Statistical mechanics of an active wheel rolling in circles

Summary

Researchers introduced a simple granular system consisting of a vertically vibrated toroid, which shows chiral active motion propelling itself along circular trajectories. The study reveals a sequence of spontaneous symmetry breaking leading to distinct statistics, including a temporal evolution involving stochastic resetting.

Highlights

• The system consists of a vertically vibrated toroid, about half a centimeter in diameter and a millimeter in thickness.
• The particle's dynamics change from localized and intermittent random motion to persistent ordered motion along circular orbits as the vibration amplitude increases.
• The mean squared displacement (MSD) shows a slope of 2, characteristic of ballistic motion, and transitions to a slope of 1, characteristic of diffusive motion.
• The speed distribution extends to a larger speed range with a new peak emerging at higher vibration amplitudes.
• The velocity components show Laplacian distribution due to stochastic resetting.
• The system exhibits chiral activity with a probability distribution of the radius of curvature showing power-law behavior.
• The study establishes the vibrated wheel as a three-state chiral active system.

Key Insights

• The researchers' system is unique in that it achieves chiral active motion without explicit asymmetries in the particle design, instead relying on spontaneous symmetry breaking.
• The study demonstrates the emergence of stochastic resetting in the particle's dynamics, which is a subject of intense recent research.
• The system's statistical mechanics are distinctly different from other systems where activity and chirality arise from explicit asymmetries in the particle design.
• The researchers observe three kinetic states: two active chiral ones with right-circular and left-circular orbits, and a passive achiral one.
• The system's temporal evolution shows stochastic resetting, which is one of the hallmarks of the stochastic resetting process.
• The study provides a model experimental system to study the non-equilibrium statistical mechanics and stochastic thermodynamics of chiral active systems.
• The simple and robust self-propulsion mechanism can find applications in designing locomotion strategies in modern robotics.

Mindmap

Citation

Sharma, S., & Kumar, D. (2024). Statistical mechanics of an active wheel rolling in circles (Version 1). arXiv. https://doi.org/10.48550/ARXIV.2412.18159