Applicability of the Mie–Grüneisen Equation of State Model to Warm Dense Matter Conditions

Abstract

The Mie–Grüneisen (MG) model provides a linear relation between thermal pressure (pressure relative to a reference temperature) and the corresponding thermal energy, which is widely used to interpolate and extrapolate equations of state (EOS) beyond experimental data. However, its applicability to warm dense matter (WDM) conditions, where strong coupling and ionization become significant, remains poorly constrained. Here we assess the validity of the MG approximation using first-principles simulations of representative materials—MgO, H, He, Si, CH₂ and others—spanning the condensed and WDM regimes. Combining finite-temperature density functional theory molecular dynamics (DFT-MD) with path integral Monte Carlo (PIMC), we compute consistent pressure and energy relations over a wide range of densities and temperatures. We show that the proportionality between thermal pressure and thermal energy is linear function of density but does depend on temperature, allowing us to build an effective Grüneisen parameter $\gamma \left(V,T\right)$. However, systematic deviations appear at high temperatures where ionization effects introduce significant temperature dependence in $\gamma$. These results establish the quantitative limits of the Mie–Grüneisen framework in the WDM regime and provide a benchmark for constructing wide-ranging EOS models relevant to inertial confinement fusion and planetary interior studies.