Equations of state (EOSs) describe how a material's internal energy and pressure change with temperature and density. They are inputs to hydrodynamic simulations in materials science and planetary science. We model the ion-thermal free-energy term for dissociative materials, where molecular bonds break apart to form new species under extreme conditions. This term is governed by two latent physical processes, a molar-mass surface and a Debye-temperature curve, neither of which is observed directly. Instead, both must be recovered from internal energy and pressure, which are derivatives of the free energy, subject to thermodynamic constraints. Existing EOS tables are typically built through material-specific hand-tuning, a process that is tedious, does not scale across materials or conditions, and offers no guarantee of thermodynamic consistency. We propose a partitioned statistical framework that infers molar mass and Debye temperature directly from EOS data, guaranteeing thermodynamic consistency by construction. Local molar-mass behavior is captured with polynomial basis functions across domain partitions, while the Debye temperature is modeled with an I-spline basis. In simulations and a carbon dioxide case study, the method accurately recovers the underlying physical quantities, improves prediction of held-out energy and pressure data, and provides uncertainty quantification while scaling with EOS table size.

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