How Far from Equilibrium Is Active Matter?

Active matter systems are driven out of thermal equilibrium by a lack of generalized Stokes-Einstein relation between injection and dissipation of energy at the microscopic scale. We consider such a system of interacting particles, propelled by persistent noises, and show that, at small but finite persistence time, their dynamics still satisfy a time-reversal symmetry. To do so, we compute perturbatively their steady-state measure and show that, for short persistent times, the entropy production rate vanishes. This endows such systems with an effective fluctuation-dissipation theorem akin to that of thermal equilibrium systems. Last, we show how interacting particle systems with viscous drags and correlated noises can be seen as in equilibrium with a viscoelastic bath but driven out of equilibrium by nonconservative forces, hence providing energetic insight into the departure of active systems from equilibrium.

Figure 1

AOUPs interacting via the potential (2) exhibit MIPS in a 2D box of size $L$ with periodic boundary conditions. Parameters: $A=100$, $a=2$, $N=10000$, $L=250$, $D=100$, $\tau =20$.

Figure 2

Parametric plot between the susceptibility $\chi (t)$ and the correlation function $C_{\text{eff}}(t)=⟨x_i(t)[x_i(t)-x_i(0)]+{\tau }^2{\dot{x}}_i(t)[{\dot{x}}_i(t)-{\dot{x}}_i(0)]⟩$ for $N$ AOUPs interacting via the potential (2). The particles experience a stiff harmonic potential when they try to exit a box of linear size $L$. Parameters: $L=30$, $N=720$, $\tau =0.01$, $A=20$. Blue, red, and cyan dots correspond to $T=2$, 1, 0.25 and the solid line correspond to the theoretical prediction (19).