Thermalization of an electron-phonon system in a nonequilibrium state characterizedby 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-|Ap∝-(${\mathrm{T}}_{\mathrm{p}}$-${\mathrm{T}}_{\mathrm{e}}$) is replaced by a nonlinear rate Q-|Ap∝-(${\mathrm{T}}_{\mathrm{p}}^{\mathrm{q}}$-${\mathrm{T}}_{\mathrm{e}}^{\mathrm{q}}$), where q⩾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.