# Thermodynamics Versus Cosmology

## Main Question or Discussion Point

I don't know if this is the appropriate forum for my dilemma, but here it goes:

Second law of thermodynamics says that the entropy in the universe increases. In every texbook I have learned, ice is considered to have low entropy. When it melts, entropy increases. When that water becomes water vapor, entropy increases. Notice the direction from solid (ice) to a gas (water vapor), entropy increases -- in mathematical terms, the degrees of freedom increase.

Now over to cosmology. Here in that subject, gas (the one in which the universe supposedly started) is low entropy. Today, the universe is in a state of higher entropy -- the galaxies and everything else, including that piece of ice, are in a higher state of entropy. Notice the direction from gas to solid, entropy increases.

There seems to be a contradiction. Anyone???

marcus
Gold Member
Dearly Missed
the entropy of the gravitational field works according to a different intuitive picture than what you are used to, maybe.

the gravitational field has very LOW entropy when it is all evenly smoothed out, with no puckers and dimples

as time goes on, stars and galaxies condense, and planets etc etc. and make all kind of little wrinkes and zits in the geometry which go whizzing around each other in all kinds of orbits. It takes more and more degrees of freedom (descriptors) to describe the situation.

The more it condenses the more the irregular the gravitational field gets, the more entropy.
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there are lots of things to say about this. what I said here is just one remark. maybe it will help resolve the apparent contradiction to some extent, and hopefully we will get other comment as well

This is exactly what bothers me. In a gravitational field, ice is considered to be in a state of high entropy, when you look at degrees of freedom. But put that ice on a counter, vis-a-vis its environment, it is in a state of low entropy.

There seems to be a logical contradiction, how can one resolve this?

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When a star or planet is formed from a gas cloud it will get hot from the gravitational contraction. A hot gas cloud has more entropy than a cold gas cloud. The heat energy will of course be radiated away, so you must include the entropy of the produced photons.

The earth currently does have a smaller entropy than the gas cloud from wich it formed, but a larger entropy if you include all photons that were radiated away while it formed and to cool it to its present temperature.

Compare the earth now, with all of its organized life forms and associated structures, to the earth at a time in the past when life had not evolved very far, if at all, but was comparable in temperature to now.

Accounting for the amazing amount of organization that has taken place on this planet, has net entropy increased or decreased, and if it has increased over this time, what has offset the decrease in entropy caused by evolution (since by the time evolution began, most of the radiated photons had left)?

marcus
Gold Member
Dearly Missed
This is exactly what bothers me. In a gravitational field, ice is considered to be in a state of high entropy, when you look at degrees of freedom. But put that ice on a counter, vis-a-vis its environment, it is in a state of low entropy.

There seems to be a logical contradiction, how can one resolve this?
Palazzo I don't understand what you said, that I highlighted.
What do you mean by "ice". I did not say anything about ice, or about any material.
My point was about the gravitational field itself.

the gravitational field is not made of atoms and molecules. The flatter and smoother and more even it is, the more boring-----and the easier to describe.

the more wrinkly and pimply and pitted with potholes the field gets the more complicated and hard to describe, and the more different ways it could be.

The gravitational field is, in a certain sense, space itself. Space is nothing but geometry and the gravitational field is a metric which describes geometry. Besides that, there is nothing called space. The gravitational field (i.e. geometry) has its own entropy.

That entropy has to be counted along with the entropy of material stuff like gas and dust and stars.

When you include the growing entropy of the geometry, you can get that the total increases. Sure at the bigbang time the MATTER had a high temperature and maybe you think it had high entropy (like steam instead of ice) but that is of minor importance. If you include the entropy of the gravitational field then you find that the total entropy was very low at the bigbang time.

Does this work for you? Let me know if I am unclear or mistaken about something.

Compare the earth now, with all of its organized life forms and associated structures, to the earth at a time in the past when life had not evolved very far, if at all, but was comparable in temperature to now.

Accounting for the amazing amount of organization that has taken place on this planet, has net entropy increased or decreased, and if it has increased over this time, what has offset the decrease in entropy caused by evolution (since by the time evolution began, most of the radiated photons had left)?
The earth receives high energy photons from the sun and sends out low energy photons. The increase in entropy of doing this for 5 billion years is enormous compared with the entropy changes in any biological process.

Palazzo I don't understand what you said, that I highlighted.
What do you mean by "ice". I did not say anything about ice, or about any material.
My point was about the gravitational field itself.

the gravitational field is not made of atoms and molecules. The flatter and smoother and more even it is, the more boring-----and the easier to describe.

the more wrinkly and pimply and pitted with potholes the field gets the more complicated and hard to describe, and the more different ways it could be.

The gravitational field is, in a certain sense, space itself. Space is nothing but geometry and the gravitational field is a metric which describes geometry. Besides that, there is nothing called space. The gravitational field (i.e. geometry) has its own entropy.

That entropy has to be counted along with the entropy of material stuff like gas and dust and stars.

When you include the growing entropy of the geometry, you can get that the total increases. Sure at the bigbang time the MATTER had a high temperature and maybe you think it had high entropy (like steam instead of ice) but that is of minor importance. If you include the entropy of the gravitational field then you find that the total entropy was very low at the bigbang time.

Does this work for you? Let me know if I am unclear or mistaken about something.

Okay, thanks for the clarification.

I actually have a question that falls pretty much in line with the above..

Usually its said that the temperature of the big bang (or "the" singularity or something else equally unclear) was infinite in the beginning.

Now I know that temperature can be defined as in a way: 1/T = dS/dE, so I was wondering if what was said above is the reason people talk about the temperature as infinitly high.

I mean if dS/dE --> 0 then the temperature --> Infinity, so if the entropy is at a maximum, or minimum with respect to energy, you would get your infinite temperature.

Normally one talks about the temperature with relation to a bunch of particles but since its the big bang and all, I dont think there were even any particles around to *have* kinetic energy... Unless you talk about light ( does light even have *kinetic* energy?)

So is this the solution? Or am I missing the point (as usual) completely?

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