Autonomous Ticking Clocks from Axiomatic Principles

Abstract

There are many different types of time keeping devices. We coin the phrase ticking clock to describe those which -- simply put -- "tick" at approximately regular intervals. Various important results have been derived for ticking clocks, and more are in the pipeline. It is thus important to understand the underlying models on which these results are founded. The aim of this manuscript is to introduce a new ticking clock model from axiomatic principles that overcomes concerns in the community about the physicality of the assumptions made in previous models. The model we introduce is autonomous and requires only finite memory per unit of time for which it is in operation. Importantly, it can achieve the same high accuracy as that reported in [arXiv:1806.00491] while being fully autonomous such as the model in [10.1103/PhysRevX.7.031022]. What is more, [10.1103/PhysRevX.7.031022] is revealed to be a special case of the new ticking clock model.