These two fall into the awful pop-sci writing category:
“And it seems that more productive—and, consequently, better-paid—workers put in less time at the office”
“So maybe we should be more self-critical about how much we work. Working less may make us more productive.”
This points out that the average worker in Greece works more hours than the average worker in Germany.
These are clearly confusing correlation with causation, and I doubt very much that any of the actual researchers involved, as opposed to op-ed writers, would even imply that if only the workers in Greece would ease up a bit, they would get the productivity of Germany. Would you make that statement?
This one covers a lot of actual research, but mostly on the relationship between overtime and worker health and safety:
I don’t find much to argue with here. I don’t dispute the premise that working very long hours can have a health impact in some cases.
It was interesting to see the clear step function in the leading graph of average annual work hours by country with the US at ~1850 as the highest of the mostly-western countries, but Thailand, Hong Kong, and South Korea in a distinctly different class, topping out at ~2450 for South Korea. That made me smile, because one of the Samsung people we work with referred to us at the Oculus Dallas office as “honorary Koreans” because of how hard we work. I do note that the chart in the Economist link with more recent data has them still at the top, but down to ~2100 hours in 2012.
A couple interesting (unrelated) counterpoints from the studies:
Sokejima and Kagamimori  observed a U-shaped relationship: as compared with 7 to 9 hours of work per day, higher risk (for cardiovascular problems) was associated with both shorter hours (less than 7 hours a day) and longer hours (more than 11 hours a day)
Nakanishi et al. [2001b], however, published the opposite results: white collar workers reporting 10 or more hours of work per day had a lower risk for developing hypertension when compared with workers reporting less than 8 hours of work per day
There are some small bits directly discussing performance:
3.2d Extended Work Shifts and Performance
Two laboratory studies reported deterioration in performance with extended shifts.
In contrast, four field studies reported no differences in their performance measures during extended shifts.
3.4b Very Long Shifts and Performance
A study in Ireland by Leonard et al.  reported declines in two tests of alertness and concentration in medical residents who had worked 32-hour on-call shifts. They reported no significant declines in a test of psychomotor performance or a test of memory. A New Zealand survey of anesthesiologists linked long working hours to self-reported clinical errors [Gander et al. 2000].
I glanced at the other links, and they look potentially interesting, but non-responsive as far as giving actual data showing that working more than 40 hours a week makes you less productive.
Perhaps there is confusion about my position, so let me clarify:
Average productivity per hour will decline with extended work. The highest average hourly productivity could be with shifts as short as six hours for many people; I have no particular thoughts on this, as I have never had reason to care to optimize it. An assembly line job that is embarrassingly parallel with minimal communication overhead may well be better served to have shorter shifts and more workers.
Total net productivity per worker, discounting for any increases in errors and negative side effects, continues increasing well past 40 hours per week. There are a great many tasks where inefficiency grows significantly with additional workers involved; the Mythical Man Month problem is real. In cases like these, you are better off with a smaller team of harder working people, even if their productivity-per-hour is somewhat lower.
This is critical: it isn’t necessary to maintain performance on an extended shift to still contribute value. Productivity per hour can deteriorate, even precipitously, and still be non-negative. Only when you are so broken down that even when you come back the following day your productivity per hour is significantly impaired, do you open up the possibility of actually reducing your net output.
There are cases where the consequences of an increased error rate can be a dominant factor -- airline pilots and nuclear plant operators come to mind. I had to work under FAA mandated crew rest guidelines while operating the Armadillo Aerospace rockets, and I made no complaints.
I believe most research that people glance at and see “declines in productivity with longer hours” are talking about declines in productivity-per-hour, and people jump to the incorrect conclusion that you can get just as much done in less time.
You called my post “so wrong, and so potentially destructive”, which leads me to believe that you hold an ideological position that the world would be better if people didn’t work as long. I don’t actually have a particularly strong position there; my point is purely about the effective output of an individual. If we were fighting an existential threat, say an asteroid that would hit the earth in a year, would you really tell everyone involved in the project that they should go home after 35 hours a week, because they are harming the project if they work longer?
We do need laws that those who work over what has long been considered healthy- 8 hours, are compensated very well for their time. To the point that the incentive lies on the employer to hire more people.
There's nothing to stop you or anyone else from forgoing your pay. But working for free to most of us is unacceptable, we don't have as much money thus our transaction of time for money means more. And many have less power to call shots because they may be less valuable or talented.
Yet everyone receiving a paycheck deserves this basic protection from abuse.
This is spot on. I think motivation is a huge factor here. Motivated workers are more capable of remaining productive over longer periods. Switching projects/tasks when you run out of gas is usually reinvigorating. Also, some people seem to have more innate motivation like an extended "honeymoon" phase when new people start a job and they are more tenacious and eager to prove themselves.
A cool project is an external motivating factor, or an existential threat ranging from potentially losing your job to being wiped out by an asteroid. As terrible as it is, fear is a great motivator. I've worked on projects so mind numbingly boring and pointless that I've had to change tasks after a couple hours because I found myself staring at my editor hating what I was doing. I've also worked on projects where I could stay motivated and productive 16 hours a day for two weeks at a time trying to meet an important deadline.
Bottom line in my opinion is there's no such thing as a broad rule of thumb for how long someone can stay productive.
Everyone? Maybe not. Those whose could make irrecuperable errors and doom the project because of fatigue, certainly. For many professions, longer hours don't necessarily lend to more production, but can certainly become hazardous.
The metric productivity-per-hour is stupid. It's useless trying to optimize it - just like you said. The natural cycle for humans is a day. The body requires rest and is tuned to have an optimal performance if the do/rest cycles are loosely synced with the day/night cycles of the sun. You need to optimize that cycle, in the long run, to maximize your total output.
"... when you come back the following day your productivity per hour is significantly impaired, do you open up the possibility of actually reducing your net output."
Yes, I do. The burnout today at work has an effect on your productivity tomorrow. In attempt to get a little extra done today, tomorrow you won't be that efficient at your peak, and you'll be more tired and unproductive at the and of the day, compared to the previous. This way your average productivity per day, from both days, can easily be lower than if you had worked 3 hours less the first night and the second day were just as efficient and productive as the first.
This effect extends in a long run. Fatigue accumulation and sleep debt are real phenomenons. Poorly managed day-to-day cycles can render people incapable of doing any meaningful work. The remedy is rest/vacation, which kills your averages even more.
You should know, even better than me, that working people don't only produce output. They are learning too. The work that you'll be required to do in a year or two is not the same as the one you do today. Mental fatigue impairs learning new stuff a lot more than it impairs doing stuff you already know.
You can live well on a whole lot less - as most people did not all that long ago. Ditch the >1000 sq ft homes, instant shirt-sleeve indoor temperatures, waste-encouraging volumes of drinking water, high-MPG with-all-the-features cars, supercomputer-in-your-pocket phones, etc. Get a catastrophic health insurance plan. Pay your way thru college. Downgrade the phone. And elect leaders who seek to make simple living legal, and otherwise decrease burdensome tax rates.
Your "living" standard is your choice. Really. Contain your costs, and you can live on a whole lot less. As always I'll be derided for these observations, but it's what I grew up on.
"Someone has to do the work", "confiscating the fruits of the productive to give to the idle punishes the former and rewards the latter".
That's absolutely not what liberating work is about, and what you describe is a pretty narrow view of economics that we're taught since childhood. Investigating a bit economy shows it get way more complicated than that, just defining "productive value" is a very deep subject. I don't believe you and I are able to assess if an economic system is sustainable or not (reality shown even the best economists can't), whereas scientist are pretty accurate about the low probability of an asteroid destroying earth in 2016.
I like what I do. Save eating, exercising, resting and socializing. I always can't wait to get back to work.
Find purpose and stop counting.
e.g. my first thought about the "increased hypertension in workers reporting < 7 hours" (a paper I haven't read, mind) is that they're stressed about finances because they're working part-time (or the "hours" was averaged over the year or something, and they spent some time without a job).
Now, if you've chosen to work many more hours then it seems intuitively obvious that you'll be more productive. There's also the hard-to-study factor of what you're working on. For example, many free-software developers are doing their free-software-developing in their "non-work" hours -- so they might be "working" (in the sense of producing code) 80+ hours a week, but will likely only get "counted" as whatever their day job was. (If there are studies that account for "what you do with your other time" against productivity, I'd be very keen to read them).
In a similar vein -- and as John said in the original post -- if you're "stuck" on something (e.g. can't do any more "design the hard algorithm" thinking) and switch to something "boring" that still needs to be done (e.g. make the Makefile suck less) that's still "more productive". But, as others have pointed out, many developers don't have that freedom -- they have to keep pounding their face against whatever bug they got assigned. And if you're stuck, but have to keep working on it, I'd bet a lot that your productivity goes to shit.
So, all that said, I personally believe (note: not scientific! ;) that we'd be far better off to have shorter expected/forced "working weeks". And I don't mean that everyone should be forced to work less! This may (or may not!) have a "productivity" impact for employers but if you looked at individuals' "productivity" (including work and "non-work" parts) I think it would go way up -- precisely because this would give the vast majority of people way more choice about what they get to work on. This -- I completely unscientifically presume -- would also have a large positive effect on people's reported happiness.
That is, they'd be spending less time smashing their face on that bug at work and get more time to do whatever else they like to do -- free-software, painting, writing, building things, etc.
In any case, I know that for me personally being forced to work 40+ hours a week on the same thing is completely toxic to my creativity and productivity at programming and I've worked very hard to get paid less (to work less). I can also tell you that nearly every co-worker or friend I've told of my myriad different arrangements to achieve this have wanted to do the same (but feel they "can't"). The only exception seems to be when people realize the bit about "paid less" ;) and can't do (or don't want) that. Interestingly, I still have spent a bunch of my increased leisure time writing software -- but for myself, or free-software instead of "for work". Of course, I've also spent a bunch of it doing things for pure enjoyment.
Now, of course, that's all just anecdotal. But, for me, less "must work on X for $" time means a lot more happiness and a lot more "productivity" (if you look at everything I do with my time).