Thermodynamic ontogeny: The emergence of persistence and complexity in pre-genetic chemical systems

Understanding how thermodynamic principles drive the emergence of organized chemical systems from abiotic geochemistry represents a central challenge in prebiotic evolution. We develop a quantitative framework for systems removed from equilibrium, establishing formulations for organizational complexity (C) and persistence (P). Complexity, the volumetric rate of free energy dissipation maintaining non-equilibrium organization, scales with substrate gradients and kinetic accessibility. Persistence is the system's capacity to export internally generated entropy across membrane boundaries, determined by geometric constraints and transport impedances. Bejan's Constructal Law provides the optimization principle by which protocell geometry morphs to achieve this balance, providing a deterministic basis for protocell dimensions and molecular architecture. For mineral-catalyzed chemistry at hydrothermal vents (〈Ea〉≈ 50 kJ/mol, T ≈ 338 K), the framework predicts optimal radius r ≈0.56μm for volume-distributed chemistry (n = 3), matching observed dimensions of experimental protocells and minimal cells. Conversely, surface-limited chemistry (n = 2) predicts mechanically unstable configurations, establishing the internalization of metabolism as a thermodynamic necessity. Geological subsidence at polar regions provides deterministic forcing driving protocell populations toward increasing complexity over multi-million-year timescales. The transition from monomers to polymers is a necessary strategy to mitigate osmotic stress during subsidence, effectively responding to a baric forcing of complexity. The framework generates falsifiable predictions where ln(r) ∝ 1/T, with a slope determined by activation energy and dimensionality. The framework transforms a prebiotic system from a statistical improbability into a predictable physical outcome, establishing the foundations for life as a thermodynamic necessity operating under early Earth constraints.