  In order to provide a comprehensive theoretical description of MgSiO$_3$ at
extreme conditions, we combine results from path integral Monte Carlo (PIMC)
and density functional molecular dynamics simulations (DFT-MD) and generate a
consistent equation of state for this material. We consider a wide range of
temperature and density conditions from 10$^4$ to 10$^8$ K and from 0.321 to
64.2 g$\,$cm$^{-3}$ (0.1- to 20-fold the ambient density). We study how the L
and K shell electrons are ionized with increasing temperature and pressure. We
derive the shock Hugoniot curve and compare with experimental results. Our
Hugoniot curve is in good agreement with the experiments, and we predict a
broad compression maximum that is dominated by the K shell ionization of all
three nuclei while the peak compression ratio of 4.70 is obtained when the Si
and Mg nuclei are ionized. Finally we analyze the heat capacity and structural
properties of the liquid.
