  Using path integral Monte Carlo and density functional molecular dynamics
(DFT-MD) simulations, we study the properties of MgSiO$_3$ enstatite in the
regime of warm dense matter. We generate a consistent equation of state (EOS)
that spans across a wide range of temperatures and densities (10$^4$--10$^7$ K
and 6.42--64.16 g cm$^{-3}$). We derive the shock Hugoniot curve, that is in
good agreement with the experiments. We identify the boundary between the
regimes of thermal ionization and pressure ionization by locating where the
internal energy at constant temperature attains a minimum as a function of
density or pressure. At low density, the internal energy decreases with
increasing density as the weight of free states changes. Thermal ionization
dominates. Conversely, at high density, in the regime of pressure ionization,
the internal energy increases with density. We determine the boundary between
the two regimes and show that the compression maximum along the shock Hugoniot
curve occurs because K shell electrons become thermally ionized rather than
pressure ionized.
