I asked this question a long while ago, but I never got an answer to whether mental exhaustion can be measured. If mental exhaustion could be measured, it would mean that I would have a way of knowing the performance I can get out of my brain in a day. I would be able to know what is best for refilling my brain with energy (maybe TV is your best option after all...;) ) As far as I understand, different parts of the brain gets used for different purposes, so they should get exhausted at different times, so the measuring would have to be on specific regions of the brain or performance of the brain in various fields.
A sleep study by Van Dongen et al (2003) uses three metrics to measure the effects of fatigue due to sleep loss. The first is cognitive throughput:
Second, alertness / vigilance (response time to stimuli):
The metrics ought to be effective for measuring mental performance due to fatigue whatever the cause of fatigue might be.
There are a several perspectives of mental fatigue. Here are a few starting points: