Late-time clusters of classical dipole-conserving fractons map to integrable polygonal billiards for compact interactions, to chaotic motion for non-compact interactions, and generic trajectories exhibit a Janus point with a bidirectional arrow of time.
Janus point
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Classical Fractons: Local chaos, global broken ergodicity and an arrow of time
Late-time clusters of classical dipole-conserving fractons map to integrable polygonal billiards for compact interactions, to chaotic motion for non-compact interactions, and generic trajectories exhibit a Janus point with a bidirectional arrow of time.