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Related Experiment Video

Updated: Sep 8, 2025

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Entropy of timekeeping in a mechanical clock.

David Ziemkiewicz1

  • 1Institute of Mathematics and Physics, UTP University of Science and Technology, Aleje Prof. S. Kaliskiego 7, 85-789 Bydgoszcz, Poland.

Physical Review. E
|June 16, 2022
PubMed
Summary

This study investigates the grasshopper escapement clock, finding its precision correlates with entropy production, similar to nanoscale clocks. Force variations are modeled using Maxwell-Boltzmann statistics, and clock errors exhibit fractal properties.

Area of Science:

  • Physics
  • Mechanical Engineering
  • Thermodynamics

Background:

  • The grasshopper escapement is a unique clock mechanism.
  • Understanding its accuracy in noisy environments is crucial.
  • Existing research highlights connections between precision and entropy production in nanoscale and quantum clocks.

Purpose of the Study:

  • To investigate the dynamics of the grasshopper escapement mechanism.
  • To evaluate the clock's accuracy and precision under noisy conditions.
  • To explore the relationship between entropy production and clock precision.

Main Methods:

  • Analysis of grasshopper escapement dynamics.
  • Modeling force variations using Maxwell-Boltzmann statistics.
  • Comparison of clock error function with Brownian motion.

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Main Results:

  • Clock precision scales linearly with entropy production rate.
  • Force variations in the mechanism are accurately modeled by Maxwell-Boltzmann statistics.
  • Clock error exhibits fractal-like properties, comparable to Brownian motion.

Conclusions:

  • The grasshopper escapement's precision is linked to entropy production, aligning with findings in quantum and nanoscale clocks.
  • Maxwell-Boltzmann statistics effectively model inherent force variations.
  • The study validates numerical findings with experimental data, confirming the clock error's fractal nature.