A question about Entropy and the heat death of the Universe

[pyrosheep]

I just started learning about Entropy in chemistry and there has been one question bugging me.

The second law of thermodynamics states that Entropy must increase in thermodynamic processes.

The third law states that the entropy of a perfect crystal is equal to zero at absolute zero kelvin.

So as time passes and matter inevitably becomes smaller and further apart in accordance with the second law, the temperature in the system must at some point approach absolute zero.

At this point the entropy must also be approaching zero, in accordance with the third law.

If this is the case, then surely the second law is violated, as Entropy must have decreased in the system to be approaching zero.

what am i missing?

PS: sorry if this question seems stupid, i'm much more a chemist than a physicist (and a second rate one at that -you wouldn't believe how many times i wrote enthalpy instead of entropy -)

[N_las]

The entropy of a system can increase while its temperature is decreasing. The universe can have a low temperature while having a high entropy. The entropy is dependent on the number of possible ways a system could be arranged. This has only an indirect connection to temperatur.

It is true that a perfect crystal at zero kelvin would have zero entropy, but this is irrelevant, since nothing can ever have zero kelvin temperature.

A good way to picture entropy: Imagine a set of ten normal dices. The are all showing the "1" face. They add up to a sum of 10 eyes. That is the only possible way to get 10 eyes, so the number of possible ways to arrange a "10-eye" system is very low. If you change one dice at random, it may show a "2" face. The sum of all dices is now 11 eyes. There are 10 possible ways to get 11 eyes (each dice could have the two), so the "11-eye" system has a "higher entropy" (in the sense of this games rules).

If you shake your dices for quite some time, you may get a "35-eye" system. This has a giant number of possible ways to be arranged. In fact, the "35-eye" system has the maximum amount of possible arrangements, hence the highest "entropy".

By slowly rolling one of your dices after the other in a random order, any system will tend to become a "35-eye" system. This is purly by chance, because there simply are more possible ways to arrange the 35-system. Getting a 10-system (or a 60-system) by chance is highly unlikely, because it has only one possible way to arrange it: only ones (or only sixes for the 60-system).

I hope this explains entropy: The entropy rises simpy because of statistical reasons. The entropy is a measure of the possible ways to arrange a particular system. If there are many ways to arrange a particular system to A, and only few ways to arrange the system to B, then it is simply more likely that you will end up with A (the higher entropy state).

Edited November 18, 2014 by N_las

[GregA]

I just started learning about Entropy in chemistry and there has been one question bugging me.

The second law of thermodynamics states that Entropy must increase in thermodynamic processes.

The third law states that the entropy of a perfect crystal is equal to zero at absolute zero kelvin.

So as time passes and matter inevitably becomes smaller and further apart in accordance with the second law, the temperature in the system must at some point approach absolute zero.

At this point the entropy must also be approaching zero, in accordance with the third law.

If this is the case, then surely the second law is violated, as Entropy must have decreased in the system to be approaching zero.

what am i missing?

PS: sorry if this question seems stupid, i'm much more a chemist than a physicist (and a second rate one at that -you wouldn't believe how many times i wrote enthalpy instead of entropy -)

Any mathematical system is merely an approximation of reality. All math systems break down in the face of it. No one tells you this while you are in school because they want you to have confidence in the tools that you have. Physics provides an really amazing description of every day reality. Im not kidding here. Here on hearth. even out into our solar system, they are all spot on.

However in all areas of science smaller than the proton, and bigger than perhaps the local stellar group(or void, I have heard both...), the science is all really well intentioned best guesses. I am sure much of it is close, but I suspect a lot of it just flat out wrong. I know this, because two different mathematicians can take the same systems of equations, and come up with different results. For a very contemporary view of this... I propose the question, do black holes exist or not?

Some day a better math/physics will describe what is going in in the second law of thermodynamics, because it is a law that currently has problems with known/suspected cosmological observations. However, here on earth, and solar system, it works as perfectly as we can measure it. But like our observations of the infinite, and infinitesimal universe, it is based on our limits of understanding.

When you are talking about the heat death of the Universe, I like Big Rip theory more. It seems less lonely that a universe filled decaying protons at 10^99 years from now.

[rodion]

the failure in the analogy you presented here is that as the universe evolves it does not tend towards the state of a crystalline structure. a crystal is an extremely ordered state by definition because its constituents must each take a unique geometric position in order to form it. the universe by contrast is in the long term process of disassociating its structure - all of its particles are collectively approaching the state of isotropically flying around in random directions, rather than organizing themselves into a specific place and time.

[Bill Phil]

I'm not a thermo guy, but I have a related question.

If entropy always increases, why did the universe become more orderly? As in planets and stars, unless I'm missing something, like if stars could have enough entropy for the whole solar system.

I know this seems stupid too, but I would like to know.

As it started as a cloud of random flying atoms with tons of energy.

[Starman4308]

I'm not a thermo guy, but I have a related question.

If entropy always increases, why did the universe become more orderly? As in planets and stars, unless I'm missing something, like if stars could have enough entropy for the whole solar system.

I know this seems stupid too, but I would like to know.

As it started as a cloud of random flying atoms with tons of energy.

Stop thinking like a human being. Physics doesn't care what humans think. The early universe might look random and disordered to you, but to the laws of physics, there was a lot of order to it. I'm not an expert on the birth of the universe, but stars are easy to explain. Fusion of hydrogen nuclei to helium (and eventually to iron) releases a lot of thermal energy to the environment. While the hydrogen nuclei are probably losing entropy from being stuck into heavier nuclei, the thermal energy this releases greatly increases the entropy of the surroundings. There may be other effects contributing to entropy: I'm a biochemist, not a physicist.

[Bill Phil]

Stop thinking like a human being. Physics doesn't care what humans think. The early universe might look random and disordered to you, but to the laws of physics, there was a lot of order to it. I'm not an expert on the birth of the universe, but stars are easy to explain. Fusion of hydrogen nuclei to helium (and eventually to iron) releases a lot of thermal energy to the environment. While the hydrogen nuclei are probably losing entropy from being stuck into heavier nuclei, the thermal energy this releases greatly increases the entropy of the surroundings. There may be other effects contributing to entropy: I'm a biochemist, not a physicist.

If we didn't think like humans, we wouldn't have physics.

Plus, it does look random, because how can it be ordered? I'm not much of a thermodynamics genius, so if wouldn't know.

[rodion]

If entropy always increases, why did the universe become more orderly?

this is a problem at the forefront of cosmological understanding. the assumption that cosmologists use at present is that there were tiny anisotropies, distortions in the quantum "fabric" of the spacetime that were present from the earliest moments of the universe's existence and so over time the deviations in gravitational density of these areas caused matter to selectively sink into them, ultimately seeding galaxy clusters and so forth. if you look at images of the larger structure of the universe - full of galactic superclusters, filaments and voids, etc. - it seems pretty credible that these tiny wrinkles in spacetime existed and that their legacies are still present in an extremely inflated form. why these defects in the structure of the universe were present from the time of the big bang is, however, basically a mystery.

[AndrewBCrisp]

Not a stupid question at all.

The key is to remember that entropy can be reversed locally - but only by consuming energy and hence increasing entropy globally.

Consider that analogy of the 10 die all displaying 1's in a previous post. We can reduce this low-entropy state to a high entropy state (where each dice shows a different number) easily enough by rolling them all once. But if we want to get that ordered state of all 1's again, we need to either roll each individual dice until we get a 1, then repeat with all the others, or roll ALL the dice until that combination of 10 1's shows up once more. Both methods consume energy and time.

Another analogy would be to consider the rack of balls on a pool table. If memory serves there are 15 balls all arranged in a triangular state, with each numbered ball in a specific location - a very ordered, low entropy state. To increase the entropy of the rack, you just have to hit it with a cue ball. But to restore the rack, you need to hit each ball with the cue ball at a certain direction and a certain amount of force to get all of those balls back into place - or pick the balls up and put them back into order manually. Again, both methods to reduce the pool table's entropy take energy and time.

Both the above analogies follow certain rules: to change the number on a dice you have to roll the dice; to change the position of a pool ball you have to nudge it with a cue ball and a cue stick. Those rules don't change.

The universe is the same. The laws of physics dictate how particles interact via the four basic forces. Opposite charges attract, masses attract each other, and the more mass the more the attractive force (gravity), and so on. But, the universe at the beginning has a LOT of energy, and not a lot of space for that energy (and mass) to spread out in, though that's changing as the universe expands. So the early universe is a FRENZY of particle-particle interactions, all obeying the laws of physics. Particles join together, atoms form, atoms combine into molecules, molecules are attracted to each other via electromagnetism or gravity, forming bigger masses still. These in turn start forming stars, then planets as more heavier elements come into play. And so on and so forth, all the way to forming life, intelligence, civilization. Each of these steps takes time - and consumes energy. And as energy is consumed, the total entropy of the universe increases.

Eventually, when all energy sources reach equilibrium, the ability to maintain ordered conditions like living things, planetary systems, even crystalline structures, fades. No new stars are formed because you can no longer gather together enough hydrogen in one spot for a star to coalesce and ignite. Existing stars die and disperse. Existing planets grow cold - those not consumed by their stars as the stars die. Eventually things will just... stop, and if anything remains "ordered" as we call it today, it will not have a chance to become more ordered. You might have a tiny salt crystal floating around, for example, but it will never get the chance to grow into a bigger salt crystal.

Does this make things a little clearer?

[K^2]

Lets start with the fact that entropy is a conserved quantity. It's a trivial proof in QM, but a more general proof exists that covers classical mechanics as well. (It is based on Liouville's Theorem, if anybody cares for the math.)

What increases is the coarse-grained entropy, which is far more important for how we perceive time, so the heat death is still a heat death, even if fine-grained entropy is conserved.

Anyways, these are just things to keep in mind when talking about 2nd law. The answer to OP's question is actually much simpler. The entropy density goes to zero as volume of the universe tends to infinity. The total (coarse-grained) entropy over all of space still increases.

[Starman4308]

If we didn't think like humans, we wouldn't have physics.

Plus, it does look random, because how can it be ordered? I'm not much of a thermodynamics genius, so if wouldn't know.

It's ordered at a microscopic scale: the particles of the early universe were not in their highest-entropy states, and subtle asymmetries in the early universe lead to the formation of distinct stars, galaxies, etc.

Again, you're looking at this with a far-too-human idea of what "chaos vs. order" is. A human's idea of chaos has nothing to do with entropy: entropy has to do with the number of possible states a system can occupy in a given configuration.

[rtxoff]

Something you might want to read if you are interessted into this matter: Maxwell's demon

[Laie]

If entropy always increases, why did the universe become more orderly? As in planets and stars, unless I'm missing something, like if stars could have enough entropy for the whole solar system.

I don't fancy that order/chaos way of talking about entropy. I prefer to think of it as "no useful energy left". Rain is pouring on the mountains, the water running downhill. Someday, when the sun has shut down (1), that will cease. The last drop of water will run downhill and stay downhill. Whatever is powering our tectonic activity will stop someday. The old mountains will erode, no new ones will form. There will also be pretty little cause for erosion, granted, but *if* anything ever happens, it will lead to the mountain becoming smaller. It will take a good long while, but eventually every planet will become a perfect sphere (2)(3).

Nothing will ever happen anymore. Not the tiniest height for anything to fall down from, no sink for it to fall into. And everything in the universe will look he same: any matter that could come together and form a new body has long done so, and all bodies that could come together to form bigger bodies have long done so, and all bodies that still remain are on stable trajectories, forever unchanging, and will never meet. Still plenty of radiation, but it has bounced between these bodies so many times that they're all in perfect equilibrium. That's entropy as I understand it. It's actually quite orderly.

(1) nevermind that our sun will swallow our earth long before that.

(2) allowing for a small bulge at the equator, of course.

(3) asymptotically. It will never quite get there.

Geez, preventing nitpicks is annoying.

Edited November 19, 2014 by Laie
a few typos

[N_las]

...

(2) allowing for a small bulge at the equator, of course.

...

Geez, preventing nitpicks is annoying.

Then let us nitpick a bit more

The rotating body will send out gravitational waves, so its rotation will stop after a long time. Therefore there wouldn't be a bulge at the equator left.

[Brotoro]

Then let us nitpick a bit more

The rotating body will send out gravitational waves, so its rotation will stop after a long time. Therefore there wouldn't be a bulge at the equator left.

I don't think that an axially symmetric rotating body emits gravitational waves while rotating around its axis of symmetry.

[N_las]

I don't think that an axially symmetric rotating body emits gravitational waves while rotating around its axis of symmetry.

While this is correct, no macroscopic body can ever by exactly symmetrical. Down to the atomic level, matter is coarse. If we talk about eternities, even that miniscule amount will stop the rotation eventually.

[Laie]

I'm surprised that noone has found worse than that -- I was afraid my description would be entirely too poetic, and not even wrong.

Edited November 19, 2014 by Laie

[Jovus]

Let's throw another couple wrenches in the works here.

For the OP, there are two other answers as well.

First, the 'heat death' of the Universe is assured only if the Universe is an energetically closed system. If it isn't, that's not what will happen. If there is some energy sink or energy source available to the universe, things may turn out differently than predicted by Newton (who, to be fair, was never talking about the whole Universe).

Second, the laws of thermodynamics govern thermodynamic processes. They do not govern non-thermodynamic processes. Most events are thermodynamic in nature, but not all.

As a side note, we're also assuming a Laplacian solution to the entropy distribution of the Universe, which is by no means assured. There may very well be (in fact, definitely are) local maxima and minima.

[kerbiloid]

http://en.wikipedia.org/wiki/Daisyworld

http://alifexi.alife.org/papers/ALIFExi_pp189-196.pdf

[Mr Shifty]

Lets start with the fact that entropy is a conserved quantity. It's a trivial proof in QM, but a more general proof exists that covers classical mechanics as well. (It is based on Liouville's Theorem, if anybody cares for the math.)

I'm totally ignorant of the relevant physics, but how does this square with the existence of black holes?

[N_las]

I'm totally ignorant of the relevant physics, but how does this square with the existence of black holes?

I think the black hole has an entropy only dependent on its surface area. If stuff falls into it, the entropy of this stuff isn't lost to the unverse, but in has increased the entropy of the black hole. By hawking radiation, the entropy can "leave" the black hole again.

[YNM]

Regarding entropy "decrease" in the Universe: you should also consider that the space (volume) expands, while matter are finite. When the volume increases, the density should decrease. Just what we see to happen on visible matter and radiation - the density decreases by a^3 and a^4 (a = scale factor).