  Several attempts to construct the thermodynamical formulation for
non-equilibrium steady states have been made along the context by Oono and
Paniconi, called the steady state thermodynamics (SST). In this paper we study
the SST for radiation field. Consider a cavity in a large black body, and put
an another black body in it. Let the temperature of the outer black body be
different from that of the inner one, and keep their temperatures unchanged.
Then the radiation field between the black bodies are retained in a
non-equilibrium steady state with a stationary energy flow. (The inner black
body may be considered as a representative of a black hole with the Hawking
radiation, and the cavity be the universe including the black hole.) According
to the total momentum carried by photons par a unit time in passing through a
virtual unit area, the pressure for the SST is defined. Then, taking this
pressure as the basis, we propose the definitions of steady state thermodynamic
functions and state variables satisfying the plausible properties: the
convexity/concavity of thermodynamic functions, the intensivity/extensivity of
state variables, the Gibbs-Duhem relation and the Legendre transformation among
thermodynamic functions.
