Translational and Rotational Temperature Difference in Coexisting Phases of Inertial Active Dumbbells

TL;DR

Motility-induced phase separation (MIPS) in inertial, anisotropic active matter is studied using 2D underdamped dumbbells. The work reveals a four-temperature landscape across coexisting dense and dilute phases, with translational and rotational temperatures ($T_{\mathrm{trans}}$ and $T_{\mathrm{rot}}$) differing between phases and from ambient temperature due to activity-driven energy input. The authors show that translational inertia (via $\Gamma$) and rotational inertia (via $I$) shape these gaps in distinct ways: increasing $\Gamma$ widens the $T_{\mathrm{trans}}$ gap, while increasing $I$ enhances persistence and raises the dilute-phase translational temperature; the rotational-temperature gap remains largely insensitive to $I$. These findings have implications for nonequilibrium thermodynamics of active matter and suggest experimental tests in systems where both translational and rotational inertia can be tuned.

Abstract

We investigate the effect of translational and rotational inertia on motility-induced phase separation in underdamped active dumbbells and identify the emergence of four distinct kinetic temperatures across the coexisting phases-unlike in overdamped systems. We find that the dilute, gas-like phase consistently exhibits a higher translational kinetic temperature than the dense, liquid-like phase, with this difference amplified by increasing the rotational inertia. Rotational kinetic temperatures display a similar trend, with the dense phase remaining colder than the dilute phase; however, in this case the temperature difference grows with translational inertia and activity, while becoming practically independent of rotational inertia. This counterintuitive behavior arises from the interplay of activity-driven collisions with both translational and rotational inertia in the coexisting phases. Our results highlight the critical role of translational and rotational inertia in shaping the kinetic temperature landscape of motility-induced phase separation and offer new insights into the nonequilibrium thermodynamics of active matter.

Figures (5)

• Figure 1: Schematic illustration of active dumbbells. Induced by a spontaneous fluctuation, a subset of dumbbells moves toward a common center, leading to the formation of a cluster. Arrows indicate the instantaneous self-propulsion directions.
• Figure 2: Panels (a), (b), (c), and (d) show snapshots from our simulations in the steady state. Panels (a) and (c) are colored according to the translational kinetic energy, $\frac{1}{2}M_\mathrm{com}\left<V_\mathrm{com}^2\right>$ of individual dumbbells, while panels (b) and (d) are colored according to the rotational kinetic energy, $\frac{1}{2}I\left<\omega_\mathrm{com}^2\right>$, both expressed in units of $\epsilon$. All simulations are performed at area fraction $\phi=0.4$ with $N=16129$ dumbbells. The parameters for (a) and (b) are $\text{Pe}=100$, $\Gamma=0.01$ and $I/m\sigma_d^2=0.5$ and the same for (c) and (d) are $\text{Pe}=100$, $\Gamma=5.06$ and $I/m\sigma_d^2=1$.
• Figure 3: Panels (a), (b), and (c) show the translational kinetic temperature, rotational kinetic temperature, and the local packing fraction peak value in the coexisting dense and dilute phases of active dumbbells as functions of the dimensionless translational inertia $\Gamma$ for $\text{Pe}=100$, $I/m\sigma_d^2=0.5$ and $\phi=0.4$. The ambient temperature, $T=0.01$ is indicated by the upright triangle on the $T_{\mathrm{trans}}$-axis in (a) and the inverted triangle on the $T_{\mathrm{rot}}$-axis in (b).
• Figure 4: Panels (a), (b), and (c) show the translational kinetic temperature, rotational kinetic temperature, and the local packing fraction peak value in the coexisting dense and dilute phases of active dumbbells as functions of the dimensionless rotational inertia $I/m\sigma_d^2$ for $\text{Pe}=100$, $\Gamma=5.06$ and $\phi=0.4$. The ambient temperature, $T=0.01$ is indicated by the upright triangle on the $T_{\mathrm{trans}}$-axis in (a) and the inverted triangle on the $T_{\mathrm{rot}}$-axis in (b).
• Figure 5: Panels (a) and (b) show the translational kinetic temperature and rotational kinetic temperature in the coexisting dense and dilute phases of active dumbbells as functions of the dimensionless Peclet number $\mathrm{Pe}$ for $\Gamma=5.06$, $I/m\sigma_d^2=0.5$ and $\phi=0.4$.