  Many physical properties of metals can be understood in terms of the free
electron model, as proven by the Wiedemann-Franz law. According to this model,
electronic thermal conductivity ($\kappa_{el}$) can be inferred from the
Boltzmann transport equation (BTE). However, the BTE does not perform well for
some complex metals, such as Cu. Moreover, the BTE cannot clearly describe the
origin of the thermal energy carried by electrons or how this energy is
transported in metals. The charge distribution of conduction electrons in
metals is known to reflect the electrostatic potential (EP) of the ion cores.
Based on this premise, we develop a new methodology for evaluating
$\kappa_{el}$ by combining the free electron model and non-equilibrium ab
initio molecular dynamics (NEAIMD) simulations. We demonstrate that the kinetic
energy of thermally excited electrons originates from the energy of the spatial
electrostatic potential oscillation (EPO), which is induced by the thermal
motion of ion cores. This method directly predicts the $\kappa_{el}$ of pure
metals with a high degree of accuracy.
