Fluctuation-based evaluation of thermal conductivity using deviational phonon Monte Carlo simulations
We develop a fluctuation based Monte Carlo method for evaluating thermal conductivity within the phonon Boltzmann transport equation (BTE) framework. Starting from the energy based variance reduced formulation of the BTE, we derive a relation between the spatial spreading of deviational phonon energy and the macroscopic heat conduction equation. The resulting formulation expresses thermal conductivity in terms of the mean square displacement of deviational phonon particles, without imposing thermal reservoirs. Consequently, thermal conductivity along multiple directions can be evaluated from a single simulation. The method is demonstrated for crystalline silicon at room temperature in bulk, square nanowires, and anisotropic polycrystalline nanostructures. The calculated thermal conductivities agree with theoretical predictions, including the size dependence induced by phonon boundary scattering and the mode-resolved contributions. For anisotropic polycrystalline structures, the method simultaneously resolves the directional thermal conductivities and captures their dependence on grain morphology. These results demonstrate the validity of the proposed fluctuation-based approach for evaluating thermal conductivity across different transport regimes and structural configurations.