Tuning nonequilibrium phase transitions with inertia

Abstract

In striking contrast to equilibrium systems, inertia can profoundly alter the structure of active systems. Here, we demonstrate that driven systems can exhibit effective equilibrium-like states with increasing particle inertia, despite rigorously violating the fluctuation-dissipation theorem. Increasing inertia progressively eliminates motility-induced phase separation and restores equilibrium crystallization for active Brownian spheres. This effect appears to be general for a wide class of active systems, including those driven by deterministic time-dependent external fields, whose nonequilibrium patterns ultimately disappear with increasing inertia. The path to this effective equilibrium limit can be complex, with finite inertia sometimes acting to accentuate nonequilibrium transitions. The restoration of near equilibrium statistics can be understood through the conversion of active momentum sources to passive-like stresses. Unlike truly equilibrium systems, the effective temperature is now density dependent, the only remnant of the nonequilibrium dynamics. This density-dependent temperature can in principle introduce departures from equilibrium expectations, particularly in response to strong gradients. Our results provide additional insight into the effective temperature ansatz while revealing a mechanism to tune nonequilibrium phase transitions.

Effect of speed fluctuations on the collective dynamics of active disks

“…3(b), in which the mean cluster size is seen to vary in a sigmoidal fashion as a function of the speed-oscillation frequency. A similar suppression of MIPS has also been observed by Omar et al 45 in a mixture of passive and active disks with periodic (and deterministic) speed fluctuation, as the frequency of speed fluctuation is increased. As shown in Fig.…”

Free and enclosed inertial active gas

“…Note that in the above expressions their initial conditions are set equal to zero, since in the steady state those are unimportant. After you apply the dot product to eqn (27) while keeping in mind the dummy variables in the integrals (t 0 , t 00 ), expressions eqn ( 4) and ( 6) naturally emerge. Take now eqn (5), as shown, there is a difficult integral to solve namely,…”

“…It is worth mentioning that there is a very recent theoretical work – which only includes translational inertial effects 27 and neglects rotational inertial effects in its Langevin equations – that finds the accumulation profile as a function of distance from a hard wall; the wall accumulation profile for a fully translational and rotational inertial active gas remains open. Fig.…”

“…Caprini et al 26 also numerically studied the effect of rotational inertia on MIPS and concluded that the increase of rotational inertia favors phase coexistence. Omar et al 27 proved that by increasing inertia in an interacting system, MIPS can be progressively eliminated and that an equilibrium crystallization is recovered. Some other active matter works (either interacting or not) but only considering the effect of translational inertia and using an ABP model have been published elsewhere.…”

Exact moments and re-entrant transitions in the inertial dynamics of active Brownian particles

“…However, inertial relaxation can be much slower for larger active elements, including insects to animals and macro-sized artificial active matter like active granular particles, vibrated rods, vibrobots, active spinners [19,[21][22][23][24][25][26][27], and as a result, can significantly influence the emergent dynamics [10-12, 18-20, 32-39]. For example, inertia can lead to the disappearance of motility-induced phase separation [40][41][42] observed for over-damped ABPs [43][44][45][46] and taming down of the instability in active nematics [47]. Moreover, it results in a distinctive impact on the dynamics of active phase separation [48], spatial velocity correlations [49], and entropy production [50].…”