The urge to sleep does not increase steadily through the day, and it does not track hours awake in a simple line. Sleep researchers explain the pattern with two separate processes running at once.
Pressure builds with time awake
The first process is homeostatic. The longer a person is awake, the stronger the drive to sleep becomes, and sleeping discharges it.
Adenosine is central to the mechanism. It accumulates in the brain during waking as a by-product of cellular energy use, and it binds receptors that dampen arousal-promoting activity.
Concentrations fall during sleep, which is why the drive is low on waking and why an interrupted night leaves residual pressure behind.
Caffeine blocks the signal without removing it
Caffeine occupies adenosine receptors without activating them, so the accumulated adenosine cannot deliver its message.
Nothing about the accumulation itself is altered. The molecule keeps building while the signal is blocked.
When the caffeine clears, the full accumulated signal reaches its receptors at once, which is the mechanism behind the sudden drop that follows.
A clock runs independently of sleep debt
The second process is circadian, governed by a small region of the hypothalamus that maintains a near-twenty-four-hour rhythm.
This clock runs whether or not a person has slept, and it drives daily cycles in body temperature, hormone release and alertness.
Light reaching specialised retinal cells is its main synchronising input, which is how the internal rhythm stays aligned with the external day.
Alertness is the difference between the two
The circadian signal promoting wakefulness strengthens through the day, roughly opposing the rising homeostatic pressure.
Subjective alertness reflects the gap between them, which is why a person can be awake for many hours and still feel reasonably sharp in the evening.
The alerting signal then falls away in the late evening while pressure remains high, and the two together produce the sensation of sleepiness.
The afternoon dip falls out of the model
Mid-afternoon brings a temporary reduction in the circadian alerting signal while homeostatic pressure has already been building for hours.
The dip appears in people who ate lunch and people who did not, which is what identifies it as a clock phenomenon rather than a digestive one.
Persistent daytime sleepiness despite adequate opportunity to sleep is a different matter and is worth discussing with a doctor.