What cognitive processes occur during a mental exhaustion or 'burnout'? Mental burnout - or mental exhaustion is not very pleasant, when one feels completely overwhelmed, something 'snaps' and it is hard to concentrate and maintain motivation.  What are the cognitive processes that occur during a burnout?  What processes allow for recovery?
One of the older theories suggested that a person literally runs out of brain-fuel when they hit the wall (Baumeister et al, 1998). They called this state "ego depletion" and it refers to the kind of mental burnout you are talking about. There is currently a lot of research activity on this topic because we (psychologists) assumed for over a decade that some resource was depleted in the brain but have found no evidence for any such resource. Newer theories suggest that people go through a kind of motivational cycle in which people tend to approach longer-term goals with delayed rewards (e.g., doing homework) for some period of time, followed by pursuit of shorter-term goals with immediate rewards (e.g., eating, leisure, etc.; see Kurzban et al, 2013 for a great discussion).

Thus, people with high self-control are people who spend relatively more time engaging in "labor" and impulsive people spend relatively more time pursuing leisure. The cyclical nature of motivation has clear adaptive qualities and the burnout that you feel after working for long periods is thought to be your brain doing exactly what it is designed to do: keep you from neglecting short term goals which are/were just as essential for survival as long-term goals. This is in direct contrast with the brain-fuel idea, which models burnout as self-control failure. See the Inzlicht article for a critique of brain-fuel models.

One interesting area of work that is related to all of this comes from the ADHD literature. The drugs developed to treat ADHD have demonstrated a clear connection between dopamine activity in the frontal lobes and the ability to persist in pursuing labor goals. It might be tempting to think that dopamine is the phantom brain-fuel we've been looking for, but note that the brain has no problem producing dopamine (i.e., it doesn't "run out"). Nobody has really pursued this, but it will be interesting to see how psychologists integrate the role of dopamine and frontal lobe functioning into self-control models. The Barkley reference below is an old one, but it is a good review of ADHD research that is relevant to this topic. 

Barkley, R. A. (1997). Behavioral inhibition, sustained attention, and executive functions: constructing a unifying theory of ADHD. Psychological bulletin, 121(1), 65.

Baumeister, R. F., Bratslavsky, E., Muraven, M., &amp; Tice, D. M. (1998). Ego depletion: is the active self a limited resource?. Journal of personality and social psychology, 74(5), 1252.

Inzlicht, M., Schmeichel, B. J., &amp; Macrae, C. N. (2014). Why self-control seems (but may not be) limited. Trends in cognitive sciences, 18(3), 127-133.

Kurzban, R., Duckworth, A., Kable, J. W., &amp; Myers, J. (2013). An opportunity cost model of subjective effort and task performance. Behavioral and Brain Sciences, 36(06), 661-679.