A statistical physics viewpoint on the dynamics of the bouncing ball

TL;DR

This paper models the chaotic bouncing ball system using statistical physics, analyzing energy exchanges and reservoir dynamics, and explores fluctuation relations in energy injection.

Contribution

It introduces a novel statistical physics framework for understanding the energy dynamics of a chaotic bouncing ball system with aperiodic vibrations.

Findings

Coupling between ball and plate modeled as dissipative and energy injection processes.

Reservoir dynamics follow a 'blurred' detailed balance.

Injection statistics obey fluctuation relations.

Abstract

We study from a statistical physics perspective the dynamics of a bouncing ball maintained in a chaotic regime thanks to collisions with a plate experiencing an aperiodic vibration. We analyze in details the energy exchanges between the bead and the vibrating plate, and show that the coupling between the bead and the plate can be modeled in terms of both a dissipative process and an injection mechanism by an energy reservoir, where the dynamics of the reservoir obeys only a 'blurred' version of detailed balance. An analysis of the injection statistics in terms of fluctuation relation is also provided.