Radiative equilibrium
Radiative equilibrium is one of the several requirements for thermodynamic equilibrium, but it can occur in the absence of thermodynamic equilibrium. There are various types of radiative equilibrium, which is itself a kind of dynamic equilibrium.
There are several types of radiative equilibrium.
An important early contribution was made by Pierre Prevost in 1791. Prevost considered that what is nowadays called the photon gas or electromagnetic radiation was a fluid that he called "free heat". Prevost proposed that free radiant heat is a very rare fluid, rays of which, like light rays, pass through each other without detectable disturbance of their passage. Prevost's theory of exchanges stated that each body radiates to, and receives radiation from, other bodies. The radiation from each body is emitted regardless of the presence or absence of other bodies.
Prevost in 1791 offered the following definitions (translated):
Absolute equilibrium of free heat is the state of this fluid in a portion of space which receives as much of it as it lets escape.
Relative equilibrium of free heat is the state of this fluid in two portions of space which receive from each other equal quantities of heat, and which moreover are in absolute equilibrium, or experience precisely equal changes.
Prevost went on to comment that "The heat of several portions of space at the same temperature, and next to one another, is at the same time in the two species of equilibrium."
Following 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 Prevost’s mode of definition, which was for regions of space. It is also slightly conceptually different from Prevost’s 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 Goody and 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 (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:
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