If I wake up and start playing a video game or eating crap, that inertia carries through the day. The reverse is also true, if I get up, workout, and start being productive that will carry through the whole day. Once I realized this about myself I adjusted my whole schedule around. Instead of after work workouts, I moved them to the morning. Instead of staying up late, I get up earlier and naturally go to bed earlier. So instead of wake up and chill and ease into my day, I wake up and go. And, that go carries through the entire day.
The balance to strike here, I think, is to give your mind & body a chance to recuperate before you get too close to that breaking point. Or phrased another way, look at 'pushing yourself into a second wind' as a critical tool for certain situations, but one to be used sparingly (preferably when you have some open calendar spots ahead).
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[1] Of course there is general fatigue, but this is different from only being able to focus on something for a couple of hours/day or not being able to start something at all.