In my experience willpower is less like a muscle and more like a habit. Right now I'm in the habit of working on side projects every day, so it's easy. Since habits come naturally, what once required willpower now requires no willpower at all. Surely there are studies that confirm habitual tasks are easier to perform than non-habitual ones?
I've spent the last few years working on my willpower. No improvement.
Recently I've been creating social pressure to keep habits (agree to do something every day) and the willpower required is 0 and the results are amazing.
When I have someone expecting me to do something I just naturally put in a lot more effort.
Recent comment on this: https://news.ycombinator.com/item?id=22920237 "The effect likely isn't too big, or it would be harder to design experiments where it doesn't show up at all."
I don't suspect that willpower will be something people can measure with any degree of usefulness.
You can personally verify that it is like a muscle by attempting to enhance your own willpower. I'm not trying to sell you on anything, this is just what I've observed in myself.
IIRC: studies have not validated this