The beginning of the Universe was in a state of extreme low entropy, but what exactly does that mean?

No that does not sound reasonable. "Entropy" is a slippery concept.

"...en·tro·py   [en-truh-pee] Show IPA

noun

1.

Thermodynamics .

a.

(on a macroscopic scale) a function of thermodynamic variables, as temperature, pressure, or composition, that is a measure of the energy that is not available for work during a thermodynamic process. A closed system evolves toward a state of maximum entropy.

b.

(in statistical mechanics) a measure of the randomness of the microscopic constituents of a thermodynamic system. Symbol: S

2.

(in data transmission and information theory) a measure of the loss of information in a transmitted signal or message.

3.

(in cosmology) a hypothetical tendency for the universe to attain a state of maximum homogeneity in which all matter is at a uniform temperature (heat death).

4.

a doctrine of inevitable social decline and degeneration. ..."

http://dictionary.reference.com/browse/entropy?s=t

Absolute zero means all molecular and atomic motion has stopped.. Temperature measures molecular and atomic motion, When there is no motion at all. that is low entropy. There was NO MATTER when the Big Bang occurred. The Big bang was PURE energy, low entropy because of HIGH temperature - HIGH energy, NOT molecular or atomic motion. Low entropy at the beginning of the very beginning of the Universe low entropy at the heat death of the Universe, but HIGH entropy when there is Big difference in temperature between the cores of stars and the temperatures of the near vacuum of outer space. . THAT is HIGH entropy. Matter was not created until the universe had expanded enough to AND cooled down enough for energy to convert into matter.

I don't think all your questions are clear or meaningful but I get the gist. Let's see if I can help you clear some of the ideas :

2nd law of thermodynamics says for an isolated system entropy can not decrease with time. so, if we don't get into multi-verse and possible communication between them, we have an isolated universe. since we have no example of 2nd law of thermodynamics being violated among all our observations over wide ranges of temperatures, we believe it holds for universe as a whole too. hence we conclude total entropy of the universe in the past was smaller than it is now.

thermodynamics also tells us that thermal equilibrium is the lowest entry state for a given total energy, also that entropy increases with temperature.

so there are a couple of opposing factor at work here. before inflation, at the very beginning of the Big Bang, universe was extremely hot and extremely uniform. hot => high entropy, uniform/equilibrium => low entropy. whatever the balance, as long as total entropy is less than what we have now, we are fine with our present understanding of thermodynamics.

after inflation, universe cools rapidly and it becomes clumpy (structure formation, stars, galaxies, clusters and thermal equilibrium breaks down locally). now, cooling => lowers entropy, out-of-thermal-equilibirum => increases entropy (black-holes are the highest entropy state of a given mass), again two opposing factors. I am not an expert and there are ambiguities in the arguments, but as long as the increase of entropy due to structure formation (effect of gravity, in essence ... remember usually we think of statistical systems of much smaller size like a bunch of molecules where gravity is not important .... not so here) makes up for the deficit of decrease of entropy due to cooling, we'll have a present day universe with more entropy than it had in the past ... and we are fine.

your statement about universe inflating into an environment 'already at absolute zero' is quite wrong/meaningless ... there was not such thing 'already at absolute zero' ... universe is an isolated system, it expanded rapidly and it cooled ... and not even then at absolute zero ... average temp ~ 3 Kelvin

You have answered your question without realizing it !!

You said, "The highest-entropy state is one in which the temperature is uniformly the same throughout."

It does not matter what the temperate of space is.

What matters, is only that the energy is expanding.

As it expands it cools.

It is that simple.

And originally the expansion was from a very high temperature.

As the expansion continues, the temperature falls.

So there is less temperature gradient.

You are starting to think like a Cosmologist now...

Allow me to help you understand, what leads you to believe that the inflation was expanding in to absolute zero... I'm gonna leave that alone for now.

At time = 10^-32sec when the Strong Force separated the inflation occurred,. Inflating the universe (in seconds) to beyond our visible horizon (billions of light years).

Toady the current excepted theory is that Dark energy is the kinetic energy from this expansion, This leads to a problem when judging the size of the universe because when you add up the math, it would be like describing our visible horizon (the cosmic microwave background) to a atom in size as a atom would be to our Visible Horizon in size for the true size of the expanding universe.

Also when understanding the initial inflation (separation of the strong force) one would need to understand that the weak force was still one with electromagnetic force. this would seem to imply that a photon would not loses its "energy"/MeV due to decay from the W or Z bosons, also having a adverse effect or unknown effect as far a entropy as we know it.

Gravity also plays a roll in this but I could write for ever when it come to this and we wouldn't of even scratched surface.

Hope this helps a little, Star for you.

<QUOTE>a state of extreme low entropy, but what exactly does that mean?</QUOTE>

It means that the number of accessible configurations (how many combinations of single-particle states produce the system's overall state) is extremely low.