General gauge symmetry in the theory and simulation of heat transport in nonsolid materials

Abstract

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 the transport coefficient thermodynamically emerges 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, in which, by construction, the same heat conductivity \ensuremath{\kappa} is ensured regardless of the choice of atomic energies. This approach is analogous to the way in which general covariance (``all coordinate systems are equivalent'') is used to construct the general theory of relativity. 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. The gauge theory not only lays a firm foundation of the Green-Kubo formalism of heat transport, but also offers a variational method for calculating \ensuremath{\kappa} of nonsolid materials, as demonstrated using machine learning inferred atomic energies of ${\mathrm{Cu}}_{2}\mathrm{S}$, an intriguing solid-liquid hybrid material for thermoelectrics.