A surfer lies on a board far from shore. Waves come and go, but he saves his strength until he sees the one that is quickly building. In that brief moment he jumps up, paddles with all his might, and glides down the slope. His efficiency is highest exactly when he syncs with the wave, not when he is bobbing calmly on the water. Likewise, adaptive systems, from biological sensors to online learning algorithms, reach their peak conversion of energy into information not in steady rest but in transient moments when the environment changes sharply.
Picture a particle that can sit in one of two wells of an energy landscape, like a ball in one of two hollows. The depth of the hollows depends on a control parameter, which in turn tries to follow an external signal. That signal does not stay put; it drifts slowly, like the water level in a lagoon subject to tides of varying strength. When the environment changes, the parameter is forced to readjust, and the system leaves equilibrium. At such moments it produces entropy, that is, it dissipates energy, and at the same time it gains information about the environment. The ratio of the rate of information gain to the rate of energy dissipation is the instantaneous learning efficiency.
Numerical simulations showed: when the environment changes rapidly, the system spends more energy and gains more information, but efficiency peaks do not coincide exactly with energy dissipation peaks. This means that a system can spend a lot of energy yet fail to learn if its internal rhythm does not match the rhythm of the external signal. When averaged over many runs, the peaks smooth out, and the average efficiency decays to zero, confirming the purely transient nature of optimal information-to-energy conversion. An empirical dependence of maximum efficiency on parameters was found: it decreases as the square root of the product of the adaptation rate and the environmental drift time.
The surfer does not spend effort on every wave in a row. He waits for the right moment, when the wave is steep and fast, and then puts all his energy into a few powerful strokes. Adaptive systems in a changing world do the same: their thermodynamic performance is highest not in calm paddling but in a short burst when they synchronize with change. This insight may be useful for designing energy-efficient sensors and algorithms that need to learn quickly during moments of change rather than spend resources constantly maintaining equilibrium.
In the model, efficiency can exceed unity or be negative at certain moments, which does not violate the second law of thermodynamics but reflects a temporary mismatch between dissipation and information gain.