  In this paper we discuss the radiation equation of state $p=\rho/2$ in
(2+1)-dimensions. In (3+1)-dimensions the equation of state $p=\rho/3$ may be
used to describe either actual electromagnetic radiation (photons) as well as a
gas of massless particles in a thermodynamic equilibrium (for example
neutrinos). In this work it is shown that in the framework of (2+1)-dimensional
Maxwell electrodynamics the radiation law $p=\rho/2$ takes place only for plane
waves, i.e. for $E = B$. Instead of the linear Maxwell electrodynamics, to
derive the (2+1)-radiation law for more general cases with $E \neq B$, one has
to use a conformally invariant electrodynamics, which is a 2+1-nonlinear
electrodynamics with a trace free energy-momentum tensor, and to perform a
volumetric spatial average of the corresponding Maxwell stress-energy tensor
with its electric and magnetic components at a given instant of time $t$.
