Thermodynamic ontogeny: From hydrothermal thioesters to a protein world.

The transition from abiotic hydrothermal chemistry to a protein world lacks a governing principle capable of deriving protocell architecture without free parameters. Here a predictive framework for the emergence of membrane-bounded complexity from Late Hadean thioester chemistry is developed: Prigogine's entropy balance, applied to the organizational complexity and persistence capacity of a membrane-bounded system, establishes C/P = 1 as the identity such a system must satisfy to remain in a sustained non-equilibrium state. Bejan's Constructal Law, Young-Laplace mechanics, and Helfrich bending energy then govern the effective radius this identity predicts and its mechanical and geometric consequences, with no adjustable parameter. Applied to a subsiding polar hydrothermal vent field at approximately 3.9 Ga, the framework yields three architectures: the thiosome (reff ≈ 29 nm), a thioester-synthesizing structure; the peptosome (reff ≈ 566 nm), a peptide-synthesizing stage emerging under increasing hydrostatic pressure; and the syntrosome, a membrane-invaginated structure whose fission follows a Helfrich-Gauss-Bonnet criterion. We argue, on thermodynamic grounds, that a protein world is a plausible, though not the only possible, precursor to nucleic-acid heredity, without excluding RNA-peptide coevolution. The framework yields falsifiable predictions testable in controlled fatty-acid vesicle systems, including a square-root scaling of fission radius with synthesis flux and a log-linear relationship between radius and activation energy, offering a parameter-free, testable pathway to membrane-bounded bioenergetic complexity under Late Hadean conditions.