Stealth entropy production in active field theories near Ising critical points

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.