Entropic tightening of knots in granular chains under vibration.

Knot cores in vibrating granular chains spontaneously tighten across different knot types, with steady-state knot-size statistics captured by equilibrium knot-tube theory and simulations.

• Why it matters: Directly tracking how knots evolve in long chains is hard, and it is unclear whether knot tightening can be explained quantitatively outside equilibrium.
• What they did: The team visualized knot dynamics in granular chains on vibrating platforms and used knot-tube theory plus Monte Carlo simulations to model entropic escape from the core.
• The result: State-transition analyses and time-reversal asymmetry indicate a weak detailed-balance violation when granular dynamics are projected onto knot size, supporting an entropic mechanism.

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