Entropy production by decay of a dominant relic ($s_{+}/s_{-}=(1+{\rho }_{\varphi }/{\rho }_r{)}^{3/4}$)

At fixed scale factor and unchanged relativistic counts, instantaneous conversion of a relic into thermal radiation gives the displayed entropy-density enhancement. It exceeds one because the gas receives energy from outside its prior equilibrium sector. This does not contradict cosmological entropy conservation, whose source-free reversible assumptions fail during decay and thermalization.