  Planck's law of thermal radiation depends only on the temperature T and
emissivity $\varepsilon$. It is one of the most fundamental discoveries about
light-matter interaction that led to the development of quantum physics.
Another basic property of a body is its ability to absorb incoming light,
characterized by absorptivity $\alpha$. Kirchhoff's law of thermal radiation
equals these two properties at thermodynamic equilibrium, i.e.,
$\varepsilon$=$\alpha$. The generalized Planck's equation extends Kirchhof's
law out of equilibrium by scaling the absorptivity with the pump-dependent
chemical potential $\mu$, obscuring emissivity as a material property. Quantum
efficiency (QE) is a material property, defined out of equilibrium, describing
the statistics of absorption followed by emission of a photon. Both emissivity
and QE depend on the interplay between radiative and non-radiative rates. Here
we theoretically and experimentally demonstrate a prime equation for emissivity
as a material property in and out of equilibrium in the form of
$\varepsilon$=$\alpha$(1-QE), which at equilibrium is reduced to Kirchhoff's
law. Our work lays out the fundamental evolution of non-thermal emission with
temperature, which is critical for the development of lighting and energy
devices.
