  We address the steady-state entropy production rate (EPR) of active scalar
$\phi^4$ theories, which lack time-reversal symmetry, close to a
phase-separation critical point. We consider both nonconserved (Model A) and
conserved (Model B) dynamics at Gaussian level, and also address the former at
leading order in $\epsilon = 4-d$. In each case, activity is irrelevant in the
RG sense: the active model lies in the same (dynamic Ising) universality class
as its time-reversible counterpart. Hence one might expect that activity brings
no new critical behavior. Here we show instead that the EPR per spacetime
correlation volume either remains finite or diverges on approach to
criticality. A nontrivial critical scaling for entropy production thus ranks
among universal dynamic Ising-class properties.
