Why a Mouse Runs Hotter Than an Elephant express

Original: "The Dynamic Origin of Kleiber's Law"

arXiv:2604.10476 · 2026-04-12 · CC BY 4.0 · 1 min

It's the pulse, not vessel geometry, that sets metabolic rate.

The heart doesn't push blood in a steady stream but in pulses. Each beat sends a wave racing through the arteries, like ripples along a taut garden hose. For a long time, it was thought that an animal's metabolic rate depended only on how vessels branch, like pipes in a house. But new work flips that view: what matters isn't the shape of the pipes but the pulse itself.

The wave meets resistance at every branching point, and nature tunes vessel thickness so the wave passes without loss. This is what sets the famous 3/4 exponent.

If the body is large, the wave dies out before traveling far, and metabolism slows down. If it's small, the wave encounters little resistance, and metabolism runs faster. The calculation predicts that for truly tiny creatures (mice, insects) the slope of the scaling relationship becomes steeper, around 0.9. And that's exactly what biologists see in measurements.

The old theory, relying only on vessel geometry, failed near the heart. The new formula works across the board, from shrews to flatworms.

The pulse isn't just a thump in the chest. It's the mechanics that determine how much food a body needs, how fast it grows, and how long it lives. Now that mechanics has a precise equation.

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A shrew's heart beats up to 1000 times per minute, while an elephant's beats about 30 times. The difference in pulse rate is directly tied to how quickly energy burns.

\beta = \frac{d\alpha}{2d+\alpha}

The exponent β depends on the spatial dimension d and the local branching exponent α. For the three-dimensional case with typical α, β = 3/4.

Scientists

Andrey Markov

Concepts

Kepler's third law Cope's rule Wien's displacement law wilks theorem microswimmer wien displacement constant Liebig's Law of the Minimum Bergmann's rule Fisher's fundamental theorem of natural selection virial theorem polymer

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Why a Mouse Runs Hotter Than an Elephant express