Testing the Maintenance Theorem

The maintenance theorem predicts an optimal return cadence ^* = (3f / (a ^2))^1/3 where is displacement magnitude, f is fixed return cost, and a is a domain-dependent parameter. This paper tests the theorem against physiological detraining—the loss of aerobic fitness during inactivity. We fit the maintenance cost function g() = (a ^2 ^2)/6 + f/ + b ^k to five landmark detraining studies (Coyle et al. 1984, Cullinane et al. 1986, Simoneau et al. 1985, Houmard et al. 1992, Mujika et al. 1995).

The fitted model explains 85.6% of variance (R^2 = 0.856). We derive parameter-free predictions for return cadence and validate them on held-out data. The prediction error is −3.5 to +1.1 days, within physiological noise. We conclude the theorem captures a genuine structure in how bodies (and potentially other systems) respond to detraining and return.