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.
Highlights
Entropy is a quantity as fundamental as energy, the analysis of the entropy content in radiation is not fully exploited yet
The importance of the radiation entropy in the scattering process is a field in current development, and the ideas are masterly investigated in ref. 4
Further research is needed in this field, and this paper provides a methodology to characterize the radiation entropy production in the atmosphere, an important topic in climate sciences
Summary
After straightforward arithmetical transformations, the solution is as simple as the expression for the energy and the calculations can be recycled, saving loads of computer time and attaining the best accuracy possible With this expression it is possible to compute the entropy fractional emissive power, in particular the Median of the spectral entropy distribution, as well as any other percentile. The polylogarithmic term of Equation 11 when the whole spectrum is studied is π4 , and the total flux is given by the well known Stefan-Boltzmann’s law σT4. Dividing Equation 11 by th1e5 total energy flux σT4, the normalized fractional emissive power is determined as: IL,norm. The total flux is obtained when the whole spectrum is considered In such situation, the polylogarithmic term is reduced to 4π4 and the total entropy flux is given by the equivalent power norm4a5lized to the total entropy flux is given by: Stefan-Boltzmann’s law
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