  The high-pressure melting diagram of iron is a vital ingredient for the
geodynamic modeling of planetary interiors. Nonetheless, available data for
molten iron show an alarming discrepancy. Herein, we propose an efficient
one-phase approach to capture the solid-liquid transition of iron under extreme
conditions. Our basic idea is to extend the statistical moment method to
determine the density of iron in the TPa region. On that basis, we adapt the
work-heat equivalence principle to appropriately link equation-of-state
parameters with melting properties. This strategy allows explaining
cutting-edge experimental and ab initio results without massive computational
workloads. Our theoretical calculations would be helpful to constrain the
chemical composition, internal dynamics, and thermal evolution of the Earth and
super-Earths.
