Entropy of timekeeping in a mechanical clock

TL;DR

This paper investigates the entropy-related dynamics of a grasshopper escapement clock, demonstrating how entropy production correlates with accuracy, modeling force variations statistically, and comparing error behavior to Brownian motion with experimental validation.

Contribution

It introduces a novel analysis of mechanical clock entropy, linking precision to entropy production and modeling force variations with Maxwell-Boltzmann statistics.

Findings

Clock accuracy scales linearly with entropy production.

Force variations follow Maxwell-Boltzmann statistics.

Clock error exhibits fractal-like properties similar to Brownian motion.

Abstract

The dynamics of an unique type of clock mechanism known as grasshopper escapement is investigated with the aim of evaluating its accuracy in a noisy environment. It is demonstrated that the clock's precision scales linearly with the rate of its entropy production, consistently with recently reported results regarding nanoscale and quantum clocks. Moreover, it is shown that the inevitable force variations present in the mechanism can be modelled with a Maxwell-Boltzmann statistic. Finally, the function of clock error is compared with Brownian motion and its fractal-like properties are discussed. The numerical results are confirmed with experimental data.