Schematic overview of the coupled atmosphere-interior evolution model. This model considers the diffusion of atmospheric H₂ into the magma ocean, redox reactions in the magma ocean, partitioning of oxide components and H₂O among each phase, and cooling through thermal planetary radiation, with Fe produced by Fe²⁺ disproportionation removed into the core as it forms. Cases 1 and 2 represent two end-member treatments of material exchange between the magma ocean and solid mantle, introduced to account for uncertainty in the efficiency of material exchange between these reservoirs. Case 1 assumes efficient material exchange and equilibrium partitioning of oxide components and H₂O between the bulk magma ocean and solid mantle with uniform chemical compositions. Case 2 assumes inefficient material exchange, in which melt is efficiently trapped in the rheological transition region without subsequent material mixing in the solid mantle. The melt-side boundary layer at the interface between the magma ocean and atmosphere is considered to evaluate the H₂ diffusion rate into the magma ocean, with its overturn frequency determined by buoyancy-driven convective instability.