I suspect that when you're dealing with the brain there's little difference between physical and psychological: if the brain's hitting a wall physically it will unconsciously invent some explanation. I suspect that's what's happening with these startup founders who think they are working 18 hour days; anecdotally, when I've pushed myself to work 12-14 hour days, I haven't felt unproductive, I suspect my brain just shut down so that it couldn't register all the time I was wasting. If I look at my actual changelist history, I'd find that the first 3 changes of the day would take a total of about 3-4 hours and then the last one would take 7+.
There's been a lot of research done into "ego depletion" - basically, 100+ studies have found evidence that the ability to focus and make yourself get things done is an exhaustible resource, and then recent studies by Carol Dweck have indicated that your abilities to do so, in some sense, depend upon your mindset going in and whether you embrace the task to begin with. The logical place to answer this would be with an fMRI study, and the first such study was just published a week and a half ago. The abstract indicates they found something, but the article itself is paywalled:
NYTimes run an article last year on "ego depletion", focusing on "decision making fatigue". Turns out sugar (M&Ms!) does play an important role in restoring the willpower and ability to make decisions.
If the phenomena was purely psychological, then it might be possible to overcome it. Possibly, rotating the specific task you are working on, or changing locations, or taking shorter but very intensive breaks (like playing street hocky for 30 minutes), might be enough to prevent the brain from switching into despondency mode and allow a few more hours of high productivity. But if the limit is physical, then switching locations or activities won't help much, the brain simply needs to rest (although perhaps a cooling helmet would work - http://www.news-gazette.com/news/health/health-care/2011-03-... - I can't wait for magazine articles with trendy startup engineers at their standing desks all wearing brain cooling headgear).
I think recent science is discovering that even physical problems with the brain can be overcome. Depression is a chemical imbalance in the brain, but talk therapy has been shown to be effective for it. The act of thinking certain thoughts changes the brain's chemistry in ways that can be either positive or negative.
Say that we find that ego depletion comes from a shortage of blood glucose in the brain. If that's the case, the cure could be as simple as stocking the microkitchens with M&Ms (man, maybe Craig Silverstein had the right idea 14 years ago). It's also known that certain stimulants like caffeine and amphetamines help you overcome your normal mental fatigue limits - the problem is that they often tend to create dependency and lose their effect if you chronically overuse them. The reason for looking into the physical mechanism is that we might then be able to find simple solutions that work and don't have long-term side-effects.
There's been a lot of research done into "ego depletion" - basically, 100+ studies have found evidence that the ability to focus and make yourself get things done is an exhaustible resource, and then recent studies by Carol Dweck have indicated that your abilities to do so, in some sense, depend upon your mindset going in and whether you embrace the task to begin with. The logical place to answer this would be with an fMRI study, and the first such study was just published a week and a half ago. The abstract indicates they found something, but the article itself is paywalled:
http://scan.oxfordjournals.org/content/early/2012/09/20/scan...