Certainly, energy in some form (glucose) is necessary for brain to work. This part is obvious. The question is, how much energy do different brain tasks require. By the way, the brain is doing some work even when I am not thinking, even when I am not using willpower. So the question is, does the brain need more glucose for tasks that require willpower, as opposed to tasks that do not require willpower?
Only if the willpower-related brain tasks need more glucose than willpower-unrelated tasks, only then we can treat the willpower as a limited resource. But if it would happen to be the opposite, if willpower-related and willpower-unrelated tasks need the same energy, then we could take the willpower as unlimited resource (and the glucose as simply the fixed cost of living).
I recently read this book. I've tried to summarize the main points below -- you can read my notes here (MSWord doc). You might also find Derek Sivers' notes useful, which can be found here.
NOTE: The general model of willpower (as a finite resource consumed with use) used in this book does not seem to represent a scientific consensus -- see the comments for more detail.
General Claims
Willpower Depletion
Restoring Willpower
Miscellaneous
I declare Crocker's Rules.
[i] I didn’t see enough evidence to conclude whether the cravings are actually stronger, or people are simply less able to resist them, or both. The book claims that both are true.
[ii] The book seems to imply this mental nagging costs willpower, but I don’t recall it being explicitly stated. GTD is also mentioned, and the lack of Next Actions which one has the materials to execute being included in plans causing people to procrastinate. (p. 79)
[iii] The relevant experiment was conducted in a laboratory, so there is no possibility of the experimental results being affected by the fact that people with more self-control may keep their house cleaner. Self-control was measured in ways like being willing/unwilling to week for a larger sum of money instead of receiving a smaller sum immediately, and choosing healthier foods over sugary snacks.
[iv] I wonder if this means that people are more likely to ignore opportunity costs.
[v] ‘Conserving willpower’ is also mentioned around here, which seemed to imply that effective precommitment helped reduce the willpower costs of overcoming constant temptation by making the decision easier.