Autonomous Temporal Probability Concentration: Clockworks and the Second Law of Thermodynamics

According to thermodynamics, the inevitable increase of entropy allows the past to be distinguished from the future. From this perspective, any clock must incorporate an irreversible process that allows this flow of entropy to be tracked. In addition, an integral part of a clock is a clockwork, that is, a system whose purpose is to temporally concentrate the irreversible events that drive this entropic flow, thereby increasing the accuracy of the resulting clock ticks compared to counting purely random equilibration events. In this article, we formalize the task of autonomous temporal probability concentration as the inherent goal of any clockwork based on thermal gradients. Within this framework, we show that a perfect clockwork can be approximated arbitrarily well by increasing its complexity. Furthermore, we combine such an idealized clockwork model, comprised of many qubits, with an irreversible decay mechanism to showcase the ultimate thermodynamic limits to the measurement of time.

Automated summary

According to thermodynamics, the increase of entropy distinguishes the past from the future, requiring any clock to incorporate an irreversible process to track this flow. A clockwork, a system designed to concentrate irreversible events and improve the accuracy of time measurements, is essential for a clock. By increasing complexity, an ideal clockwork model can be approximated, showcasing the thermodynamic limits of time measurement when combined with irreversible decay mechanisms.