Universality in grey-body radiance: Extending Kirchoff's law to the statistics of quanta

An ideal grey body is a macroscopic object with definite temperature which absorbs only a fraction of the radiation incident on it. Assuming that a grey body always emits in a mixed state, and that the radiation density matrix factors into matrices for the various frequency modes, we employ general arguments to derive the complete statistic of grey-body radiance elicited by incident radiation. These depend only on the temperature and the absorptivities for the various frequencies (hence are of universal form), and coincide with the statistics of black-hole radiance first derived a decade and a half ago.