Abstract. The thermal expansion coefficient is presented as the coupling between heat energy and mechanical work. It is shown that when heat and work are uncoupled then very unusual material properties occurs: for example, acoustic p waves are not damped and heat is not generated from mechanical motion. It is found that at pressures defined by the bulk modulus divided by the Anderson–Grüneisen parameter, then the thermal expansion coefficient approaches zero in linear-elastic models. Very large pressures always reduce thermal expansion coefficients; the importance of a very small or even negative thermal expansion coefficient is discussed in relation to physical processes deep in the core and mantle of Earth. Models of the thermal expansion coefficients based on interatomic potentials which are always relegated to isometric conditions preclude any changes in volume due to temperature changes. However, it is known that the pressures in the Earth are large enough to effectively reduce thermal expansion coefficients to near zero which decouples heat from mechanical work.