Entropy and extremely long spans of time

[Zero]

If my understanding of entropy is correct, entropy increases because it's extremely statistically likely for it to do so, not because it necessarily must do so. If this is true, then wouldn't the heat death of the universe be something that wouldn't really last? If something's only a statistical unlikelihood, then on an infinite timespan, such as the duration of time to pass after the heat death of the universe, shouldn't the statistical unlikelihood still occur infinite times? And of course, there's a much much lower likelihood of this same statistical deviation occuring many times in conjunction, but on an infinite timespan, isn't even the most unlikely event necessarily going to happen by virtue of having infinite chances to happen? My ideas about entropy may be completely flawed, but I'm curious about possible implications if my ideas are correct.

[drachefly]

Sure, why not? Just, you'll have to wait a zillion years to find within a gigaparsec an amount of entropy difference that we take for granted day to day... and it will be in a form you likely won't be able to use... not to mention that you yourself don't exist at that point.

[Sriad]

If my understanding of entropy is correct, entropy increases because it's extremely statistically likely for it to do so, not because it necessarily must do so. If this is true, then wouldn't the heat death of the universe be something that wouldn't really last? If something's only a statistical unlikelihood, then on an infinite timespan, such as the duration of time to pass after the heat death of the universe, shouldn't the statistical unlikelihood still occur infinite times? And of course, there's a much much lower likelihood of this same statistical deviation occuring many times in conjunction, but on an infinite timespan, isn't even the most unlikely event necessarily going to happen by virtue of having infinite chances to happen? My ideas about entropy may be completely flawed, but I'm curious about possible implications if my ideas are correct.

I'm almost certainly talking out of my ass, but this line of thinking has long seemed to me like a reasonable explaination for the occurance of our universe in the first place.

[Talanth]

If my understanding of entropy is correct, entropy increases because it's extremely statistically likely for it to do so, not because it necessarily must do so.

Acording to my maths prophesor statistics is the one part of mathematics that humans canot grasp intuitively. It is statisticly posable for the heet of a table to cause a pen to leep upwards (the reverse of it being dropped) but the probability is so infinitesamaly small that it would most likely take the entire age of the universe to happen *but it still eventualy will*.

I think your right about it being an absolute certainty (or as near as makes no bones) for reverse entropy to happen, but only on the proviso that time and space aproach infinity. After all, if time and space are truly infinate then not only will *everything* happen somewhere, but everything will happen an infinite number of times.

P.S. First post ever! Wohoo! sorry

[Molyneux]

If my understanding of entropy is correct, entropy increases because it's extremely statistically likely for it to do so, not because it necessarily must do so.

Acording to my maths prophesor statistics is the one part of mathematics that humans canot grasp intuitively. It is statisticly posable for the heet of a table to cause a pen to leep upwards (the reverse of it being dropped) but the probability is so infinitesamaly small that it would most likely take the entire age of the universe to happen *but it still eventualy will*.

I think your right about it being an absolute certainty (or as near as makes no bones) for reverse entropy to happen, but only on the proviso that time and space aproach infinity. After all, if time and space are truly infinate then not only will *everything* happen somewhere, but everything will happen an infinite number of times.

P.S. First post ever! Wohoo! sorry

Welcome to the board! ^_^

And yeah, I've never been able to grasp probability; it appears to me that most other people share the same problem. Why else would so many play the lottery?

[General Trelane (Retired)]

I think your right about it being an absolute certainty (or as near as makes no bones) for reverse entropy to happen, but only on the proviso that time and space aproach infinity.

Reverse entropy? Am I missing some kind of new thermodynamics?

[Talanth]

Reverse entropy? Am I missing some kind of new thermodynamics?

Entropy is the measurment of disorder. All it realy says is that if you have an ordered system (say a sugar crystal in water) then it will go from its ordered, regular form into a more disordered one. So the sugar will disolve and its molecules scatter randomly. However there is no physical law anywhere that says this must be the case. So we're stuck with saying it's a statistical likelyhood.

It's perfectly posable, if you wait long enough, for the random motion of the water to bounce the sugar molecules back into their origional, ordered positions. Its not very likely but theres nothing to stop it. Thats decreacing entropy folks!

[drachefly]

Entropy is not physical disorder per se, it is the logarithm of the multiplicity of micro-states which correspond to the same macro-state.

To make that more concrete: imagine a gas with a mole of individual particles in it. To fully describe the system (a micro-state), you would need to use at least 6 moles of dynamical variables, which is a lot (position, momentum... possibly angular momentum too).

So, if you choose to lower the resolution of your theory, you can just count the number of gas particles in a large number (but not close to a mole) of arbitrarily defined cells, and their total kinetic energies. This, we call a macro-state (there are large numbers of ways of defining macro-states, and one of the interesting things about statistical mechanics is that it doesn't matter much how you do it). A macro-state is, then, a set of numbers of particles and total energies, one pair for each cell.


Suppose all of the gas was, strictly by chance, bunched up into just one of the cells (suppose also that this gas is dilute enough that it remains gas when doing so). This has a probability that is quite small, 1/(number of cells)^(number of particles).

Now, suppose that the 'first' half of the gas particles were, strictly by chance, bunched up into one cell, and the 'second' half of the gas particles were similarly bunched up into a different cell. If we say it that way, we have exactly the same probability -- BUT!
That is not the only way of achieving that macro-state: We could swap the positions of the first and last molecules, and everything would be the same... but it would not be the same micro-state.
And we could do the same with any other pair of particles in different boxes.

So, just by splitting them up that little bit, we managed to get an enormous probability gain.

This swapping effect introduces a probability factor of N! / (product of the various n!) where N is the total number of particles, and each n is the number of particles in a particular box.
To maximize this, you should get the denominator as small as possible, and that means spreading out the particles among the boxes.

Very small deviations create moderate probability drops; large deviations create incredibly large probability drops.

[Talanth]

Am I right in saying that the concept or entropy came from information theory? Or were they both developed in parallel?

[Prozac the Robert]

Am I right in saying that the concept or entropy came from information theory?

Don't know for sure, but I suspect it was the other way round.

As for the OP, you have to realise that the heat death of the universe leaves an awful lot of nothing, with a bit of background radiation and a scattering of stuff. All of it is probably moving apart and space is probably still expanding.

This means that the odds of any two unrelated bits of stuff getting together is absolutely tiny. The chances of enough of it getting together to form something like a star are pretty much non existant.

We could be talking about times orders of magnitude greater than the current age of the universe. And during these long periods of nothing happening, everything is moving even further apart, which further reduces the chance of anything interesting happening.

So based on something of a complete guess, it's probable that once the universe reaches maximum entropy, nothing very interesting will ever happen again.

[Lord of the Abyss]

As I remember, this idea used to be seriously proposed as the source of the observable universe. In an infinitely old & large universe, by sheer random chance, once every looooong while, enough matter would drift together to begin a new universe.

This was back before the theory that the universe could expand infinitely, however; when the static universe was the standard theory. Like Prozac the Robert says, when the universe expands to death there just isn't much there anymore. In the old days they just thought everything ran down.

[Zero]

But even if the odds are astronomically low, on an infinite timespan, shouldn't they happen anyways? If the chance is actually 0, then of course it can never happen that way, but if it's simply increadibly unlikely, on an infinite timespan, there ought to still be significant reverse entropy at some point, shouldn't there?

[Lord of the Abyss]

I'm not a cosmologist, but I think it is impossible for an expanding universe; there's just not enough matter and energy available.

[Zero]

If the universe is expanding at an increasingly fast rate, then I can understand that the timespan for events of such astronomically low probabilities would be finite, since eventually, it will actually be impossible for any two particles any distance apart to ever come in contact with each other, since the universe is expanding faster than they can move. Even if it isn't expanding at an increasingly fast rate, eventually every lil thing in the universe will be so far apart that it is absolutely impossible for them to ever come into contact, since the speed of light is the upper limit for velocity.

But is the universe infinitely large? I've never actually understood that...

[drachefly]

Sure, if space has infinite extent in all directions, it must happen somewhere. It could happen to occur 10^10^250 light years from here, though. Not very useful.

[Thinkmarble]

Look up Poincare recurrence theorem.
Which states that after a long time a system is going to reapproach its initial state.

I am not quite happy about the usage of probability and "statistically likely" in the context of classical thermodynamics. I admit that it makes my headache and that I still have to think long about it before I can claim to understood the the physics of it, but the "probabilities" are only something we use to express our ignorance of the system.

Enter macrostate and microstate.
Macrostate is nailed down by things like total energy, total particle number, total volume, while a microstate specifies all momentum and displacement vectors.
A macrostate does not contain enough information for a complete description of the system, but we do not stand a prayer to get a complete description of the microscopic state for any macroscopic system (eg. 10^23 gas atoms, try to measure 10^23 displacement vectors and 10^23 momentum vectors). So we can only measure and specify the macrostate, and assign probabilities to the microstate which the system could be in, eventhough that in "reality" the system is in actuality in just one of them (afterall in classical physics an atome has exactly one position and no probabilities about it).
In that way the probabilities in classical thermodynamics are reflecting our ignorance.

What now the 2nd law of thermodynamics comes down to is that with time a system goes from a macrostate with a small number of microstates to a macrostate with a large number of microstates.
While all along the system is actually in just one microstates and undergoes an deterministic time evolution.

[drachefly]

The Poincarè recurrence theorem has a variety of conditions on it, only some of which are met by the universe as a whole.

In particular, the universe is monotonically expanding. This causes a great many other asymmetries which doom recurrence to... not... recurring.

[Talanth]

But even if the odds are astronomically low, on an infinite timespan, shouldn't they happen anyways?

Yes. But the point is that our universe has only been around for a relitively short span of time compared to what would be needed. We are very definatly finite.