A model-free uncertainty-aware equation of state for gold*

This study introduces an advanced Uncertainty-Aware Equation of State (UEOS) toolkit rooted in the error-in-variables Gaussian process. Our approach deviates from traditional methods by generating a gold EOS table (U790) directly from quantum simulation data, bypassing the need for fitting into conventional EOS models like the Mie-Grüneisen equation. The toolkit meticulously accounts for systematic and model-derived uncertainties originating from quantum simulations and experimental data. These uncertainties are seamlessly integrated using Gaussian operations, including additions and derivatives, to obtain the final free energies, specifically the Gibbs free energy.

A critical validation of our methodology involved a comparative analysis between our new EOS table and the existing LEOS 790 table. Remarkably, the disparity between these tables falls well within the 5% margin for the temperature-density grid considered in this study, affirming the robustness of our results.  Furthermore, we have expanded this analysis into the challenging domain of plasma data, including the recent Hugoniot measurements.