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

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.

💡 Research Summary

In this work the authors investigate how translational and rotational inertia affect motility‑induced phase separation (MIPS) in a two‑dimensional system of active rigid dumbbells. Each dumbbell consists of two identical beads linked at a fixed distance; a constant self‑propulsion force acts along the bond axis. The dynamics are governed by under‑damped Langevin equations that retain both the mass m (translational inertia) and the moment of inertia I (rotational inertia). The key dimensionless parameters are the Péclet number Pe (ratio of active force to thermal noise), the inertia number Γ = m f_a / (γ²σ) (ratio of momentum relaxation time to the active time scale), and the normalized rotational inertia I/(mσ²).

Simulations are performed at high activity (Pe = 100) and very low ambient temperature (k_B T = 0.01 ε) so that activity dominates. By varying the friction coefficient γ (hence Γ) while keeping I fixed, the authors explore the effect of translational inertia. Conversely, by varying I at fixed γ they probe rotational inertia. The system exhibits classic MIPS: dense liquid‑like clusters coexist with a dilute gas‑like background. However, unlike overdamped active particles where kinetic temperatures are equal in both phases, the under‑damped dumbbells develop four distinct kinetic temperatures: translational T_trans and rotational T_rot each measured separately in the dense and dilute phases.

Key findings:

1. Translational inertia (Γ) amplifies the temperature difference in translational motion. As Γ increases, the dilute phase’s T_trans rises sharply, while the dense phase’s T_trans changes only modestly. Consequently the dilute phase becomes “hotter” in translational kinetic energy than the dense phase. This is attributed to reduced collisional dissipation in the gas‑like region, allowing particles to retain higher velocities when inertia is large.

2. Rotational inertia (I) influences translational temperature more than rotational temperature. Increasing I leads to a pronounced rise of T_trans in the dilute phase, while the dense phase remains almost unchanged, thereby widening the translational temperature gap. The authors link this to an increase of the effective persistence time of active dumbbells when rotational inertia is large; particles travel more persistently before reorienting, gaining translational kinetic energy.

3. Rotational temperature differences are largely insensitive to I. Even though activity generates torques during collisions, a larger moment of inertia suppresses the resulting rotational motion, leaving T_rot in both phases almost constant as I varies. The dense phase shows only a weak increase of T_rot with Γ, reflecting that rotational degrees of freedom experience limited spatial rearrangement compared with translation.

4. Structural metrics (local packing fraction peaks) remain essentially unchanged when Γ or I are varied. The density contrast between the coexisting phases is stable, indicating that the observed temperature gradients stem from kinetic energy dissipation mechanisms rather than from changes in the static structure of the phases.

The paper thus uncovers a novel nonequilibrium thermodynamic landscape: four kinetic temperatures coexist, and their hierarchy can be tuned independently by adjusting translational inertia, rotational inertia, and activity strength. The mechanism is a subtle interplay of activity‑driven collisions, momentum relaxation, and torque generation.

Implications are twofold. First, the results demonstrate that the equipartition‑like equality of kinetic temperatures, a hallmark of overdamped active matter, breaks down when inertia is non‑negligible, especially for anisotropic particles where translation and rotation are coupled. Second, by controlling inertia (e.g., through particle mass distribution or shape) one can engineer temperature gradients without external heat baths, opening pathways for designing macroscopic active engines, directed transport, or energy‑harvesting devices in granular or robotic active matter.

Overall, the study provides a comprehensive computational analysis of how translational and rotational inertia shape the kinetic temperature landscape of MIPS in active dumbbells, offering fresh insights into nonequilibrium statistical physics and suggesting practical routes for temperature‑gradient manipulation in real‑world active systems.