Every heartbeat is a fuel token the body burns as it edges toward exhausting its supply. A mouse spends tokens by the hundreds per minute, an elephant by thirty, yet by the end of life both have burned roughly the same number. So age isn't calendar years; it's the number of tokens spent, and each token carries its own price in the disorder it introduces into the body.

The model proposed in the paper introduces an internal clock that ticks not in seconds but in physiological cycles, weighted by their entropy price. Biological age becomes the fraction of the budget spent: if the heart beats faster, or each beat costs more, the clock runs faster. This explains why people born in the same year can have different biological ages: their internal clocks tick at different rates.

But the most interesting part comes when the body tries to repair damage. Repair isn't infinite: if the recovery rate falls below a critical threshold, the healthy stable point vanishes and the system slides toward runaway damage. That threshold is a saddle-node bifurcation, the moment a stable state disappears and aging accelerates sharply, like an avalanche breaking loose from a slope.

Testing the model on synthetic data showed that internal clocks reconstructed from noise align aging trajectories better than chronological age or plain cycle frequency. The prediction error was 0.124 versus 0.453 and 0.329 respectively. That means entropy-weighted clocks really do capture something important that other measures miss.

In practice, such a model lets us classify anti-aging interventions: slowing the tick, making the tick cheaper, expanding the budget, or fighting hypertemporal disease. Instead of guessing which drug works, we can ask how it affects the internal clock: the rate at which fuel tokens are spent and their price.