Greg is clearly brain damaged, we know that selectively damaging certain areas of the brain causes drastic and "interesting" changes in behaviour. For example damage to area 24 of the anterior cingulate cortex can divorce people from their normal emotional responses to being in pain; they still feel pain normally but they don't get upset by it or feel the need to stop it happening. The effect you're looking for is unlikely to be attainable through a single piece of brain damage and will probably mean extensive damage to many separate areas of his brain. Such damage may occur due to disease but it's more likely that someone deliberately damaged Greg's brain through surgical intervention.

Greg has more 'volition' in his head

A relatively famous study from Baumeister, et al., 1998. The study concerns ego depletion, which is

temporary reduction in the self's capacity or willingness to engage
in volitional action (including controlling the environment,
controlling the self, making choices, and initiating action) caused by
prior exercise of volition.

Please note that volition is the expenditure of willpower on some task.

The money quote:

Taken together, these four studies point toward a broad pattern of ego
depletion. In each of them, an initial act of volition was followed by
a decrement in some other sphere of volition.

Now we can see 'volition' as a finite pool of willpower that you have in your head/psyche.

So, let us assume that there exists a physical manifestation of volition. Some set of neurons, some chemical component, something, it doesn't really matter what it is. Greg has more of it than you do.

How does Greg have more?

If volition is a physical resource, then there are two possible ways to explain how Greg has an infinite amount of it. Either, Greg 'regenerates' volition faster than other people, faster than he can expend it; or Greg 'burns' volition at a slower rate than other people, less quickly than it is regenerated. Or, both can be true.

I started this as a comment, but then it developed into an oblique answer to the question, so I'm posting it as such:

Everyone has unlimited willpower. Most choose not to exercise it.

Also: No skeptic can have it proven to them that Greg has unlimited willpower. Because he can simply decide that convincing some silly skeptic is not worth his time. Unless his "super power" is the inability to change his mind, rather than the ability to not change his mind—in which case I'd argue that is a handicap, not a super power.

However, let's explore this further: Is it possible for Greg to try to convince others that he is addicted, or that he can't break a bad habit, or that he doesn't have a choice?

Of course it is. And it provides such an easy excuse. He chooses some course of action, and someone else doesn't like it. So he apologizes and says, "Sorry, that's a bad habit I have...I'll try really hard not to do it again." And then he keeps doing it. He is perfectly capable of ceasing the bad habit at any time, but he chose this course of action, so of course he can just continue it.

Calling it a "bad habit" is a way of escaping domination by others. Since he apparently can't stop his bad habit, they probably wouldn't even bother torturing him to try to get him to. (Well, actually, people are sometimes tortured for bad habits under the heading of "aversion therapy," such as at the Rotenberg Center, but note that the "bad habit" i.e. the decision wouldn't be changed or cured by mere torture.) He could just keep on with his selected course of action forever under the guise of it being a "bad habit" or an "obsession" or what have you.

Honestly, the real question is:

How could anyone differentiate Greg from anyone else?

You mention he could do a physical exercise without stopping no matter the pain, so long as he's physically capable. There are such people.

He could also stop the exercise any time by his own free choice. And he could claim that "the pain was too bad." But he actually could have continued, he just chose to stop. This sounds like most people.

People take 12-year degrees in subjects they aren't particularly interested in, or spend decades-long careers doing mind-numbingly dull tasks.

Take any course of action you can imagine Greg doing, and you'll be able to find people who DO take or HAVE taken that course of action.

So, again, if you reinterpret your question as a hypothesis that "everyone has unlimited willpower" you will be 100% unable to find a counter-example. It's literally not falsifiable. According to Popper that makes it unscientific, but it's sure an interesting stance to take.

(Notably, it's also not falsifiable, and is therefore just as unscientific, to claim that there exists a person whose willpower is limited—we've just all socially agreed to accept that willpower is limited as a matter of course. That way, we can hold on to our own bad habits.) ;)

As for him being super fit, super intelligent, a super capable leader—perhaps. But it's also just as likely that he would not be, in order to win an argument.

John: We're making you the head of research because we know you're smart enough.

Greg: I don't want the position.

John: We're appointing you anyway. Don't pretend.

Greg: I'm not smart enough. I'm not capable of handling that post. I don't want it!

John: Shut up and take it.

Greg: Spends the next 50 years proving he is stupid and that John was wrong to give him this appointment.

Spending 50 years to prove someone wrong and to win an argument is an easy consequence of having unlimited willpower.

TL;DR: Greg's subconscious is weak, or is under control of the conscious mind.

@kingledion is correct in pointing you to Baumeister's research.
There is more in his popular-science book: https://www.amazon.com/Willpower-Rediscovering-Greatest-Human-Strength/dp/0143122231

Here are couple more books:
https://www.amazon.com/Nudge-Improving-Decisions-Health-Happiness/dp/014311526X/
https://www.amazon.com/Thinking-Fast-Slow-Daniel-Kahneman/dp/0374533555/

It was a while since I read them, but I have an idea based on what I do remember.

Impulsive and addictive behaviors happen b/c they release dopamine into the brain. Dopamine tells the brain "you are doing the right thing", and make the person feel good about themselves. What releases the dopamine is the sub-conscious part of the mind. It evolved to encouraged a person to do things that improve chances of survival despite no immediate benefit: e.g. social interactions mean you are part of tribe and will have easier time surviving, and finding food when you are not hungry means you are less likely to go hungry later. In modern society, these instincts power addictions: to sex and social media make your subconscious think you are part of a tribe, and gambling or videogames make you feel you are collecting valuable resources.

But Greg got over it. Either his subconscious does not release dopamine at all, or he learned to suppress/control/redirect his subconscious instincts. "No dopamine" might be causes by genetic mutation, radiation, or physical trauma, and it might have nasty side effects: https://en.wikipedia.org/wiki/Dopamine

Edit (thanks to RToyo for suggestion): I should have said "no dopamine from satisfying subconscious cravings". He can still get dopamine from the events that his conscious/logical mind views as good.

Weakened subconscious could be results of psychological trauma or abuse: all social and random events are negative; the only positive outcomes come from his own thinking and control. Control over subconscious can be learned (see the books). One trick is to associate unwanted behavior with negative feelings, e.g. if your body starts craving a drug, think about drug addicts and how disgusting they are. And then redirect your dopamine craving to exercise, which releases dopamine directly ("runner's high"), and lets you daydream about how strong and muscular you will be. The cost of doing this is slower thinking (subconscious is fast), less happiness, and more stress. You can have Greg go berserk occasionally.

Finally, if you want to get more sci-fi'ish, you can have Greg directly control dopamine release, and time it with things he considers a successes. Or he was a subject in a program that did that.

PS I should take some of my own advice and break my addiction to WorldBuilding.SE :)

"Infinite" is not a word that should be thrown about. It's the kind of word that initially leads to questions like "Can Greg stop the progress of entropy with will power alone?" and progresses onward towards questions like "Can Greg overthrow God" or similar questions tailored to your religion of choice.

If we sidestep "infinite" and just look at people with really strong willpower, there are examples of people who do what you say. The top of that scale consists of people whose willpower is so strong that they will spend their entire lives pursuing something, and when they die you get the distinct impression that they're not yet done pursuing it. Indeed, this will actually be critical for constructing Greg. If Greg spends most of his efforts on something that he can achieve within his lifetime, he will rapidly turn out to not be so average. He needs to be looking one step beyond his own life to appear average to the unaided eye.

The Eastern cultures have characters such as these in plenty. You see them in the Western cultures too, but in the West we tend to recognize that which the person did accomplish rather than what they strove towards, so we don't raise them on the same pedestal.

An example I remember reading about was a yogi that had completely mastered his startle reflex. Startle reflex is the jerking motion we make when surprised, such as when a loud noise goes off near us. It is preparing for the unknown assailant. There was a researcher who was looking into this reflex. He had put together an audio device that played a sound like a gunshot. From testing it on police and military and others, he had found that it was loud enough and unexpected enough that everybody startled. So he went out to find people who might not be startled. He went to Nepal and was directed to a yogi who lived in the mountains. The yogi agreed to be tested, put the headphones on, and listened. When the sound went off, the yogi didn't flinch at all. He simply smiled. When asked to describe it, he described the sound as "clear as a bell."

I say the West doesn't put these people on the same pedestal, but there are cases where we do. You mention resisting torture, and that's one case where we do appreciate it. If you look back through religious history, you'll found countless souls tortured to death for their beliefs. They had enough willpower to face torture and death -- it is hard to argue there's a higher level of willpower than that.

A common pattern I see in such characters is that they all have the "never move backwards" mentality. They may approach their goal very slowly, limited by things such as their frail and aging body, but they never move away from their goal. They're constantly rolling and sliding and finding every which way to take one step closer to their goal. Never back. A word I have been given for this is "yielding," and the phrasing I have been given for it it is "yielding is using your opponent's force to move you to a better position."

I do believe this yielding pattern is crucial for a character like Greg. Willpower on its own doesn't cause anything to happen, unless it is coordinated with the movement of the world around you. When you are opposing the world, it is essential that you not lose ground, and you simply wait for the opportune moment.

I also notice characters such as this have a very fluid concept of waiting for the opportune moment. They don't wait for the seas to part and put their goal in sight. They're constantly maneuvering with every cell in their body, trying to find a better position. In martial arts, they're not waiting for me to lose balance. They're waiting for my wrist to be slightly out of position, and then they jump on that mistake just enough to let them apply their willpower towards my elbow. If I keep control of my elbow, but lose control of my shoulder, they wont sit back and wait for me to lose the elbow. They'll happily jump one step closer to their goal without caring which step I presented to them.

Daring to use a well trodden meme, sending Greg to a monastery that specializes in such growth would be the easiest to write way to accomplish this. The Shaolin Monks are famous for their brutal training which instills an amazing amount of willpower. They depend heavily, of course, on the wisdom and practice of the monks before them, which must apply this brutal training regimen not merely to apply it, but with the willpower required to shape a soul with the training.

But you don't have to go that far. All you need is the mysterious mentor who just seems to put you on the right path. We can find it in fiction books such as Richard Bach's "Illusions." We can also find it all over in reality once we realize we can look for it. You can find it in some celebrity rappers and how they try to raise the next generation of rappers. You can find it in the coach who spends their time at the YMCA trying to keep children off the streets. You can find it in a chess coach who treats chess not as a game, but as a lesson in how to approach life.

You can find it in the lifelong pursuit of many fathers, as they strive to raise their child as best as they possibly can. And you will find it in every mother -- it's simply a rule. That's how being a mom works.

You need look no further than normal humans. What you describe is already a natural part of humanity.

Your own examples

• withstand any amount of torture

We will have few examples of this to cite since torture generally is not publically documented. However, we have historical examples of this. Religious martyrs are an obvious one. Other martyrs as well: Braveheart was based on real events, but I'm not sure if the scene at the end is real or not where he is being tortured to denounce the defense against the English occupation and he refuses to do so, shouting "freedom!" instead.

• exercise until collapse

This is known to happen often. In fact, I have nearly done this myself. I have stopped myself when it has become difficult to stand, but I decided to stop since continued activity would not be beneficial. I could have kept going if I decided that there was some good reason to do so.

Article: "Why Do So many Triathletes Collapse Just Before the Finish Line?"

• refrain eating until fainting

People have done more than this; people have refrained from eating until they died, or refrained from eating until someone else force-fed them (and still resisted this force feeding). This is often done as a form of protest.

Cite for lots of people hunger striking until they died: Irish Hunger Strike

• hold breath until passing out

This is difficult for many people to do, but I have read it's not because of a lack of willpower, but rather because breathing is not entirely under conscious control. You can prove this to yourself by doing something else so that you are not thinking about breathing and then notice that you still keep breathing sub-consciously.

This is also another one that I have personal experience with as well. When I was younger, I wanted to be able to hold my breath for a long time, both to help with underwater swimming and as an impressive party trick. It did not take much practice to realize I could hold it a lot longer than I thought I could.

I never did it until I passed out, but again, when I stopped it was because I feared I was doing damage to my body. I once held my breath until the people watching told me that my skin was changing color and darkening. I held it a bit more but then let it out because the viewers were concerned for my health. I started to have the same concern and so stopped by choice.

Usually, I was not timed. One time I was timed at about 4 or 5 minutes, but that was not my best breath-hold, not by far. Since my longest holds were longer than that (but of unknown exact duration), we can assume that I was probably close to passing out. I do not consider that super-human, and I assume that there are a lot of other people that can do it (albeit a small fraction of the overall population).

However, if I was stopped from holding my breath before I actually did pass out, it would not be because of a lack of will power, but rather would be a biological process known as an "involuntary muscle movement". Moving your finger is known as a "voluntary" movement, while heart beats are involuntary. Breathing has aspects of both, so some people claim it impossible to hold your breath until passing out not due to lack of will power but rather due to the involuntary aspect of breathing.

Other examples

• 
  Aron Ralston cut off his own arm with a dull knife to save his life after a boulder pinned him in place

You might argue that is not will power since he had to do it to save his life. However, most people would not do it, and many others have died rather than do such gruesome things. I would say it counts as a mountain of willpower.

• Emergency responders

In order to save other people, heroes have walked into burning buildings and searched for others until they have died trying to save them.

Many police have rushed into situations where they put themselves knowingly in great danger of injury or death.

Some personal security agents have made a conscious choice to sacrifice themselves for another person.

Others have had their security roles (whether professional, or otherwise [love, etc.]) put to the test and shown that they would sacrifice themselves for another.

Summary

It seems that humans have demonstrated that a small fraction of them actually have the power that you describe, or at least close enough that they do the types of activities that you mention and worse.

Because there are so many humans around, that small fraction of the populace who practically do have the power you describe is actually a rather large number of people.

Many of these people have not induced this power by drugs, nor by brain damage. They are healthy, happy, not diseased (in that manner, anyway), and are normal humans who possess this ability.

Greg's friend is Willy

Greg indeed have a very powerful willforce. So powerful that it deserves a name. Lets call him Willy!

Willy is Greg's imaginary friend (and sometimes not-so-friendly). Greg literally sees Willy around all the time. Wherever he go, whatever he does, Willy is with Greg. However, although Willy is imaginary, Greg has very vivid hallucinations about him.

Willy however, is extremely bossy, manipulative, selfish, sadistic and cruel. Say that Greg is too tired to keep running and is thinking about stopping for five minutes. Then Willy will react with violence and severely hurt Greg. Although the hurting is imaginary, Greg feels severe pain from that.

So, let's suppose that Greg is being tortured to be induced into saying something. Greg will actually feel the torture at least doubled, because Willy would also be torturing Greg to a greater extent to make him not say anything.

If Greg needs to study calculus and is tired from that, whenever Gregs put the eyes out of the book due to tiredness without a very good reason for doing that, Greg will see Willy punching his face and actually feel all the pain from that. Going back to the book makes the pain immediatelly disappears and makes Willy happy!

However, although cruel and violent, Willy is always working hard to ensure that Greg is focused into reaching his objectives, so he is friendly afterall.

Greg do not talks directly to Willy, because Willy seems to be able to read his mind (in fact, he is part of his mind). Also, Greg is intelligent and acknowledges that Willy is imaginary, so he won't present him to somebody else. In fact, he is unlikely to be able to mention anything about Willy to somebody else because Willy wants Greg to be sucessful and most people won't be successful if they talk seriously about their imaginary friends to other people. This means that it is very unlikely that other people acknowledges that Greg's features an imaginary friend and everybody will perceive him as an extremely determined person.

But in fact, Greg is a severe paranoid schizophrenic person.

Another way of looking at this would be to have Greg possess the ability to truly calculate costs and benefits, relative to his own personal situation - in the way that some people have "perfect pitch" relative to sound.

Willpower is generally seen as required to undertake some action that benefits you or is of use to you, but is unpleasant in the short term. When you experience a "failure of willpower", it's because you are overvaluing the short term unpleasantness and undervaluing the longer term benefit. If you simply never did that, you would not need what we call "willpower".

This would grant Greg the ability to perform the feats used in your examples, but only in specific situations. He would be able to exercise until overcome by physical exhaustion, but only if it made sense for him to do so from a cost/benefit perspective. (Perhaps he would do this to win a bet, but not merely to prove that he could?)

Perhaps Greg is overly sensitive to adrenaline affects, even when compared to an Adrenalin Junky. This would create both a condition where he could will himself through anything as the small release of adrenaline from motivating himself would result in a stronger drive to stay on target or keep it in. Since he can get more response out of smaller amounts, it isn't that he's immune to dopamine, but that dopamine release by adrenaline (which is where the Junky aspect comes in) would not occur and he'd be less likely to become addicted to reckless behavior. In fact, he'd be prone to some incredible feats of strength compared to base line humans because adrenaline is linked to hysterical strength (the term for a phenomena where a life and death situation would cause people to show incredible feats of strength that they ordinarily couldn't achieve. The typical story is of a mother being able to lift a car off her son, who was pinned under it).

This also comes with a down side and it would be one he would have to be aware of and mindful of: a state of hysterical strength is an emergency override of a biological safety feature... think of it as a natural strength limiter so we don't hurt ourselves. Running at constant hysterical strength level would actually do a lot of physical damage to the human body... just like red lining a car would actually start to be detrimental to the engine. So Greg's feat of strength could actually do a lot of damage to himself if he was in a big superhero fight for a long period of time.

If he is overly sensitive to Adrenaline, than introducing any level of stress to Greg will actually start to put him in a red-line state. He would need to take a lot of the same precautions Bruce Banner does to stay calm for a very similar reason... just when Greg gets angry, he doesn't go green.

Another thing is that the Hysterical Strength level is also a "heat of the moment" response... basically the person exhibiting the feat isn't trying to... they are so hyperfocused on the task of saving their buddy that they don't realize they are actually successful in lifting the car. This could put Greg into a "beserker state" where his will is so targeted at the task, he effectively loses situational awareness, opening him up to some really bone-headed sneak attacks or possible endangerment of partners. If you watch any cop show, this kind of behavior is followed up by a scene where Da Chief reads the cop Da Rules and asks for his badge and his gun and tosses him off the case. And for good reason, as detective work requires emotional checks... you may violate some rules that are there for good reasons because of the emotional investment you put into it.

Too anyone Greg has to work with on a superhero team (and he seems more suited for Super-Teams than Solo work. Superman he ain't), Greg is going to have difficulty getting along well with a leader barking orders without understanding that Greg is a sledgehammer, not a scaple. For maximum drama, there could be someone else on the team who gets what's going on and would have to defend Greg when his hyper-focus messes up. Heck, Greg will need to employ every distress technique he has to keep from putting team leader through a wall.

Additionally, Greg could get some humor and bizarre conflicts as a minor issue as well. Since he is always hyperfocused on the task, there could be a scene where Greg is walking through the Halls of Justice in a Tartan Kilt and hat (wearing everything a Scottish man does under the Kilt). When question on why he's doing this, he'd give a quick response of "Decided to learn to play the Bag-Pipes Today," and leave as if that satisfies the question (Which it doesn't). And then the team has a miserable day at the Halls of Justice because Bagpipes are not indoor instruments and no one can tell if he's really good or really bad at any given moment.

Greg is the opposite of ADHD. Greg's brain produces an abundance of dopamine while concentrating.

Dopamine is a neurotransmitter that is responsible for a whole lot of things in the brain. It is perhaps most famous as a "pleasure and reward" inducing neurotransmitter that drugs like marijuana and cocaine stimulate, but it is key for all sorts of things, from attention to learning. Until a few years ago, it was pretty well agreed that, in simple terms, ADHD behavior was linked to reduced levels of dopamine in certain areas of the brain. I won't get into the details, but the over-simplified/partially-wrong idea is that a lack of dopamine makes the current task uninteresting/unenjoyable/understimulating, so your brain seeks out other stimulation.

If you start with the (somewhat incorrect) view that ADHD is a lack of willpower, and your goal as a writer is to come up with a way to increase willpower, then increasing dopamine levels in the brain may be a way to induce more willpower. In fact, that's what ADHD medication does - amphetamine-containing drugs like Adderall and Ritalin increase dopamine levels in the brain. You could then make the hand-waving jump to the explanation that when Greg concentrates on what he is doing, his brain begins releasing more dopamine to key regions throughout the brain, such as into the limbic system where it will help Greg focus, and increase the brain's sense of reward for doing whatever he is or is not doing, allowing him to continue what he has set his mind to, and reinforcing any habits.

Personal thoughts:

Personally, I would not try to root this "power" on science. The brain is incredibly complex, and there are so many different (and competing) reasons for any given behavior or motivation (such as the willpower to diet vs the willpower to read a textbook), that trying to root it in biology would result in a completely different brain and nervous system than what a human has, and it would make Greg pretty non-functional.

More directly, the concept of "willpower" does not translate to things that are controlled by the autonomic nervous system (such as breathing, hunger, or tiredness), nor is consciousness itself a good way to monitor willpower (your brain brings many things to your conscious attention, but the decision has been made long before it reaches your conscious thought). It's similar to someone having psychic powers - you're better off just coming up with a hand waving/sci-fi explanation, than to try and root it in hard science.

Some common disorders you could research:

• ADHD is a good disorder to research for "attention" willpower.


• OCD is a good disorder to research for the brain overriding willpower through intrusive conscious thoughts.


• Addiction is a good disorder to research for how the brain hijacks survival areas of the brain to motivate behaviors "below" conscious thought.


• Autism has a very broad array of symptoms, but it may help understand why a person is able to maintain interest.


• Bipolar disorder, specifically the manic symptoms, is a good demonstration of why too much dopamine in the brain is NOT a good thing.

What is Willpower Really?

We don't say we are exercising willpower when the choice is easy or obvious. In an election of reactions to some stimulus, when a weaker idea wins out over some of the stronger ones, that is when we usually say that willpower is being exercised.

What is Suppression Neurologically?

There is evidence in the brain the some neurons suppress the behavior of their neighbors. The brain slowing down it's own reaction seems to allow things such as depth perception and better pattern recognition.

This demonstrates the the brain has the ability to learn to still feel the impulse to respond to a stimulus while, nevertheless, not allowing that "learned-not-to-do" impulse to reach the final decision-making layer of how the brain processes a problem.

Surround suppression lingers longer than an immediate signal. This is indicated by changes to visual responses being held back for longer than a single time slice. At this point I can not point to published research (this is my own idea) - I believe if you are exposed to a great deal of need for suppression (a lot of tough choices over the course of a day) your brain ends up incrementally suppressing more and more of itself until there is some downtime for the system to reset. This would mirror the "erosion of ego" over the day that kingledion referenced in his great answer (from Baumeister, et al., 1998.).

We also tend to ruminate - going over the same situation in our head long after the decision has been made - which would mean the brain has to suppress those other ideas for a longer period of time. Rumination is part of the brain's process to reconcile new experiences with the whole so that we learn. However, it likely requires prolonged suppression by those neurons to keep us from rushing back to reverse or reconsider our earlier tough call.

How Could Greg Be Different?

Greg could possess an overabundance of whatever chemical or process ends surround suppression. As a result, there is probably some threshold at which enough tough decisions start to pull Greg down, but that amount is much higher than a normal human could hope for. He would recover from the drag of tough decisions much more quickly. He might not be doped up on hormones, or damaged by a lack of empathy. Instead, he might be encountering each difficulty with a clear head, but just not dragged down by it.

Greg is a robot, or perhaps a cyborg. He does exactly what he is programmed to do, and is not subject to temptation or distraction, or self-preservation instincts.