First principles phase diagram calculations in group IV carbides and Mg2SiO4 liquid from molecular dynamics Atomistic simulations on stability and physical properties of Earth materials are playing an increasingly important role in high pressure mineralogy. Such computations can provide guidance for experimental studies and insight into underlying causes of observations or explore conditions and properties that are inaccessible to experiments at the current time. A variety of approaches have been applied in such research with density functional theory based methods having become a reliable tool in computational mineral sciences. Despite this progress there are interesting problems which density functional theory based methods are not able to tackle on a routine basis. These include computations of phase diagrams and transport properties in liquids ...