@Olivier5,
Olivier5 wrote:How do you propose to estimate the entropy delta of the solar system as a whole between two arbitrary dates, say between 5 billion years ago and now, since life did not exist 5 billion years ago.
First of all, my original point was that this is difficult. So if I couldn't do it at all, in spite of being a physicist making an honest effort, that would support my original point rather than contradict it.
Second, I needn't know how to cook soup in order to tell that the soup in my cup tastes rotten, or that my cup doesn't even contain any soup for me to taste. Correspondingly, even if I had absolutely no idea how to run this calculation, it wouldn't change the fact that you have not put forward a coherent argument.
All that being said, here is an outline of how I would do it:
1) Calculate the marginal increase in enthropy (dS) that a given marginal amount of energy created by nuclear fusion (dQ) generates in the sun, given the sun's temperature Ts. To do that, use the (differential) version of the macroscopic definition of enthropy.
dS = 1/Ts dQ,
2) For purposes of testing if life on Earth violates the Second Law, the relevant closed system consists of Earth and the part of the sun that generates all light reaching Earth, but no more. As you pointed out in an earlier post, this fraction is very small. So, calculate the amount of energy the sun sends in the Earth's direction, divide it by the amount of energy the sun sends in every direction, and multiply this tiny quotient by the amount of energy you found in step #1.
3) It is hard to measure the amount of entropy that life subtracts from the closed system I described in step #2. (The term "life" is sort of vague for purposes of physics.) But we could estimate an upper limit from the amount of chemical energy created Earth-wide by photosynthesis. (It's an upper limit because everything life does after photosynthesis consists of exothermic chemical reactions that increase entropy.) Again, we would use the macroscopic definition of entropy to do it:
dS = Te * dQ,
where Te is the temperature on Earth and dQ is the amount of chemical energy generated on Earth by photosynthesis.
It would take some more research, and perhaps some more back-of-the-envelope calculations, to get all the numbers that go into these formulas. But in the end, you would have two numbers with matching units that you can compare. On the left side, you'd have the product of steps #1 and #2; on the right side, you'd have the result of step #3. If the left side is greater, the creationists' Second-Law challenge is rebutted.