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The internal circadian clock and sleep-wake homeostasis regulate the timing of human brain function, physiology, and behavior so that wakefulness and its associated functions are optimal during the solar day and that sleep and its related functions are optimal at night. The maintenance of a normal phase relationship between the internal circadian clock, sleep-wake homeostasis, and the light-dark cycle is crucial for optimal neurobehavioral and physiological function. Here, the authors show that the phase relationship between these factors—the phase angle of entrainment (ψ)—is strongly determined by the intrinsic period (τ) of the master circadian clock and the strength of the circadian synchronizer. Melatonin was used as a marker of internal biological time, and circadian period was estimated during a forced desynchrony protocol. The authors observed relationships between the phase angle of entrainment and …