The steady state of flow equilibrium of a body, absorbing incident radiation of arbitrary frequency distribution and emitting either temperature or luminescent radiation, is determined by the condition of an extremal rate of entropy production. Without any constraints on the emission process, entropy production is maximal if the body emits temperature radiation, i.e. with zero chemical potential, with the temperature of its phonon system regardless of the incident radiation. This is the Planck case. Luminescent bodies deviate from this behaviour. Their emission is subject to additional constraints. The result of two constraints is discussed in detail. Firstly, when subjected exclusively to the constraint that the total emitted energy current is any given fraction of the total absorbed energy current, a body is a temperature radiator. Secondly, when subjected to the constraint that the total emitted photon current is a given fraction (quantum efficiency) of the total absorbed photon current, a body is a luminescent radiator, characterised by a frequency-independent chemical potential of its excitations and of the emitted radiation. For the determination of the spectral intensity distribution of the radiation leaving the excited body, the absorption, reflection and transmission of the body are taken into account, Kirchhoff's law is generalised to the flow equilibrium state with non-zero entropy production in both the temperature and luminescent radiators.
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Würfel et al. (1985) studied this question.
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