The problem is - other than observing deterioration of results, I have no idea if I'm in such a state or not. I cannot be sure if it's also true for others...

It doesn't need to get to results, the quality of the process can also be observed, so that lack of productivity is catched early:

• Being sleepy
• Not being able to follow a math book fast enough
• Not being able to reliably set up a problem statement in imagination
• Not being able to find a right word in conversation/writing

Performing some activity that isn't in itself useful seems like a waste of time anyway, since the problem is finding a task for the day that you can actually cope with -- so, if something is too difficult, degrade gracefully :-)