Not "nothing important", but nothing at all. All my work contracts around here clearly stated that what you write in your worktime is the company's intellectual property.
It doesn't matter that you are not writing a thing.
It doesn't matter that you are not writing a thing.
If you're doing it on your private machine over which you have full control then how can anyone prove it was done during work hours?
I can sit bored (with a couple of hours worth tracking in the timesheet software) for a month or two, but then I usually start looking for something interesting.