# Relation between entropy, order and structures

#### benjayk

Hi everyone.
I'm very interested in how order and structures arises in the universe, but I don't get how thermodynamics (which seem to be closely linked to order, especially the second law) relates to that... So I will ask a few questions. Please don't be too technical, I study computer science and not physics, so I have only basic knowledge of physics that I learned in school (I vaguely know what classical mechanics, electromagnetism, theory of relativity and quantum mechanics, etc are about, but don't have in-depth knowledge).

If I understood correctly entropy always (or at the very least almost always) increases with time in closed systems. The universe started with 0 entropy (or something close to it) and evolves towards a state of more entropy. Often entropy is equated to disorder, or the unability of a system to do work.
But I imagine the Bing Bang to be a in very uniform state, but this would mean it had high entropy (which is not the case), so in what way was the Bing Bang most far from equillibrium?

Also, the universe at the Bing Bang as I imagine it can hardly said to exhibit (complex) structure. But our universe now does exhibit complex structure. Does this mean that structural complexity and entropy are not related? Or does increasing entropy even mean increased structural complexity? But this would mean that disorder is higher complexity, while I would call higher complexity more orderly. So is physical disorder really not disorder in the sense of disorder of information (=lack of useful information), but means something unrelated or even inversely related in physics?

I find it hard to imagine a universe which starts at order and devolves into an disordered/more random state. If we assume observers need order to exist this seems to entail that observers should occur most near to the Bing Bang, which doesn't seem to be the case at all.
It also makes no sense from my metaphysical perspective that information can not be - ultimately - destroyed (relations simply do exist, they determine the form of the physical universe, not the other way around). Most importantly consciousness can not cease to exist (forever). I think subjective immortality is the only thing which makes sense given that I can not conceive what the opposite could even mean *at all*. Saying consciousness will not be there at all makes as much sense as existence will not be there at all (since from my perspective - the only one that I have - my existence IS consciousness) - none, since there IS only existence.
I assume concsiousness will always tend to order, so this would suggest the opposite of a universe where less things can happen (less work can be done) and order decreases as time goes on.

Is it maybe possible that even though entropy tends to infinity for the entire universe some subsection of the universe can forever remain in a state of low entropy or even decrease in entropy (maybe due to intelligence dispersing the entropy it causes into outer space)? It seems to me that the universe tends to seperate regions of high entropy (eg space) from regions of low entropy (eg structures on our earth). So could it be that the universe ultimately evolves to region(s) of infinite order and region(s) of infinite disorder (possibly much bigger or even unboundedly much bigger if the trend since the Bing Bang continues), in a way that the total entropy still increases forever?

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#### Andrew Mason

Homework Helper
Hi everyone.
If I understood correctly entropy always (or at the very least almost always) increases with time in closed systems. The universe started with 0 entropy (or something close to it) and evolves towards a state of more entropy. Often entropy is equated to disorder, or the unability of a system to do work.
It is misleading to equate entropy to disorder. You would have to define "disorder" in a very special way.

Entropy's usefulness is in comparing different states of a system and surroundings - the difference in entropy $\Delta S$ between two states. The difference in entropy between those states tells you how much of the useful work that could have been realized was not realized in the thermodynamic process between those states.

But I imagine the Bing Bang to be a in very uniform state, but this would mean it had high entropy (which is not the case), so in what way was the Bing Bang most far from equillibrium?
Again, it is not very useful to speak about the entropy of a single state. It is really only meaningful to measure the difference in entropy between two states. Does a red giant star have high or low entropy? It depends on what you are comparing it to and it depends on the state of the rest of the universe in each of those states.

Suppose you are comparing it to the higher temperature sun-like star that it was before it became a red giant. Since the star has experienced a great deal of negative heat flow, its entropy has decreased ($\Delta S = \int_{rev} dQ/T < 0$). But if that heat flow just warmed up its lower temperature surroundings, the surroundings have experienced an increase in entropy of a greater magnitude than the negative entropy that the star has experienced. If that heat flow has been used to run a Carnot heat engine whose work output has been stored in some useful form, there is no increase in entropy at all.

Also, the universe at the Bing Bang as I imagine it can hardly said to exhibit (complex) structure. But our universe now does exhibit complex structure. Does this mean that structural complexity and entropy are not related? Or does increasing entropy even mean increased structural complexity? But this would mean that disorder is higher complexity, while I would call higher complexity more orderly. So is physical disorder really not disorder in the sense of disorder of information (=lack of useful information), but means something unrelated or even inversely related in physics?
Again. Don’t equate entropy with disorder. Pouring a glass of boiling water onto an iceberg results in a total increase in entropy. It all ends up as ice. So is the final state (ice) more disordered than the initial state (ice + boiling water)? What does “disorder” mean?

AM

#### benjayk

Thanks for the clarification. So order cannot generally be equated to entopy.

But still it seems to me that there is a relation between formation of structures and entropy. I presume formation of structures needs work to be done and increase of entropy means less capability of doing useful work. This would imply that as entropy increases there is less formation of structures.
But this is at odds with what we observe; entropy has increased in the universe, but still structures have formed (and in some regions the speed of formation of complex structures has vastly increased).

Is there anything in physics suggesting that there is an increase in difference between entropy of different regions in the universe? Because this seems to be the case.

Does order != entropy mean that it is possible that the universe continues to develop into ever complex non-random structures (I have no exact definition for this but I think we can vaguely agree what would constitute complexity, eg uniform gas would not, while an ever developing intelligence would) despite increasing in entropy?

If that heat flow has been used to run a Carnot heat engine whose work output has been stored in some useful form, there is no increase in entropy at all.
But surely the engine lets the entropy of the regions where it dumps its heat increase?

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#### Andrew Mason

Homework Helper
Thanks for the clarification. So order cannot generally be equated to entopy.

But still it seems to me that there is a relation between formation of structures and entropy. I presume formation of structures needs work to be done and increase of entropy needs less capability of doing useful work. This would imply that as entropy increases there is less formation of structures.
Entropy increase is not really necessarily related to the formation of structures. Structures often require a loss of entropy locally. For example, water vapour loses entropy (negative heat flow) when it condenses to water in clouds. Those clouds lose entropy when the water droplets turn to snow. Snow flakes are highly structured.

AM

#### Andrew Mason

Homework Helper
But surely the engine lets the entropy of the regions where it dumps its heat increase?
Yes. By the exact same amount that the star has lost. So total entropy change = 0. (the second law states that total entropy change of the universe cannot be less than 0).

AM

#### Andrew Mason

Homework Helper
Is there anything in physics suggesting that there is an increase in difference between entropy of different regions in the universe? Because this seems to be the case.
The second law says that total entropy cannot decrease in any process. So the entropy of the universe is always increasing. Apart from that, there is no law that says where the entropy has to increase and where it has to decrease. It can decrease locally so long as it increases by an equal or greater amount somewhere else.

Does order != entropy mean that it is possible that the universe continues to develop into ever complex non-random structures (I have no exact definition for this but I think we can vaguely agree what would constitute complexity, eg uniform gas would not, while an ever developing intelligence would) despite increasing in entropy?
Intelligence and structure is not really limited by entropy considerations. Life requires heat flow. But it doesn't need very much compared to all the heat flow that goes on in the universe.

AM

#### benjayk

Entropy increase is not really necessarily related to the formation of structures. Structures often require a loss of entropy locally. For example, water vapour loses entropy (negative heat flow) when it condenses to water in clouds. Those clouds lose entropy when the water droplets turn to snow. Snow flakes are highly structured.

AM
OK, so what is wrong with my reasoning?

The second law says that total entropy cannot decrease in any process. So the entropy of the universe is always increasing. Apart from that, there is no law that says where the entropy has to increase and where it has to decrease. It can decrease locally so long as it increases by an equal or greater amount somewhere else.
Can entropy decrease locally even compared to the Big Bang (that is, if we assume the entropy at the Big Bang to be 0, can it become negative locally)?

#### Andrew Mason

Homework Helper
OK, so what is wrong with my reasoning?
Entropy increase is associated with the inefficiency of a thermodynamic process - the amount of useful (mechanical) work obtained from a given amount of heat flow. Change in entropy does not determine the complexity of what results from the work. The more inefficient the process, the greater the increase in entropy of the system and surroundings.

Effectively, this means that entropy increase depends on rate at which useful work is needed to be done for a given amount of heat flow. The slower the process can be done, the closer to equilibrium it can occur and consequently, the lower the entropy increase. The more rapidly useful work is needed in order to change something, the greater the increase in entropy.

Can entropy decrease locally even compared to the Big Bang (that is, if we assume the entropy at the Big Bang to be 0, can it become negative locally)?
The Big Bang was a process that happened very quickly and very far from equilibrium. So there was a huge increase in entropy from the very beginning.

If the Big Bang was an enormously rapid expansion of volume into nothingness, it was something like a free expansion of a gas, which always involves an increase in entropy.

AM