Entropy of timekeeping in a mechanical clock

The dynamics of a 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 modeled 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.