(a) Internal energy (E), (a, inset) thermal electronic entropy (S_el), (b) Pressure (P), (c) thermal pressure coefficient (αK_T), (d) isochoric heat capacity (C_V) and (e) Grüneisen parameter (γ) of MgO liquid. Coloured circles in (a) and (b) show values from FPMD simulations at 3000 K (blue), 4000 K (cyan), 5000 K (green), 6000 K (yellow), 7000 K (orange) and 10000 K (red) (Karki et al. 2006, except for points at V/V_X = 0.35 and V/V_X = 0.42). Black lines indicate the fit of P and E to eq. (16) with (solid lines; first order in T, see text) and (dashed lines; second order in T, see text), and a third-order expansion in finite strain. Errorbars are smaller than the size of the symbols. Black lines in (a, inset) indicates the fit to eq. (30). Lines in (c), (d) and (e) are second derivatives of the fundamental relation, coloured by temperatures as the symbols in (a) and (b). These lines follow the trend previously found (Karki et al. 2006) by independent linear fits of FPMD results along each simulated isochore (white symbols), but it should be kept in mind that these points represent mean values over a large temperature range, which is not thermodynamically self-consistent, and may also be off due to the glass transition.