One of the approaches for micro/nanoscale heat transfer in semiconductors and dielectric materials is to use the Boltzmann transport equation, which reduces to the equation of phonon radiative transfer under the relaxation time approximation. Transfer and generation of entropy are processes inherently associated with thermal energy transport, yet little has been done to analyze entropy generation in solids at length scales comparable with or smaller than the mean free path of heat carriers. This work extends the concept of radiation entropy in a participating medium to phonon radiation, thus, providing a method to evaluate entropy generation at both large and small length scales. The conventional formula for entropy generation in heat diffusion can be derived under the local equilibrium assumption. Furthermore, the phonon brightness temperature is introduced to describe the nature of nonequilibrium heat conduction. A diamond film is used as a numerical example to illustrate the distribution of entropy generation at the walls and inside the film at low temperatures. A fundamental knowledge of the entropy generation processes provides a thermodynamic understanding of heat transport in solid microstructures; this is particularly important for the performance evaluation of thermal systems and microdevices.

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