Equipartition of rotational and translational energy in a dense granular gas

TL;DR

This study demonstrates that in a dense, driven 2D granular gas, kinetic energy is equally partitioned among translational and rotational degrees of freedom, with velocity distributions resembling those in equilibrium systems.

Contribution

It provides experimental evidence of energy equipartition in a dense granular gas and shows that statistical mechanics concepts can apply to non-equilibrium systems.

Findings

Energy is equally divided between translational and rotational motions.

Velocity distributions have exponential tails and scale with particle size.

The system obeys a granular Boyle's Law with a van der Waals-like equation of state.

Abstract

Experiments quantifying the rotational and translational motion of particles in a dense, driven, 2D granular gas floating on an air table reveal that kinetic energy is divided equally between the two translational and one rotational degrees of freedom. This equipartition persists when the particle properties, confining pressure, packing density, or spatial ordering are changed. While the translational velocity distributions are the same for both large and small particles, the angular velocity distributions scale with the particle radius. The probability distributions of all particle velocities have approximately exponential tails. Additionally, we find that the system can be described with a granular Boyle's Law with a van der Waals-like equation of state. These results demonstrate ways in which conventional statistical mechanics can unexpectedly apply to non-equilibrium systems.