Effective temperature of active matter

We follow the dynamics of an ensemble of interacting self-propelled motorized particles in contact with an equilibrated thermal bath. We find that the fluctuation-dissipation relation allows for the definition of an effective temperature that is compatible with the results obtained using a tracer particle as a thermometer. The effective temperature takes a value which is higher than the temperature of the bath, and it is continuously controlled by the motor intensity.

Figure 1

(Color online) The static structure factor $S\left(Q\right)$ for a system in equilibrium and driven out of equilibrium by motors with $f^M=50\%\overline{F}$.

Figure 2

(Color online) Main panel: the incoherent intermediate scattering function at $Q=Q_{\max }$ for motor force intensities given in the key. Data are shown as a function of simulation time measured in molecular dynamics integration steps (MDS). Inset: the dependence of the $\alpha$ relaxation time on the strength of the motor forces with an exponential fit ${\tau }_{\alpha }\sim A\text{exp}-\left(f^M/f^0\right)$ with $f^0\simeq 0.90$.

Figure 3

(Color online) Parametric representation of the fluctuation dissipation relation for passive and active matter. The strengths of the applied forces are given in the key.

Figure 4

(Color online) Main panel: probability distribution function of the velocity $v$ of different tracers with masses $m_{\text{tr}}$ given in the key. The motor force intensity is $f^M=60\%\overline{F}$. The solid lines are fits to the Gaussian form (3). Inset: $T_{\text{eff}}$ as function of $m_{\text{tr}}$ as obtained from the Gaussian fits to the data-points in the main panel.

Figure 5

(Color online) Effective temperature obtained from response-correlation and massive tracer calculations for different motor force intensities.