Fundamental accuracy-resolution trade-off for timekeeping devices

TL;DR

This paper establishes a fundamental universal bound on the accuracy and resolution of all clocks based on memoryless thermalization events, highlighting the thermodynamic limits of timekeeping devices.

Contribution

It introduces a universal bound for clocks driven by memoryless irreversible processes, linking thermodynamics to clock precision and resolution limits.

Findings

Proves a universal accuracy-resolution trade-off bound.

Shows the stochastic nature of thermalization limits clock performance.

Highlights thermodynamic constraints on timekeeping devices.

Abstract

From a thermodynamic point of view, all clocks are driven by irreversible processes. Additionally, one can use oscillatory systems to temporally modulate the thermodynamic flux towards equilibrium. Focusing on the most elementary thermalization events, this modulation can be thought of as a temporal probability concentration for these events. There are two fundamental factors limiting the performance of clocks: On the one level, the inevitable drifts of the oscillatory system, which are addressed by finding stable atomic or nuclear transitions that lead to astounding precision of today's clocks. On the other level, there is the intrinsically stochastic nature of the irreversible events upon which the clock's operation is based. This becomes relevant when seeking to maximize a clock's resolution at high accuracy, which is ultimately limited by the number of such stochastic events per reference time unit. We address this essential trade-off between clock accuracy and resolution, proving a universal bound for all clocks whose elementary thermalization events are memoryless.