnitude?'

I don't know. I doubt that it is possible to reach the state of 'total entropy', for example if the universe will continue to expand, it is impossible to reach the state of total entropy. (This state would look like if all matter is dispersed uniformly all over the universe, it doesn't seem feasible with expanding universe.)


'A second question - if we can choose what process to let happen (say use an engine vs using horsepower, etc), does that mean we get to choose to some extent the speed at which the entropy of a system progresses to?'

Yes we can but it will have a negligible influence in comparison to increase of entropy brought about by the reaction in the sun.

'
And a third, related one: If a system has an X "level" of entropy, does that mean that in average, all processes will yield Y progress in entropy? In other words, given a set amount of entropy, is the average speed at which processes produce entropy fixed, or can it vary?'

No, it is not fixed. It depends on the specifics of the process.



'Thanks a lot for taking the time to read (and hopefully answer!) these questions. If you want to add any additional information that you consider relevant, I'll be grateful for that aswell.'

You should keep in mind the statistical nature of the 2nd law of thermodynamics and probably check the statistical mechanics foundations of this law.

[soon2bepro]

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'And as I understand that, in a system with total entropy, there's no time.'

I've never heard about that, source? As far as I know time has no connection with entropy.

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Since time is a representation of how fast something changes (or moves) in relation to something else, if no process can happen with total entropy, there's nothing to measure time by, so there's no time. Of course then again you're saying that I got this all wrong and that change can happen without it leading to more entropy.

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You should keep in mind the statistical nature of the 2nd law of thermodynamics and probably check the statistical mechanics foundations of this law.

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I will, but I was hoping to get some answers or pointers here aswell [img]/images/graemlins/smile.gif[/img]

[Metric]

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I've read a bit about the 2nd law of thermodynamics.

As I understand it, no process can happen if it's not increasing the overall entropy of a system, therefore the universe is always going towards more entropy.

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Right (statistically speaking, of course, which I'm sure you understand).

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And as I understand that, in a system with total entropy, there's no time.

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Right -- starting with a state of thermodynamic equilibrium (maximum entropy), you won't be able to define a thermodynamic arrow of time. There will be occational fluctuations from equilibrium, but these take place equally often in either direction of time (evolving "backwards" or "forwards").

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Now my question is, is this change towards entropy slowing, accelerating, or neither? Put another way, does the 2nd law imply that the universe will at a certain point reach total entropy, or could it be the case that even though it has more entropy as time progresses, it can never reach a state of total entropy since this change is being slowed by orders of magnitude?

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It's very difficult to be precise here since the observable universe isn't a closed system -- things can, for example, fall beyond the cosmological horizon and then never interact with us again. However, off the top of my head I'd tend to think "locally" that the increase of entropy is slowing -- stars are entropy producing factories (eventually producing lots of thermal radiation, heavy elements, and black holes), and the first generation of stars were extremely short-lived compared to the ones currently burning.

Ultimately in standard cosmology, though, we will reach a state of "asymptotic de Sitter space," which will be in a state of thermodynamic equilibrium at some incredibly minute temperature.
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A second question - if we can choose what process to let happen (say use an engine vs using horsepower, etc), does that mean we get to choose to some extent the speed at which the entropy of a system progresses to?

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Yep. Who knows, maybe if hyper-intelligence eventually saturates the cosmos, we'll be able to postpone the heat death of our corner of the universe for a very long time.

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And a third, related one: If a system has an X "level" of entropy, does that mean that in average, all processes will yield Y progress in entropy? In other words, given a set amount of entropy, is the average speed at which processes produce entropy fixed, or can it vary?

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It can vary.

[Drag]

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'And as I understand that, in a system with total entropy, there's no time.'

I've never heard about that, source? As far as I know time has no connection with entropy.

[/ QUOTE ]

Since time is a representation of how fast something changes (or moves) in relation to something else, if no process can happen with total entropy, there's nothing to measure time by, so there's no time. Of course then again you're saying that I got this all wrong and that change can happen without it leading to more entropy.


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If we can't measure it doesn't mean that it doesn't exist. I look at it as an extra dimension, like it is present in Special realtivity, while entropy is just a statistical quantity. I am even not sure if there is a good definition of entropy for quantum system. (There could be, I just don't know, and don't remember reading about it.)

Metric is probably more versed in this subject than me, but it seems to me that if we have fluctuations, time should exist.

In most processes that we observe entropy increases, but I'm cautious about applying the notion of entropy to cosmological processes. We can't be sure if it still valid on that scale. We don't have experimental evidence to be sure about it.

[Metric]

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I am even not sure if there is a good definition of entropy for quantum system. (There could be, I just don't know, and don't remember reading about it.)

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Yes, there is a good definition of entropy in quantum theory. It goes by the name "von Neumann entropy."

Interestingly, the von Neumann entropy was discovered well in advance of the classical information theoretic entropy (which is a more general version of the thermodynamic quantity), which is usually called the "Shannon entropy."

Shannon apparently had a conversation with von Neumann about his information theoretic quantity, where von Neumann was quoted as saying, "Call it entropy. It is already in use under that name and besides, it will give you a great edge in debates because nobody knows what entropy is anyway."

[Drag]

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I am even not sure if there is a good definition of entropy for quantum system. (There could be, I just don't know, and don't remember reading about it.)

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Yes, there is a good definition of entropy in quantum theory. It goes by the name "von Neumann entropy."

Interestingly, the von Neumann entropy was discovered well in advance of the classical information theoretic entropy (which is a more general version of the thermodynamic quantity), which is usually called the "Shannon entropy."

Shannon apparently had a conversation with von Neumann about his information theoretic quantity, where von Neumann was quoted as saying, "Call it entropy. It is already in use under that name and besides, it will give you a great edge in debates because nobody knows what entropy is anyway."

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Yeah, now I remember that we studied it. After all we should have had it at 'Quantum Statistical Mechanics', I've just never had to use it after the university.

[vhawk01]

As a complete sidenote that only barely relates to the OP, the 2nd Law of Thermodynamics, when used in evolution debates, is absolutely hilarious. Creationists talk about how the Theory of Evolution is only a theory, and then they speak of the 2nd LAW like it is a law. Its a great example of how the nomenclature used is so misleading to the average person. It is at least POSSIBLE that the 2nd Law is wrong. Its based on empirical data, its a statistical law, and it is impossible to test it in every possible condition. It is really "just" a theory. But its used like a divine weapon against the "theory" of evolution. Makes me chuckle a little bit.