Thermodynamic properties resulting from anharmonicity in minerals decrease with pressure but are expected to increase across high-pressure phase transitions that are characterized by small volume changes and an increase in coordination number. This conclusion is supported by simple ionic models (based on either a molecular approach or crystal-independent potentials applied to the Bl(NaCl structure)--B2(CsCl structure) transition), as well as by the available high-pressure data. The enhanced anharmonicity of the high-pressure phase is caused by the increase in first-neighbor interatomic distance with a coordination change. The Gr¿neisen parameter and coefficient of thermal expansion are expected to increase by factors of order 20 to 50% across transitions involving changes from fourfold to sixfold and from sixfold to eightfold coordination in halides and oxides. Thus, lower mantle phases are expected to exhibit relatively large coefficients of thermal expansion (e.g., perovskite: α~3 to 4¿10-5 K-1 at 300--1000 K and zero pressure), and the driving force for convective heat transfer may be augmented by the occurrence of phase transformations deep within the Earth's mantle.