Likewise. I can easily work for 10 or 12 hours. It's fitting in things like friends and family, according to their schedules, that makes it difficult. I don't mean to say this in a resentful way at all; it's definitely a me problem, not them.
Productivity doesn't correlate super closely with fatigue in my experience. The worse sessions are when I'm banging my head against something and getting nowhere. When I'm flowing, I can go for hours.
I’m not sure it makes sense to differentiate between energy spend while being “productive”, and energy spent whole trouble shooting and problem solving.
After all, trouble shooting can be viewed as a productive thing.