The Green-Kubo theory of atomic heat transport relies on the ambiguous decomposition of total energy into “atomic” energies of individual atoms. The challenge is to understand how measurable quantities such as heat conductivity emerge from such ill-defined atomic energies. Here, we show that a simple symmetry principle for atomic energies (that is, “all possible ways of distributing energy among atoms are equivalent”) dictates the general theory of atomic heat transport. To this end, we define atomic gauges that regulate the redundant degrees of freedom in atomic energies. The atomic gauge symmetry then uniquely determines the gauge-invariant form of macroscopic energy transfer, which is identified as heat. As a result, arbitrary choices of atomic energies lead to the same heat conductivity 𝜅. The gauge theory not only lays a firm foundation of the Green-Kubo formalism of heat transport, but also offers a novel variational method for calculating 𝜅 of nonsolid materials. The developed concepts are numerically demonstrated using machine-learning driven molecular dynamics simulations of solid-liquid hybrid phases of Cu2S.
Host: Prof. Ji-Sang Park