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 by integrating Prigogine's entropy balance, Bejan's Constructal Law, Young-Laplace mechanics, and Helfrich bending energy into the identity C/P = 1. This identity derives protocell architecture as a sustainable non-equilibrium steady state, predicting an effective radius from the activation energy of the encapsulated chemistry, membrane thickness, and temperature, with no adjustable parameter. Applied to subsiding polar hydrothermal vents at approximately 3.9 Ga, the framework yields three architectures: the thiosome (r_eff ≈ 29 nm), a thioester-synthesizing structure; the peptosome (r_eff ≈ 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. The same equation predicts the contrasting mechanical behavior of each architecture through the Young-Laplace relation. We argue, on thermodynamic grounds, that a protein world is a plausible precursor to nucleic-acid heredity, while noting that this ordering does not exclude 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. The thiosome-to-protein-world sequence is offered as one physically coherent, parameter-free, and testable pathway to membrane-bounded bioenergetic complexity under Late Hadean conditions - consistent with the physics, but not the only route available to a nascent biosphere.