A ubiquitous formula for thermal conductivity applicable for liquids, polymers and amorphous solids

The microscopic mechanism of thermal transport in liquids and amorphous solids has been an outstanding problem for a long time. There have been several different approaches to explain the thermal conductivities for these systems, for example, the Bridgman's formula for simple liquids, the concept of the minimum thermal conductivity for amorphous solids, and the thermal resistance network model for amorphous polymers. Here, we present a ubiquitous formula to explain the thermal conductivities of liquids and amorphous solids in a unified way. The calculated thermal conductivities using this formula without fitting parameters are in excellent agreement with the experimental data for these systems. Our formula is not only providing detailed implications on microscopic mechanisms of heat transfer in these systems, but also solves the discrepancies between existing formulae and experimental data.