The Heart as a Candle: Why All Animals Burn Out the Same Way

Original: "Thermodynamic Parametrisation of the Vertebrate Lifetime Cycle Invariant: Biological Proper Time, Allometric Mass-Cancellation, and Clade-Specific Predictions"
· Mesfin Taye
arXiv:2604.24458 · 2026-04-27 · CC BY 4.0 · 1 min
In every warm-blooded animal, the heart beats roughly a billion times over a lifetime, because each beat burns the same amount of energy.

A shrew hammers away at eight hundred beats per minute; an elephant manages twenty-eight. Yet over a lifetime, both hearts contract about a billion times. Why does it work out that way?

Every heartbeat spends energy, and that energy dissipates as heat. It turns out that per kilogram of body weight and per single beat, all warm-blooded animals spend almost the same amount of energy. A mouse burns through it faster, an elephant more slowly, but the total lifetime budget is the same. That is why the number of beats matches too.

In humans, the brain consumes 20% of the body's energy even though it makes up only 2% of body mass. That is why our heart beats more times over a lifetime than the hearts of other mammals of the same size.

Some animals break the general rule. Bats live longer because they often enter torpor and save energy. Birds burn fuel more efficiently. Whales slow their pulse when diving, and once you factor that in, their budget turns out to be larger than usual.

If you measure life not in years but in heartbeats, then every species has its own biological time. It runs faster for a mouse and slower for an elephant. This helps estimate biological age: the less energy spent per beat, the more slowly an animal ages.

A shrew's heart beats 800 times per minute, while an elephant's beats 28, yet over a lifetime both perform roughly the same number of beats. In humans, the brain consumes 20% of the body's energy despite making up only 2% of its mass.

The idea of biological proper time echoes Greg Egan's novel 'Permutation City', where virtual personalities live in accelerated or decelerated subjective time, and their 'lived life' is measured by internal events rather than external seconds.

\dot{e}_{p,i} = \sigma_{0,i} f_i
The rate of entropy production is proportional to heart rate, with coefficient σ₀ being the entropy per beat
\theta_i(t) = \int_0^t f_i(t') dt'
Accumulated number of cardiac cycles up to time t
\Phi_C = \frac{N_\star^{(C)}}{N_0}
Ratio of the actual number of beats to the baseline invariant
Scientists
Rudolf ClausiusJames Clerk MaxwellLudwig BoltzmannAlbert EinsteinBarry BarishKip Thorne
Concepts
second law of thermodynamics third law of thermodynamics boltzmann constant energy conservation lifetime