 Radiation entropy from the first law

For $u=A{T}^4$, $P=u/3$ and physical cell volume $R^3$, the first law integrates to $S=4u{R}^3/(3T)$ with zero chemical potentials and a fixed relativistic species set. Entropy conservation through a species threshold instead requires tracking $g_{\ast s}{T}^3{R}^3$.