Big productivity boost if you're setting your own schedule or you're often being the night owl --
Once you start to feel your mind wind down and the fog set in, sleep ASAP!
It sounds simple, but the execution is life-changing. I used to waste about the last two hours of the day in a daze on many days where I wasn't totally spent at the end of the day. Now I've got it down to usually recognizing between 40 and 90 minutes that my mind isn't going to clear, and crashing out.
There's no sense trying to push through it if legitimate exhaustion is there... the quality of thinking will be low. If you must stay up (deadline, etc) grab a cold shower or go running or do pushups. But if you don't have to -- grab some sleep. The you-of-tomorrow will be grateful you did.
"you-of-tomorrow" reminds me of this: http://formalsweatpants.com/journal/2012/2/27/future-me.html#.UJBq_cXA_zM
I was never sure if it made sense to sleep if you're going to be underslept anyways, but then I read the science in "Take a Nap, Change Your Life."
The verdict? When you're tired, getting more sleep can never make you more tired. The disorientation coming out of sleep is from being in a deep sleep mode, but it passes quickly. From empirical testing - I take almost any amount of sleep now if running low, and it works better.
Around ten years ago, a friend of mine bet me that he could run a mile faster than I could. We each had a month or two to train, and then we met at the high school track near my old house. He ran first, and did the mile in seven and a half minutes. That was actually faster than I'd run a mile before.
What would my strategy be? Well, the oval track was a fourth of a mile long. I figured that I'd run my usual pace for the first three laps, and then for that last lap, I would just murder myself on the pavement. May as will give it everything I've got, since there's nothing after the finish line.
When I hit he finish line, I had to grab the bleachers to avoid falling down. My legs were shaking, my head was pounding, and I was gasping for breath. I had won, running a 6:59, my fastest mile ever.
A few nights ago it was eleven pm, and my non-negotiable computer-off time of midnight was drawing close. I'd had an amazingly productive day, and the thought crossed my mind that I'd already gotten enough done during the day, and could afford to take a break for the last hour.