Nonlocal two-temperature model: Application to heat transport in metals irradiated by ultrashort laser pulses

Extended two-temperature models with allowance for time (relaxation) and space nonlocal effects have been developed to describe, in particular, heat conduction in metals under ultrashort laser irradiation, which overheats the electron gas in comparison with the lattice leading to energy exchange between them. The time nonlocal effects arise when the electron gas is driven out of local (thermal) equilibrium, whereas the space nonlocal effects begin to be significant when the spatial extent of the temperature gradient is comparable with the mean-free path of the heat carrier. The electron-lattice energy exchange as well as the space-time nonlocal effects in the electron gas leads to a hierarchy of space-time nonlocal heat conduction equations for the electron and lattice temperatures, which are partial differential equation of higher order in comparison with the classical heat conduction equation. The models presented here may be used in combination with molecular dynamic and phase-field approaches.