The scaling of the entropy production rate in a $\varphi^4$ model of Active Matter

Matteo Paoluzzi

Published 2021-09-03Version 1

Active $\varphi^4$ theories consider non-equilibrium terms that play an important role in describing active phase separation but are irrelevant, in the Renormalization Group sense, at the critical point. Their irrelevance makes the critical exponents the same of Ising universality class. Despite their irrelevance, they contribute with a non-trivial scaling of the entropy production rate at the critical point. However, active baths also constitute a continuous source of correlated noise. We consider the non-equilibrium dynamics of a non-conserved scalar field $\varphi$ (Model A) driven out-of-equilibrium by a persistent noise that is correlated on a finite time scale $\tau$. We perform the computation of the density of entropy production rate $\sigma$ and we study its scaling near the critical point. We found that the critical exponent of $\sigma$ is $\theta_\sigma=\nu(4-d)$. Above the upper critical dimension ($d=4$), where the critical point is the Gaussian fixed point, $\sigma$ vanishes faster than its natural scaling meaning that, although non-linear interactions are responsible for a non-vanishing $\sigma$ as soon as $\tau>0$, their contribution is negligible at criticality. Below the upper critical dimension, where the critical behavior is governed by the Wilson-Fisher fixed point, the non-linear $\varphi^4$ term causes a divergence in $\sigma$.