Infinite ergodic index of the ehrenfest wind-tree model

TL;DR

This paper proves that for typical configurations of the Ehrenfest wind-tree model, the dynamics exhibit infinite ergodic index in almost every direction, implying strong statistical mixing properties.

Contribution

It establishes the infinite ergodic index for the wind-tree model configurations, advancing understanding of its ergodic and mixing behavior.

Findings

Typical configurations have infinite ergodic index in almost every direction

Initial parallel particles' directions decorrelate over time

Supports ergodic theorems with implications for particle dynamics

Abstract

The set of all possible configurations of the Ehrenfest wind-tree model endowed with the Hausdorff topology is a compact metric space. For a typical configuration we show that the wind-tree dynamics has infinite ergodic index in almost every direction. In particular some ergodic theorems can be applied to show that if we start with a large number of initially parallel particles their directions decorrelate as the dynamics evolve answering the question posed by the Ehrenfests.