Thermalization of an electron-phonon system in a nonequilibrium state characterized by fractal distribution of phonon excitations

The thermalization of an electron-phonon system in a nonequilibrium state characterized by a fractal distribution of phonon excitations is calculated in a novel way, which takes into account the unusual, inverse power-law type distribution of phonon energies. The calculations are done from the first principles, based on a nonequilibrium statistical operator combined with the recently proposed generalized, nonextensive thermostatistics. As a result the usual linear (Newtonian) energy transfer rate (Q) over dot proportional to - (T-p-T-e) is replaced by a nonlinear rate (Q) over dot proportional to - (T-p(q)-T-e(q)), where q greater than or equal to 1 is related to the fractality of the excitation energy distribution. Consequences of this result for a thermal relaxation of the nonequilibrium phonon system are discussed.