In this talk I will discuss the evolution of the possible descriptors of the thermal conductivity of materials. Despite recent progress on the ab initio calculations of the thermal transport based on either Boltzmann Equation for phonons or direct ab-initio molecular dynamics, such calculations remain time consuming. Therefore appropriate descriptors that permit faster calculation will be beneficial for exploring chemical composition space. Possible candidates will be reviewed and discussed based on the complete solution of the Boltzmann transport equation for phonons.
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