Can mental exhaustion be measured? 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:

A serial addition/subtraction task was included in the assessment
battery to measure cognitive throughput. The serial
addition/subtraction task is a subject-paced task requiring the
completion of 50 mental arithmetic trials. The average number of
correct responses per min was used as a neurobehavioral assay of
cognitive throughput performance.

Second, alertness / vigilance (response time to stimuli):

The neurobehavioral assessment battery included a psychomotor
vigilance task to measure behavioral alertness. The psychomotor
vigilance task (PVT) is a sustained-attention reaction time task with
a random inter-stimulus interval of 2–10 s. Lapses (reaction times
greater than 500 ms) were counted per 10 min test bout as a measure of
performance.

Third, memory:

The neurobehavioral assessment battery also included a computerized
digit symbol substitution task to measure working memory. This
subject-paced task involves the matching of digits (0–9) to symbols
(circle, triangle, etc.). The number of correct responses in 1.5 min
was counted to measure working memory performance.

The metrics ought to be effective for measuring mental performance due to fatigue whatever the cause of fatigue might be.
References

Van Dongen, H.P.A., Maislin, G., Mullington, J.M., Dinges, D.F. &amp; others (2003). The cumulative cost of additional wakefulness: dose-response effects on neurobehavioral functions and sleep physiology from chronic sleep restriction and total sleep deprivation. SLEEP-NEW YORK THEN WESTCHESTER-, 26, 117-129.