Entropy of radiation: The unseen side of light

Abstract

Despite the fact that 2015 was the international year of light, no mention was made of the fact that radiation contains entropy as well as energy, with different spectral distributions. Whereas the energy function has been vastly studied, the radiation entropy distribution has not been analysed at the same speed. The Mode of the energy distribution is well known -Wien's law- and Planck's law has been analytically integrated recently, but no similar advances have been made for the entropy. This paper focuses on the characterization of the entropy of radiation distribution from an statistical perspective, obtaining a Wien's like law for the Mode and integrating the entropy for the Median and the Mean in polylogarithms, and calculating the Variance, Skewness and Kurtosis of the function. Once these features are known, the increasing importance of radiation entropy analysis is evidenced in three different interdisciplinary applications: Defining and determining the second law Photosynthetically Active Radiation (PAR) region efficiency, measuring the entropy production in the Earth's atmosphere, and showing how human vision evolution was driven by the entropy content in radiation.