Prebiotic Thermodynamics: An Energy-Coupling Model in Adaptive $S(t,x)$ Matrices

The emergence of life is conceptualized here as a process of thermodynamic coupling between a high-energy planetary environment (the "substrate") and emerging chemical networks (the "dissipative system"). This work introduces the $S(t,x)$ matrix, an encapsulated viscoelastic model describing how primitive chemical networks harnessed environmental energy gradients to maintain structural integrity under destructive conditions.

Prebiotic chemical networks required a physical boundary (encapsulation) to act as a thermodynamic interface, extending their lifespan ($t_{1/2}$) in the face of ionizing and ultraviolet radiation. The $S(t,x)$ model posits that, under extreme planetary dynamics, encapsulation not only provides protection but also facilitates selective impedance matching. This mechanism allows the chemical network to absorb and dissipate environmental kinetic and thermal energy, transforming external stress into internal organizational work (local entropy reduction) through molecular hysteresis mechanisms.

To quantify this relationship, we propose a dual evolutionary dynamics methodology that integrates adaptive learning models; these simulate the shift of the "invader's" chemical equilibrium toward resonance with the "substrate." We conclude that the origin of life depended critically on the ability of encapsulated networks to function as efficient dissipative structures, thermodynamically "parasitizing" planetary energy to initiate biological evolution.