From single-particle to collective effective temperatures in an active fluid of self-propelled particles

Abstract

-We present a comprehensive analysis of effective temperatures based on fluctuationdissipation relations in a model of an active fluid composed of self-propelled hard disks. We first investigate the relevance of effective temperatures in the dilute and moderately dense fluids. We find that a unique effective temperature does not in general characterize the non-equilibrium dynamics of the active fluid over this broad range of densities, because fluctuation-dissipation relations yield a lengthscale-dependent effective temperature. By contrast, we find that the approach to a non-equilibrium glass transition at very large densities is accompanied by the emergence of a unique effective temperature shared by fluctuations at all lengthscales. This suggests that an effective thermal dynamics generically emerges at long times in very dense suspensions of active particles due to the collective freezing occurring at non-equilibrium glass transitions.Introduction. -Statistical mechanics provides a unified theoretical description of systems at thermal equilibrium in terms of the probability distribution over phase space, from which thermodynamic quantities such as temperature can be defined [1]. A similar framework is lacking for out-of-equilibrium systems for which the definition of a temperature remains an open issue [2]. Active matter formed by assemblies of living cells [3], bacteria [4], selfpropelled colloids [5][6][7][8] or grains [9,10], is a coherent class of non-equilibrium systems receiving increasing attention, because they raise fundamental issues and for potential applications in soft matter and biophysics [11,12]. A number of recent studies have addressed the question of whether "effective" thermodynamic concepts can be fruitfully applied to describe the phase behaviour and microscopic dynamics of active matter. This question is natural because if some mapping to an equilibrium situation exists, then the whole arsenal of equilibrium statistical mechanics becomes available for further theoretical treatment. In particular the definition of a non-equilibrium temperature [13][14][15][16][17][18], of an active pressure [8,19,20], of activityinduced interactions [8,21] and non-equilibrium free energies [22,23] have been investigated for self-propelled particles.

The nonequilibrium glassy dynamics of self-propelled particles

“…This broad conclusion implies that self-propelled particles undergo a glass transition at low effective temperatures or large densities accompanied by a complex time dependence of time correlation functions, locally-caged particle dynamics, and spatially heterogeneous dynamics very much as in thermal equilibrium. Despite the local injection of energy [14,35] and violations of equilibrium fluctuation-dissipation relations [24] the overall phenomenon studied here is therefore best described as a nonequilibrium glass transition [21]. While this conclusion is broadly consistent with the experimental reports of glassy dynamics in active materials, it remains to be understood whether the present model of self-propelled particles and the generic concept of a nonequilibrium glass transition are sufficient to account for experimental observations.…”

“…Along the way, we systematically study changes in the structural and dynamic properties of the system. Overall, our results suggest that activity induces profound changes in the detailed structure of the nonequilibrium fluid, but the glassy dynamics of active particles, despite taking place far from thermal equilibrium [21,24], is qualitatively similar to that observed in equilibrium fluids. We find that active particles display slow dynamics, complex time dependencies of relaxation functions, and spatially heterogeneous dynamics with only quantitative differences between equilibrium and active systems.…”

Emergent behavior in active colloids

“…For example, as already discussed in section 4.3.1, motility-induced phase separation can sometimes be addressed with an effective free energy [40] and the activity-induced collisions of the particles mapped to an effective attraction potential [319]. Another example is the controversial discussion about the concept of effective temperature in active particle systems [71,184,[399][400][401][402]. Indeed, sometimes one can assign an effective temperature to the stochastic motion of active colloids.…”

Mode-coupling theory for active Brownian particles

“…At high densities, such systems (with suitable size polydispersity) are known from simulation to form glasses [18][19][20], as do related active-particle models [5,16,[21][22][23][24][25].…”