An organism's set of proteins is like a library. In bacteria, all the 'books' are roughly the same size — short instruction manuals. In humans, the library is vast: mountains of pamphlets and a few epic tomes. The longest human protein is 130 times longer than average — a genuine 'War and Peace' among recipes.

This difference can be measured using generalized entropy with a q parameter. In Boltzmann's physics, entropy describes chaos, but for interacting proteins the formula had to be made more complex. When q < 1, proteins are tightly clustered, as in bacteria (q ≈ 0.75). When q > 1, their range is broad, as in humans (q ≈ 1.15). Numerical simulations and machine learning have confirmed that q increases from microbe to human across 22 studied species.

Thus, simple atoms of carbon, oxygen, and hydrogen form an ensemble whose spread of lengths becomes a biosignature of evolutionary complexity. It's a bridge from biology to quantum thermodynamics — a metric where order and chaos paint a portrait of the organism.