One of the problems with some of these conversations is that imprecise use of terms leads to incorrect understandings. This is particularly true with concepts that are more abstract, like entropy.Really? In light of this quote from Dr. Styer: I would have figured you could forgive me the layman's transfer of terms... you know what I meant.
Since I cannot see the numbers, just let me know if this is true: Styer measures the amount of entropy required for evolution and it turns out the sun is more than adequate to provide this increase. Does that pretty much sum it up?
With that proviso, let me address your evolution – energy question.
How much energy has to be available for evolution to occur?
Simple case – envision a really simple, yet alive, and reproducing, single-celled organism. Now if some mild DNA change occurs, that organism can exist in environments where it could not have before – more tolerant of the destructive effects of sunlight, or able to metabolize some new nutrient, or a limited amount of new mobility, or whatever. Evolution.
How much energy is required for that? Well, if I light a match and hold the flame directly under my palm, I am very quickly and painfully aware that the energy in that modest flame is sufficient to destroy, and even vaporize, literally hundreds of my skin and nerve cells every second. If that match flame has enough energy to totally rip cells by the hundreds apart (breaking literally millions of atomic bonds in each cell), then do you think that might be enough energy to rearrange a couple of atomic bonds in a single strand of DNA in that single-celled creature?
Now remember that in big animals (like me) evolution is initially just the change in a single germ cell that will mature to become another “me”. So for me to have kids that are evolutionarily different from me involves not much more energy than the change in that single celled creature.
Yeah, the sun is ‘nuff. The simple availability of energy is not the issue.
(But this is apart from entropy. You asked about the “amount of entropy required”. Entropy is not a quantity that you store on a shelf, like energy. No object has 10 “units” of entropy.)