# in an isolated system, entropy never decreases

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#### NewAmerica

##### Banned
Does "in an isolated system, entropy never decreases" also imply "in an isolated system, entropy never decreases, (nor increases)"?

Well, we know in school that the second law tells us in an isolated system, entropy always increases. But when it is expressed as "in an isolated system, entropy never decreases" , it gives me the feeling that it also never increases, and equilibrium is the destination of the isolated system.

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The second law of thermodynamics ensures (through statistical probability) that two bodies of different temperature, when brought into contact with each other and isolated from the rest of the Universe, will evolve to a thermodynamic equilibrium in which both bodies have approximately the same temperature.[6] The second law is also expressed as the assertion that in an isolated system, entropy never decreases.[6]

-Wiki

Source

##### Senior Member
I know nothing about entropy or isolated systems. But I see no grammatical or logical reason to add "(nor increases)". One might as easily - and as wrongly - say "In a bucket with a hole in it, the water never rises (nor falls)".

#### entangledbank

##### Senior Member
'Entropy never decreases' implies that it might stay the same for a while, but not that it will stay the same.

#### lingobingo

##### Senior Member
You only have to click on the title in footnote 6 to access the article this statement came from. But I don't quite get why you're trying to change the meaning of the sentence? Isn't it just stating that there's another way of saying that entropy always stays the same or increases – i.e. that it never decreases?

#### se16teddy

##### Senior Member
Does "in an isolated system, entropy never decreases" also imply "in an isolated system, entropy never decreases, (nor increases)"?
No.

I am not a physicist, but this is how I understand it.

Sometimes entropy seems to decrease. For example, if I make a pot from clay, it becomes more structured: entropy decreases. But the pot is not isolated. As the pot is made, the process forces entropy to increase even more in the rest of the universe, so overall the entropy of the universe increases.

Let us imagine part of the universe that had no contact whatsoever with the rest of the universe: no incoming or outgoing matter or energy: an isolated system. Total entropy within this isolated system is always on the increase.

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#### NewAmerica

##### Banned
so overall the entropy of the universe increases.
The overall the entropy of the universe should have included the entropy of the pot, which has decreased. So there is more of a possibility that the overall the entropy of the universe stays the same.

#### NewAmerica

##### Banned
'Entropy never decreases' implies that it might stay the same for a while, but not that it will stay the same.
How long is "a while"? One billion years on the cosmic scale?

#### entangledbank

##### Senior Member
No, doing work to make the pot increases entropy. Entropy decreases locally only by adding to it elsewhere in the system. You can't change states of one thing and offset it by something else - you can't swap amounts of entropy, decreasing here by the same amount you increase there.

#### NewAmerica

##### Banned
Isn't it just stating that there's another way of saying that entropy always stays the same or increases – i.e. that it never decreases?
Yeah, stays the same! For how long?

#### NewAmerica

##### Banned
No, doing work to make the pot increases entropy. Entropy decreases locally only by adding to it elsewhere in the system. You can't change states of one thing and offset it by something else - you can't swap amounts of entropy, decreasing here by the same amount you increase there.
It would have meant the orderly information can automatically loss to nowhere. Supposed there are two cups of water, one cold and the other hot. The cold has less entropy than that of the hot. Now mix the two, you get the water with moderate temperature. And supposed the two is an isolated system, will the entropy of it stay the same forever? Will it increase forever?

#### se16teddy

##### Senior Member
It would have meant the orderly information can automatically loss to nowhere. Supposed there are two cups of water, one cold and the other hot. The cold has less entropy than that of the hot. Now mix the two, you get the water with moderate temperature. And supposed the two is an isolated system, will the entropy of it stay the same forever? Will it increase forever?
In practice, you cannot ever mix the water so perfectly that the hot and cold water are perfectly evenly distributed. Entropy will therefore continue to increase in the cup forever, because the water is not at absolute zero, and so the water is circulating through convection and still destroying the ordered, separate, location of the hot and cold parts. Mixing is, I understand, an aspect of entropy: ultimate entropy is when all matter and energy are finally evenly distributed throughout the universe: everything is then perfectly disordered.

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#### PaulQ

##### Senior Member
Does "in an isolated system, entropy never decreases" also imply "in an isolated system, entropy never decreases, (nor increases)"?
No, there is no mention of increase, because the entropy of an isolated system does increase - it is simply that it cannot decrease.

#### manfy

##### Senior Member
No, there is no mention of increase, [...] - it is simply that it cannot decrease.
That covers the simple part, linguistics.

Supposed there are two cups of water, one cold and the other hot. The cold has less entropy than that of the hot. Now mix the two, you get the water with moderate temperature. And supposed the two is an isolated system, will the entropy of it stay the same forever?
Yes, once the mixing process of hot and cold water is finished and the system has reached equilibrium - the state of maximum thermodynamic entropy in this specific system - the entropy will remain unchanged forever and a day.

The really interesting but hitherto unasked question is: Will this specific process increase entropy or will the resulting entropy be the arithmetic mean of the hot and the cold cup of water?
Answer: Entropy will increase (at least from a microscopic point of view). Mixing of fluids leads to friction between colliding molecules and that will create losses that cannot be utilized as work. The same is true for the process of heat transfer.
Entropy in thermodynamics can often be simplified as energy that is not available to perform work, often also described as 'internal energy' of an object, which manifests itself as the temperature of the object.

This last statement is a gross oversimplification of the subject, of course, but it is worth mentioning because Maxwell used the same idea in his thought experiment.

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