Viscosity and effective temperature of an active dense system of self-propelled particles

TL;DR

This paper develops a nonequilibrium theoretical framework for active dense systems of self-propelled particles, introducing an effective temperature that captures their dynamic behavior and relates to viscosity changes.

Contribution

It presents a novel nonequilibrium theory for active dense systems, defining an evolving effective temperature and analyzing its impact on viscosity.

Findings

Effective temperature saturates at long times.

Transition time scales with persistence time as τ_p^0.85.

Viscosity diverges near the effective temperature threshold.

Abstract

We obtain a nonequilibrium theory for a simple model of a generic class of active dense systems consisting of self-propelled particles with a self-propulsion force, $f_0$, and persistence time, $\tau_p$, of their motion. We consider two models of activity and find the system is characterized by an evolving effective temperature $T_{eff}(\tau)$, defined through a generalized fluctuation-dissipation theorem. $T_{eff}(\tau)$ is equal to the equilibrium temperature at very short time $\tau$ and saturates to $T_{eff}=T_{eff}(\tau\to\infty)$ at long times; The transition time $t_{trans}$ when $T_{eff}(\tau)$ goes to the long-time limit depends on $\tau_p$ alone and $t_{trans}\sim \tau_p^{0.85}$ for both models. $f_0$ reduces the viscosity with increasing activity, $\tau_p$ on the other hand, may increase or decrease viscosity depending on the details of how the activity is included. However, as a function of $T_{eff}$, viscosity shows the same behavior for different models of activity and $\eta\sim (T_{eff}-T)^{-\gamma}$ with $\gamma=1.74$. Our theory gives reasonable agreement when compared with experimental data and is consistent with several experiments on diverse systems.