Heat transport in superionic materials via machine-learned molecular dynamics

Precise modeling and understanding of heat transport in the superionic phase are of great interest. Although simulations combining Green-Kubo (GK) molecular dynamics with machine-learned potentials (MLPs) stand as a promising approach, substantial challenges remain due to the crucial impact of atomic diffusion. Here, we first show that the thermal conductivity (${\kappa}$) of superionic materials calculated via conventional GK integral of the energy flux varies notably with the MLP model. Subsequently, we highlight that reliable, model-independent $\kappa$ values can be obtained by applying Onsager's reciprocal relations to correctly capture the coupled heat and mass transport. Remarkably, an anomalously invariant $\kappa$ can be observed over a wide temperature range, distinct from the characteristic trends in traditional crystals and glasses. In addition, we illustrate that conventional $\kappa$ decompositions into kinetic, potential, and cross terms suffer from ambiguities in the physical interpretation, despite their mathematical rigor. Finally, we propose a criterion for the necessity of the Onsager correction and reveal the underlying mechanism as a competition between thermally and chemically driven ion fluxes.