The brain uses about 20% of the body’s total energy, and an interesting question is how this power requirement changes during sleep. A website run by the American College of Neuropsychopharmacology says the brain "receives 15% of the cardiac output, 20% of total body oxygen consumption, and 25% of total body glucose utilization". Given its small size, the brain uses a disproportionate amount of the body’s energy. We know the brain is active during sleep, but does it slow down at all from the daytime, as the rest of the body tends to?
And how feasible is the hypothesis, posited many times, that sleep evolved so individuals could save energy? In an environment of food scarcity – which we evolved in and which wild animals live in – it is possible that sleep helped conserve energy when it wasn’t optimal to be looking for food. Overall energy metabolism is as much as 10% lower during sleep (http://healthysleep.med.harvard.edu/healthy/matters/benefits-of-sleep/why-do-we-sleep).
A study http://jp.physoc.org/content/589/1/235.full showed the body’s energy use does not vary much with stage of sleep. The extra energy consumed by the brain in REM sleep is balanced out by the less energy used by the skeletal muscles that are paralyzed during REM.
In the same study scientists found that sleep deprivation increases resting energy expenditure, which is consistent with other symptoms of sleep deprivation such as a subjective feeling of coldness.
Positron emission tomography allows scientist to see which areas of the brain are consuming the most glucose and presumably the most active, during sleep. The pontine tegmentum, thalmic limbus, and the back of the cortex are more active during REM while the prefrontal cortex and parietal lobe are less active. More on this is here: http://www.ncbi.nlm.nih.gov/pubmed/11012860
Does the brain get tired? Actually, yes, it can. Individual cortical columns in the brain go into a sleep state with a probability that depends on the length of prior waking.
The longer the column has been in the "waking" the position, the more likely it is to switch to a sleep position, even if the animal as a whole is awake. (It has even been experimentally shown that local micro-injection of tumor necrosis factor can flip a column into a sleep state.)
Experiments have shown the brain can be made tired. When an animal is made to use its right side of the body (which is controlled by the left side of the brain), the EEG readings of the left side in the following sleep shows more intense delta waves.
It has been hypothesized that the evolution split NREM and REM sleep as a way to allow different parts of the brain to experience restorative sleep during the night. If the cortex enjoys this rest period during NREM, it is conceivable that during REM other parts of the brain rest. But while NREM coincides with lower metabolic activity, REM sleep occurs when there is more activity in the lower portions of the brain.
After epileptic seizures (a period of very high brain activity), the levels of tumor necrosis factor and interleukin-1 are higher (these chemicals are known to be associated with sleepiness).
However, brain scientists feel that hard thinking such as study of a challenging academic sort does not use much more energy than vegging out does
The extra energy used during sleep deprivation seems to be balanced by a lower-than-normal energy use during recovery sleep. Sometimes people describe a night as one of particularly restorative sleep. This subjective description has no correlation with energy use. Restorative sleep does not use more or less sleep than non-restorative sleep.