Max Delbruck Prize in Biological Physics (2021): Equilibrium to off-equilibrium crossover in homogeneous active matter near its ordering transition

In active matter systems as flocks and swarms, off-equilibrium effects are due to the interplay between the effective alignment interaction and the dynamical rewiring of the interaction network, which gives rise to a non-Hamiltonian coupling between density and velocity, as a consequence of which heterogeneous density structures may emerge. It therefore seems that the coupling between density and velocity stays at the very core of off-equilibrium active matter.

In fact, active motion and density-velocity coupling are related but distinct phenomena. The fact that particles continuously enter and exit the alignment interaction range of any given particle can violate detail balance also in a system with homogeneous density. We may therefore ask: Can activity lead to relevant off-equilibrium dynamics even without any significant coupling between velocity and density, and therefore in absence of heterogeneous density structures?

To address this question I will consider the crossover between equilibrium and off-equilibrium dynamical universality classes in homogeneous active matter near its ordering transition. Starting from the incompressible hydrodynamic theory of swarms, I will show that increasing the activity leads to a renormalization group (RG) crossover between the equilibrium ferromagnetic fixed point, with dynamical critical exponent z~2, and the off-equilibrium active fixed point, with z~1.7. I will present simulations of the compressible Vicsek model in the homogeneous near-ordering regime and find that critical slowing down indeed changes with activity, displaying two exponents that are in good agreement with the RG prediction.

The equilibrium-to-off-equilibrium crossover is ruled by a characteristic length scale beyond which active dynamics takes over. Such length scale is smaller the larger the activity, suggesting the existence of a general trade-off between activity and system's size in determining the dynamical universality class of active matter.