A gas in a mini universe reaches maximum entropy

[Jeronimus]

Assuming a mini-universe with the same laws as our current one.

A gas within that universe reaches a state of maximum entropy. Would it remain in that state of maximum entropy once it is reached? Maybe the question does not make much sense. In that case, forgive my ignorance.

edit: the mini-universe contains nothing but that gas.

 

[Dmitry67]

You should define the cosmology of your toy universe

 

[Demystifier]

A gas within that universe reaches a state of maximum entropy. Would it remain in that state of maximum entropy once it is reached?

It would remain in that state for a long time, but not forever. After a sufficient time, it would even return to the initial low entropy state. (See Poincare recurrence.)

 

[Dmitry67]

... if you don't take gravity into account
With gravity becomes unstable, forming 'stars', and ultimately, black holes, which evaporate into photon gas, which can occasionally create secondary black holes, so in infinite time there will an equilibrium between gas and black holes :)

Of course, it is true is 'stable' infinite universe with gravity which is not realistic AFAIK (Dark energy can be balances with matter attraction, but it is still unstable)

 

[Jeronimus]

It would remain in that state for a long time, but not forever. After a sufficient time, it would even return to the initial low entropy state. (See Poincare recurrence.)

Isn't according to the second law of thermodynamics entropy supposed to increase over time, with usable energy getting lost irretrievable?

How is energy lost irretrievable if the universe could, given enough time, pop back into it's initial state?

 

[Jeronimus]

... if you don't take gravity into account
With gravity becomes unstable, forming 'stars', and ultimately, black holes, which evaporate into photon gas, which can occasionally create secondary black holes, so in infinite time there will an equilibrium between gas and black holes :)

Of course, it is true is 'stable' infinite universe with gravity which is not realistic AFAIK (Dark energy can be balances with matter attraction, but it is still unstable)

Assume a very small universe with not enough gas to form a black hole.

 

[JustinRyan]

Isn't according to the second law of thermodynamics entropy supposed to increase over time, with usable energy getting lost irretrievable?

How is energy lost irretrievable if the universe could, given enough time, pop back into it's initial state?

It is overwhelmingly probable...yes, but given enough time, the overwhelmingly improbable (returning to original state) will occur.

 

[Jeronimus]

It is overwhelmingly probable...yes, but given enough time, the overwhelmingly improbable (returning to original state) will occur.

I assume you meant overwhelmingly improbably.


If this is the case, then shouldn't someone come up and state clearly that usable energy is NEVER lost irretrievable as stated in several textbooks?
If above is correct, then as far as i think, this statement is as wrong as it could be.

While it might be EXTREMELY improbable for it to happen in a given short time interval. Given enough time it WILL happen.


Imagine such a mini-universe with filled out with small boxes, containing the gas in such a way, that the sealed gas retains it's total energy over time. No heat transfer out of the boxes(theoretically). The boxes contain just enough gas, for talking about entropy and usable/extract-able energy regarding the gas inside to make sense.


Every of those little boxes starts with a gas at minimum entropy. Given enough time, we would get all gas inside every box to reach a maximum state of entropy.

From the maximum entropy state in every box now, it is extremely improbable for all gas in every box to reach a minimum entropy state.
But what about one volume of gas inside a box to reach back to it's initial state, given enough of those little boxes? (the exact numbers would have to be solved mathematically)
That does not seem all that improbable to me.

What about several of those boxes reaching a low enough entropy level for usable energy to be extracted out of the gas?

 

[mfb]

It is lost irretrievable, as you cannot extract it to do something. Even if you could somehow contact that universe from another one (to extract "useful energy" - or better "negative entropy"): The observation (to see the recurrence) would generate more entropy than you can dump into this universe.

 

[JustinRyan]

I don't think you need to invoke another universe to create such a scenario. We can use our own. If you box the gas in such a way, given enough boxes, one will surely do the improbable. So for that particular box, the decrease in entropy will seem to violate the second law.
So I think you are correct in that an increase in entropy is not irreversable, in the same way that the 2nd law is not a true law. It more a statement of statistical likelyhood.
I do not want to say the textbooks are wrong. Just that there is a possibility, however small that the 2nd law can be violated.