Oh, tiredness due to knowledge work is real, and relatively easily explained: you spend energy (real, physical energy - calories) on computation in your brain. Whether you're learning at school, designing bridges, driving, or what have you, there are measurable outcomes of your work.

But there is no obvious relationship between this and the concept of "expending mental energy" on combating your cravings. It's not at all clear that there is any measurable "effort" involved in not doing something like eating a sweet. Chess masters consume more calories during a tournament. People who avoid eating cake at a birthday party don't.

And yes, I have of course experienced the difficulty with not giving in to a craving. But I'm not at all convinced that it is the same thing as the difficulty of taking a math exam. If anything, my experience is that it's easier to control my cravings after accomplishing a difficult mental task then it is if I've just idly been watching TV all day.