Your Personal Energy Curve

Your performance fluctuates throughout the day. The two-process model from sleep research explains why, and what you can do about it.

The Two-Process Model

Alexander Borbély described two processes that regulate wakefulness and sleep in 1982.[1] Process S (sleep pressure) builds during wakefulness and dissipates during sleep. Process C (circadian rhythm) oscillates independently of sleep in an approximately 24-hour cycle.

Achermann formalized the mathematical description of both processes and their interaction in 2004.[2] The resulting curve from the superposition of S and C is your energy curve: it shows when you are performing well and when you are not.

Why Your Afternoon Dip Is Not a Coincidence

Many people blame their post-lunch slump on the meal itself. Monk showed in 2005 that the so-called post-lunch dip occurs regardless of food intake.[3] Whether you eat lunch or skip it: the dip comes anyway.

Dijk and Czeisler demonstrated in 1994 that the circadian low point of alertness falls between 2 and 4 PM for most people.[4] At that point, both Process S and Process C work against you: sleep pressure is already high, and the circadian drive hits a local minimum.

The practical takeaway: schedule deep work for the morning or late afternoon. Move routine tasks, emails, and admin into the dip.

2-4 PM
Circadian low point, regardless of whether you ate lunch (Monk 2005)[3]
2 processes
Sleep pressure and circadian rhythm combine to form your individual energy curve (Borbély 1982)[1]

What Shapes the Curve

Sleep debt. Van Dongen et al. (2003) showed that chronic sleep loss shifts the entire curve downward.[5] Even during normally high-performance phases, capacity remains reduced.

Chronotype. Roenneberg et al. (2003) described how chronotype shifts the phase of the curve.[6] Early types peak earlier, late types peak later. The curve looks similar, just time-shifted.

Light exposure. Khalsa et al. (2003) demonstrated that morning light advances the circadian phase.[7] Getting daylight in the morning means reaching your performance peak earlier.

Physical activity. Exercise produces a short-term energy boost (arousal boost) that locally raises the curve before a recovery dip follows.

Deep Work at the Right Time

Peak cognitive performance occurs in the morning for most people, typically 1-3 hours after waking. During this phase, working memory, concentration, and logical thinking are at their highest.

A second peak follows in the late afternoon or early evening, when the circadian drive rises again. Creative tasks often benefit from this phase, as increased associative thinking paired with slightly reduced focus promotes new connections.

Routine tasks belong in the afternoon dip. Late chronotypes should adjust their planning: their performance peak shifts 1-2 hours later, and the afternoon dip shifts accordingly.

Note: The energy curve is a statistical model. Individual factors such as caffeine, stress, illness, or irregular sleep can shift the curve on any given day.

Your curve. Not the average.

Most productivity advice is based on averages. Circadian Energy calculates your individual curve from your real data.

  • Calculates your energy curve daily from sleep times, HRV, and workouts via Apple Health
  • Factors in your chronotype, sleep debt, and physical activity
  • Shows you when your next peak and dip are coming
  • iOS widget for a quick glance at your current energy level
  • No subscription, no account, 100% on your device

References

  1. Borbély AA (1982). A two process model of sleep regulation. Human Neurobiology, 1(3), 195-204.
  2. Achermann P (2004). The two-process model of sleep regulation revisited. Aviation, Space, and Environmental Medicine, 75(3), A37-A43.
  3. Monk TH (2005). The post-lunch dip in performance. Clin Sports Med, 24(2), e15-e23.
  4. Dijk DJ, Czeisler CA (1994). Paradoxical timing of the circadian rhythm of sleep propensity serves to consolidate sleep and wakefulness in humans. Neurosci Lett, 166(1), 63-68.
  5. Van Dongen HPA, Maislin G, Mullington JM, Dinges DF (2003). The cumulative cost of additional wakefulness. Sleep, 26(2), 117-126.
  6. Roenneberg T, Wirz-Justice A, Merrow M (2003). Life between clocks: daily temporal patterns of human chronotypes. J Biol Rhythms, 18(1), 80-90.
  7. Khalsa SBS, Jewett ME, Cajochen C, Czeisler CA (2003). A phase response curve to single bright light pulses in human subjects. J Physiol, 549(3), 945-952.