At each point, a local temperature can be defined such that emission is given by Kirchhoff's law
where is emission, is absorption, and is the brightness given by the Planck law. A system is not in local thermodynamic equilibrium if the local kinetic (Maxwellian) temperature is not equal to the Planckian temperature of the radiation field.
Real atmospheres are not in local thermodynamic equilibrium since their effective infrared, ultraviolet, and visible brightness temperatures are different. Scattering is another non-local thermodynamic equilibrium effect.
