An extremum principle is developed for radiative transfer in a gray atmosphere by using a purely thermal example from Planck's (1913) work on heat radiation. Entropy is accounted for, as is Prigogine's (1947, 1967) theorem describing equilibrium as a thermodynamic state of minimal entropy. Attention is given to cases where thermodynamic equilibrium is not present. An isothermal black slab heated on one side is considered. The extremum is shown to be an unconstrained steady state and a minimum. The steady state is also demonstrated not to be equilibrium and a countering force on the slab is modeled. The discussion is extended to local thermodynamic equilibrium and to absorption by two isothermal gray slabs. Energy balance conditions for the latter are calculated in order to obtain a generalized extremum. Constraints on the equilibrium are found using irreversible thermodynamics. The problem of a gray atmosphere is then approached in terms of a continuum of isothermal slabs.