Pre-Biotic Earth and a More Complete Theory of Heat Transformation, Part I

Prebiotic Earth builds with zero entropy while dissipating with maximum entropy. This is demonstrated by a new physical model presented in this paper, the type of physical model that is needed to determine a theoretically grounded statistical probability of abiogenesis. The thermodynamic mechanism behind this capacity has not been explained by existing frameworks, none of which capture all properties of dissipative structures that would form a coherent, internally consistent set derived from a single physical model. A close reading of Clausius's foundational papers reveals a convention and properties for far-from-equilibrium systems that modern thermodynamics has overlooked, pointing to a framework of an Earth that builds with zero entropy while dissipating with maximum entropy. This paper introduces the gravitational dissipative structure (GDS) and provides that complete quantitative framework. Grounded in Clausius's interior/exterior work distinction, his force-balance reversibility criterion, and his dynamic equivalence values of compensated and uncompensated transformations, the GDS model derives six thermodynamic properties, including complexity yield, specific heat quality, and heat transformation effectivity, and proves two theorems. The first theorem establishes that dissipative structures are more effective at transforming heat into stored energy at greater local heat sink temperatures. The second theorem proves that the ratio of real efficiency to Carnot efficiency is constant regardless of boundary temperatures. Applied to Earth's tropospheric water and air cycles, the model yields auto-powering capacities of 82 W/m² and 345 W/m², with greater than 98% of initial heat quality retained. Their combined heat quality outputs estimate jet stream velocity to within the same order of magnitude, cross-validating the GDS model and the concept of heat quality networking. When GDSs network at planetary scale, the result is the delivery of heat at temperature to the molecular scale and a massive mixing that is a geological-timescale concentration of dissolved salts, acids, bases, and minerals that delivers the physical preconditions for prebiotic chemistry on Earth. This is Part I of a four-part series. Parts II through IV build on these preconditions. The objective is to conceptually and quantitatively describe the physical systems that are the context for the emergence of life.