Systems with a constant heat flux with applications to radiative heat transport across nanoscale gaps and layers

We extend the statistical analysis of equilibrium systems to systems with a constant heat flux. This extension leads to natural generalizations of Maxwell–Boltzmann's and Planck's equilibrium energy distributions to energy distributions of systems with a net heat flux. This development provides a long needed foundation for addressing problems of nanoscale heat transport by a systematic method based on a few fundamental principles. As an example, we consider the computation of the radiative heat flux between narrowly spaced half-spaces maintained at different temperatures.