Following Max Planck (1914), a radiative field is often described in terms of specific radiative intensity, which is a function of each geometrical point in a space region, at an instant of time. This is slightly different from Prevosts mode of definition, which was for regions of space. It is also slightly conceptually different from Prevosts definition: Prevost thought in terms of bound and free heat while today we think in terms of heat in kinetic and other dynamic energy of molecules, that is to say heat in matter, and the thermal photon gas. A detailed definition is given by R. M. Goody and Y. L. Yung (1989). They think of the interconversion between thermal radiation and heat in matter. From the specific radiative intensity they derive , the monochromatic vector flux density of radiation at each point in a region of space, which is equal to the time averaged monochromatic Poynting vector at that point (D. Mihalas 1978 on pages 9–11). They define the monochromatic volume-specific rate of gain of heat by matter from radiation as the negative of the divergence of the monochromatic flux density vector; it is a scalar function of the position of the point:
They define (pointwise) monochromatic radiative equilibrium by
: at every point of the region that is in radiative equilibrium.
They define (pointwise) radiative equilibrium by
: at every point of the region that is in radiative equilibrium.
This means that, at every point of the region of space that is in (pointwise) radiative equilibrium, the total, for all frequencies of radiation, interconversion of energy between thermal radiation and energy content in matter is nil(zero). Pointwise radiative equilibrium is closely related to Prevost's absolute radiative equilibrium.
D. Mihalas and B. Weibel-Mihalas (1984) emphasise that this definition applies to a static medium, in which the matter is not moving. They also consider moving media.