Indeed, willpower and working memory are both strongly mediated by the dorsolateral prefontal cortex, so “distraction” could just be the two functions funging against one another. To use the terms of Stanovich popularized by Kahneman in Thinking: Fast and Slow, “System 2” can only override so many “System 1″ defaults at any given moment.
So what’s going on when people say “willpower depletion”? I’m not sure, but even if willpower depletion is not a thing, the following distracting phenomena clearly are:
Thirst
Hunger
Sleepiness
Physical fatigue (like from running)
Physical discomfort (like from sitting)
That specific-other-thing you want to do
Anxiety about willpower depletion
Indignation at being asked for too much by bosses, partners, or experimenters...
… and “willpower depletion” might be nothing more than mental distraction by one of these processes. Perhaps it really is better to think of willpower as power (a rate) than energy (a resource).
If that’s true, then figuring out what processes might be distracting us might be much more useful than saying “I’m out of willpower” and giving up. Maybe try having a sip of water or a bit of food if your diet permits it. Maybe try reading lying down to see if you get nap-ish. Maybe set a timer to remind you to call that friend you keep thinking about.
The last two bullets,
Anxiety about willpower depletion
Indignation at being asked for too much by bosses, partners, or experimenters...
are also enough to explain why being told willpower depletion isn’t a thing might reduce the effects typically attributed to it: we might simply be less distracted by anxiety or indignation about doing “too much” willpower-intensive work in a short period of time.
Of course, any speculation about how human minds work in general is prone to the “typical mind fallacy”. Maybe my willpower is depletable and yours isn’t. But then that wouldn’t explain why you can cause people to exhibit less willpower depletion by suggesting otherwise. But then again, most published research findings are false. But then again the research on the DLPFC and working memory seems relatively old and well established, and distraction is clearly a thing...
All in all, more of my chips are falling on the hypothesis that willpower “depletion” is often just willpower distraction, and that finding and addressing those distractions is probably a better a strategy than avoiding activities altogether in order to “conserve willpower”.
Note sure if you consider this a relevant answer, but previously Critch had argued that willpower seemed distractible.
I definitely consider this a relevant answer.