  A candidate for a consistent steady state thermodynamics is constructed for a
radiation field in vacuum sandwiched by two black bodies of different
temperatures. Because of the collisionless nature of photons, a steady state of
a radiation field is completely determined by the temperatures of the two black
bodies. Then the zeroth, first, second and third laws can be extended to steady
states, where the idea of local steady states plays an important role for the
system whose geometrical shape is anisotropic and inhomogeneous. The
thermodynamic formalism presented in this paper does not include an energy flux
as a state variable. This is consistent with the notable conclusion by "C.
Essex, Adv. Thermodyn. 3 (1990) 435; Planet. Space. Sci. 32 (1984) 1035" that,
contrary to the success in the irreversible thermodynamics for dissipative
systems, a nonequilibrium radiation field does not obey the bilinear formalism
of the entropy production rate using an energy flux and its conjugate force.
Though the formalism given in this paper may be unique to a radiation field, a
nonequilibrium order parameter of steady states of a radiation field is
explicitly defined. This order parameter denotes that the geometrical shape of
the system determines how a steady state is far from an equilibrium. The higher
the geometrical symmetry is, the more distant the steady state is.
