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

TL;DR

This paper formalizes the concept of autonomous clocks driven by thermodynamic irreversibility, demonstrating how clock accuracy can be improved by increasing complexity and exploring thermodynamic limits using quantum systems.

Contribution

It introduces a formal framework for autonomous thermal clocks and shows how clock accuracy scales with complexity, connecting thermodynamics and quantum information.

Findings

Perfect clockwork can be approximated by increasing system complexity.

Thermodynamic limits constrain the precision of time measurement.

Quantum systems can be used to approach ideal clock performance.

Abstract

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 formalise 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 idealised clockwork model, comprised of many qubits, with an irreversible decay mechanism to showcase the ultimate thermodynamic limits to the measurement of time.