This is an argument of christian apologists against evolution as well: "evolution can't be true because it violates the 2nd law of thermodynamics". And this superficially apparent conflict has the same resolution: if energy can be put into a system, it absolutely can have less entropy (or more organization, or more specialization) over time.
What are you comparing them to? Sure, we humans can do this in a lab, but in a nucleus, there is only the anti-copy of the other side of the nucleotides. Most eukaryotes just use one of their chromosomes and both are needed for mytosis/myosis. Cells have no way of knowing which copy is the 'correct' one. If there is more than one copy of a DNA strand floating about, cells really do not like this and, in many eukaryotes, will deal with it in a very complicated dance. Prokaryotes/Archea are a wildly different story however.
That's the point. If we would fall for the authors interpretation of the second law of thermodynamics humans couldn't exists, as they wouldn't be able to develop in the first place.
> Either way it'd be an unqualified success.
Certainly. I'm just picking nits on the math.
That is, when the protons are gone, so is chemistry, electronics, and so forth.
Of course lots of protons -- likely the vast majority of them -- will end up in stellar collapse remnants anyway, and in the black hole cases you're also not getting the protons back, whether or not they would eventually have decayed. The rest will be in an extremely tenuous gas and dust far outside the black-hole-dominated remnants of no-longer-star-forming galaxies, and most of that will be neutral hydrogen (and in that case if the proton decays, the residual positive charge will annihilate the electron, so all you have left is light flashing off in several random directions).
"Mining" for new components in the extreme future looks like a losing proposition even without proton decay; with proton decay, you run out of usable material all the sooner.
Entropy always increase in closed systems, but we are not talking about a closed system here.
My understanding is that, from the point of view of physics, there is not a reason for not being possible to decrease entropy in the body increasing entropy outside (expending energy).
Also, this is untrue: "DNA can only be repaired when there is an intact replica to copy".
If you have, for instance, three incorrect copies of a DNA sequence you can compare them in order to get the original sequence. The probability that the copies are damaged at the same point being very small.