Abstract The Earth can be viewed as a complex nonequilibrium system that exchanges primarily radiative energy and entropy with its surroundings. The energy balance equation provides an important constraint on the distribution of outgoing radiation since the net global energy exchange will be close to zero over some appropriately long time interval. The entropy of the radiation does not obey such a conservation law, instead the outgoing entropy irradiance is much greater than the incoming amount. Most of this increase in the entropy flux is due to the conversion of short wavelength photons from a small solid angle into longer wavelength photons that are emitted nearly isotropically. If the entropy irradiance is calculated with sufficient precision, it is possible to relate it to the distribution of radiative temperature over position, direction, wavenumber and polarization spaces. The radiative entropy decreases as the variance of the radiative temperature distribution increases over any of the four spaces...