Does limiting mental activity during the day increase mental performance later in the day? Is there any scientific evidence to support the idea that you only have so much cognitive energy in a given day; and if so, would the mental abilities of someone who focuses on as little as possible all day be greater than someone who stays engaged all day long?  Can the brain experience fatigue?

In Mihaly Csikszentmihalyi's book Flow: The Psychology of Optimal Experience (1990), he says:


  At this point in our scientific knowledge we are on the verge of being
  able to estimate how much information the central nervous system is
  capable of processing. It seems we can manage at most seven bits of
  information - such as differentiated sounds, or visual stimuli, or
  recognizable nuances of emotion of thought - at any one time, and that
  the shortest time it takes to discriminate between one set of bits and
  another is about 1/18 of a second.


He goes on to infer that "psychic energy" should be invested and shouldn't be wasted. At least, this was my interpretation.
Very interesting question, however, cognitive exhaustion may be a learned phenomena ( https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5413468/ ) as referenced by this 2017 article finding it to be conditioned to the individual. Though I cannot provide a concrete answer, I would estimate that cognitive stamina, so to speak, can be trained into the individual much like aerobic or muscular stamina.