The two forces in the model
The two-process model describes sleep timing as the interaction of two systems. Process S is the homeostatic sleep drive: pressure to sleep that builds the longer you stay awake and dissipates during sleep. Adenosine, a byproduct of cellular energy use that accumulates in the brain during wakefulness, is a leading candidate for the molecular signal behind it.
Process C is the circadian alerting signal driven by the master clock, which promotes wakefulness on a roughly 24-hour rhythm independent of how long you have been awake.
How the curves combine to set sleep and wake
Through the day, sleep pressure (S) climbs while the circadian signal (C) also rises to counter it, keeping you alert despite mounting fatigue. In the evening the circadian alerting signal falls, and with high accumulated pressure the gap favors sleep.
This framework helps explain afternoon dips, the alerting effect of caffeine (which blocks adenosine receptors), and why timing of sleep matters as much as duration. General educational information only.