To replenish my willpower, i watch a lot of TEDx conferences about positivity, mindset, success and ways of working and i write down what i've learned after each conference and i think about it. Also, when i just can't begin to work, i go outside for a long run with motivating music or i do some yoga. To sum up, you just have to create your own motivation/willpower rituals, just observe your way of living and the things that motivate you and try to use them as a tool to replenish your willpower.

For me, the best way to replenish willpower is a long solitary walk. 2 hours, 5 kilometers or longer, preferably in nature or a non-crowded park, with minimized exposure to cars, dogs, people, speech, loud sounds, and any other attention-taxing things. I've been going on these walks for over 20 years, so the technique is time-tested.

Also: mini-vacations. Basically the same as above, but they should provide at least a week-long period of uninterruptible time ahead. This works wonders for me.

I've read (I can't remember where) that completing difficult tasks gives a boost to willpower, but then how do you convince yourself to start that difficult task? And what difficult task do you use?

In my case, the concepts of Trivial Inconvenience and Trivial Impetus were very helpful. I soften difficult tasks up by removing trivial inconveniences standing between me and the task, and facilitate my future work on them by creating trivial impetuses. Breaking a big monolithic task into smaller chunks also works well.

Seems to me that the "willpower depletion" happens when some part of a brain decides that continuing the work is no longer the best action. That can happen for various reasons, so the strategy to "replenish willpower" should reflect the specific reason. For example:

If you feel tired, hungry, or need to visit the bathroom -- do what your body needs. (This assumes you are genuinely hungry, not merely using food as an excuse to avoid something unpleasant.)

If you feel uncertain whether you are progressing correctly -- try to get some feedback. (Again, assuming that uncertainty is the real problem.)

If you feel lack of motivation -- try to remind yourself, in near mode, why are you doing this.

Essentially, try solving the problem you actually have, instead of trying to find a universal solution for all kinds of problems. (Eating sugar is not a solution for depression; chanting motivational slogans is not a replacement for missing data.)

I eat or drink something sugary and for me this seams to work. I think the theory that glucose is somehow involved in keeping you motivated has been shown to be wrong though, so i think this is probably just some sort of conditioning on my side.

Caution is advised.

I simply don't know. I ask myself this question everytime I notice someone seems depressed and in want to do something meaningful. It just seems to arrive. In the case of personal projects, sometimes I simply get an idea, get excited about it and start working on it immediately. As the project takes shape I keep on getting excited wanting to improve it, maybe in search of a certain goal like feedback and recognition. I once worked on an editor for months, polished it a lot, for some reason I lost the code to it. After a while when remembering how much I liked that project I started feeling terrible, I still had an older version of the code and part of me wanted to restore it. I debated myself for days, argued with ideas of how it just wasn't worth it, but somehow I found the willpower to do it. Maybe it's like a rational decision, you decide it's the best way to go and do it. So it's not entirely controllable as you can't genuinely force your convictions and especially not all the outside stimuli that shape your thoughts.

One reason for the problems with the "willpower depletion" theory is that people think it should work like a gas tank. As long as you have gas, you can drive. When it runs out, your car stops, and that's it.

Obviously, willpower does not work like that, and it would be bad if it did. If it did, you would feel normally and do whatever you wanted, until you ran out, when you would suddenly lose all control.

Now the gas analogy is not totally false, and there are people who do run into a point like that, just like you can run and run until you literally fall to the ground. But that's not what normally happens, either with running, or with will power.

Instead, you get lots of warning signals when your willpower is running low, and therefore your brain starts telling you to conserve willpower by avoiding activities that seem especially unnecessary or especially difficult.

It also tends to work a bit like money. Money does not work like gas. How many people do you know who literally run out of money, so that they can't spend a single cent more? Not many. Instead, people become less willing to spend money as they have less left. Similarly, if you are planning to spending $300 on a party for your friends, you might do so fairly easily, but if you go out for dinner with your friends without planning on that, and suddenly they ask you to pay for it, that might be a bit upsetting. In a similar way, if you are planning to work Mon-Fri, it may be easy enough to do so. But if your boss calls you up and tells you that you have to work on the weekend, that might be a bit upsetting, in a similar way.

Basically, it is just really complicated and people who expect to confirm willpower depletion by simplistic testing are just doing it wrong. But it does work like a quantity, and as gwern says, lots of different things will tend to build it up, generally things you feel like doing, so which aren't using up as much willpower.

Usually I don't view willpower as a resource, and instead think of not doing something as a bug in my doing-something procedure, that I need to fix by something that wouldn't make sense from the willpower-as-a-resource perspective, like working with another person or making my planned schedule better.

But sometimes I just feel really wiped out and like I can't do anything, and then I usually just read or browse the internet for as long as I feel like. Eating refined starches is sometimes good too.