The thermodynamics of optical étendue

The concept of étendue is applied to the propagation of luminescent radiation, and to the transformation of such radiation in absorbing and luminescent media. Central to this analysis is the notion of étendue as a measure of the number of rays in the beam which permits the definition of entropy and transition to the formalism of statistical mechanics. When considered from the statistical viewpoint, étendue conservation along the path of a beam in clear and transparent media then implies the conservation of entropy. The changes in thermodynamic parameters of a beam upon absorption and re-emission can then be determined in terms of the corresponding changes resulting from the addition or removal of photons from the incident and emitted beam. The thermodynamic theory which follows gives the rate of entropy generation in this process. At moderate light intensities, the results resemble the thermodynamics of a two-dimensional gas. The formalism allows an extension to absorption/emission processes where a high-temperature incident light beam is transformed reversibly into low-temperature luminescent radiation, corresponding to a potential increase in the open-circuit voltage of a solar cell.