# Entropy and Expansion, A Puzzle?

1. Jun 13, 2004

### Antonio Lao

Entropy is increasing. I am accepting this statement as a fact which I don't know how to verify by experiment.

Entropy, as I understand, is related to number of arrangement of objects found in a given system. The more objects there are, the higher is the entropy. For a universe of just one object and if the object is not spinning and shape like a sphere, then the number of arrangement of this object in the universe is 1. This is the minimum for a quantum universe.

Obviously, the physical universe is full of many objects: planets, stars, galaxies, interstellar clouds and dust. So there are many possible arrangements for these objects. The entropy should have a large value. But out of these random chaotic arrangements, some semblance of order emerge and I can pressume that this order should lower the value of entropy. Does this emergence of order gave a reason for the universe to expand for entropy to keep on increasing?

For black holes, entropy is at a maximum and according to Bekenstein and Hawking, entropy is dependent on the surface area of the black hole not its volume.

Relatively speaking, when the universe expands the relative size of an object should decrease toward becoming a point-object and eventually all objects would become of the same size as the spacetime point (either quantized or continuous). So the maximum entropy of the universe is at the time when all objects turn back to the identity of a point of spacetime ( there should be an infinite number of arrangement for an infinite points of spacetime).

Last edited: Jun 13, 2004
2. Jun 13, 2004

### Janitor

When some big nebulous cloud of gas and dust and junk collapses into a spherical star plus a thin disc of rotating dust around it, the motion of individual particles is more tightly constrained than it used to be, so that would appear to be a decrease in entropy. But the overall entropy would have to include radiation emitted from the heat generated by the collapse of the cloud, in addition to the temperature of the material being higher after than it was before, and I would think that if you could properly account for those things, the net effect is an increase in entropy.

3. Jun 13, 2004

### Antonio Lao

I dont't understand. Are you saying that the creation of radiation contributes to the increase of entropy? Does the universe ends in darkness? Or in light? Is the final quantum state of the universe at minimum temperature? Or maximum temperature?

4. Jun 13, 2004

### BCRion

Take the statistical mechanics version of entropy as order and disorder with a grain of salt. Although it is a correct description, it is not always the best model to view entropy.

A given system or amount of energy has a certain type of quality related to it. This quality is the ability of the system to produce useful work. It is possible for a system to have a lot of energy, but unable to do anything useful, for instance a dead battery. Entropy is sort of the inverse to this quality. Every process generates entropy. The higher the entropy of a system, the lower the quality or availability to do useful work.

In terms of the cosmos, think of Hydrogen having the highest potential to produce energy through nuclear fusion or having the lowest entropy. As Hydrogen is fused into Helium, and then Carbon, and so on, the quality decreases and entropy increases, although the total energy in the universe remains constant. Eventually, the elements reach Iron, which has the highest entropy of the nuclides.

You can make elements heavier than Iron (ex. Uranium which can release energy in fission) but, you must have a net input of energy. Although you decrease the entropy of the Iron nucleus through this process, it must be incorporated with an even greater increase of entropy somewhere else, say a supernova.

So my point is, sometimes entropy requires a different perspective.

5. Jun 13, 2004

### Janitor

I don't have a thermal physics reference at my fingertips, but I am confident that thermodynamics has a way to account for the change in entropy when a molecule or an ion emits photon(s). The net change in total entropy would be positive.

ADDED NOTE: Strictly speaking, I probably should have said that the process results in a net increase in entropy in certain environments. If the molecule is being bathed in high-temperature blackbody radiation, the reverse process (molecule absorbs photon and moves to a higher-energy state, possibly even being ionized) would involve a net increase in entropy.

Last edited: Jun 13, 2004
6. Jun 13, 2004

### Antonio Lao

I still don't understand the usefulness of energy. The usefulness of energy derive from food stuff makes sense only for the living and healthy people not for the sick and the dead. Useful energy (hydrogens) is good for young stars in their formative period not for dying red giant or white dwarf or sick nova and supernova.

As I get older, I realize that my body does not burn sugar or carbohydrates as good as it use to. So these sugar compounds is really useless to me. Now I am avoiding alcohol and ice cream and other fatty foods.

If the system cannot process the available energy then the extra energy is useless. Relatively speaking, the usefulness of energy depends on the system that is going to use this energy for it to stay alive.

7. Jun 13, 2004

### BCRion

The usability is more from a practical engineer's standpoint and not a physicist's, but they are both valid ways of looking at the entropy.

Suppose I want to make a new electricity source. I choose metal blocks at different temperatures. Yes, I can do this. The only requirement to produce electrical energy (useful work) from thermal energy (less useful energy) is to have a temperature difference or temperature gradient.

Suppose I gather up all the metal blocks in the universe and I select two metal blocks, one at 80 C and the other at 20 C are placed next to each other in an insulated environment. After a long (actually infinite) amount of time, the blocks will equilibrate to one temperature and remain there forever -- this is an increase in entropy. It is impossible to get the blocks back to their original state without doing some work on the blocks to cool one down and heat the other back up. By doing this, you actually increase the entropy of the surroundings by more than the decrease of the entropy of the blocks.

Again, a difference in temperature is required for thermal cycles to produce electricity. If you merely hooked up your objects of two different temperatures, you would be able to generate some electricity or usable work, but not for long. Once they equilibrate, you may not extract any more work out of this system. Suppose you modify it and place the two old blocks next to another block at a different temperature. Eventually you will have three blocks of equilibrium temperature. Do this again, and again, until you have used up all the metal blocks in the universe and then you will have no way to get useful work from our metal block energy source. This is what I mean by useability of energy. The blocks still have thermal energy after they are expended, whatever their equilibrium temperature turns out to be. However, you cannot extract work from them.

As far as stars, the only reason they become red giants and supernova is because they run out of Hydrogen to burn. Once they run out, they have no choice but to burn their heavier elements. If you were able to give a red giant a massive influx of Hydrogen, it would burn just fine and the life of the star would be extended. My point being, once you run out of Hydrogen, you will be unable to generate new stars.

Biological systems are extremely complicated, but I'll do my best to explain your example. As you age, the cells and other mechanisms in your body run down, increasing entropy. Theoretically, if you could reverse your aging and repair the damage, you could process hydrocarbons just as well.

In a sense, you are correct. The usefulness depends on what is using it. If I gave you a gallon of gasoline and you did not have any way to burn it, it would not be of any use to you. However, in thinking of usefulness, we have to think of the possible work we could get out of it and the number of ways of doing it. If we put it in your car and let it run the engine we could get some work out of it. However, if we collected the byproducts after burning the gasoline, and put them back into the engine, it would be of little use. That's one less potential use we have for what was gasoline. Suppose we can find a way to use the byproducts. However, the products of the original byproducts will be even less useful than the ones before it. In other words, unless you put energy into them, you will never get back to gasoline.

Hope this helps.

8. Jun 14, 2004

### Antonio Lao

From a practical standpoint, it does. Thanks. But I am still trying to find the direct connection between the universal expansion of space (spacetime?) and the increase of entropy. And indirectly find a resolution for time's arrow.