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 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.
- Received 13 July 2020
- Revised 26 November 2020
- Accepted 24 December 2020
DOI:https://doi.org/10.1103/PhysRevX.11.011046
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
The laws of physics know no directionality of time. Nevertheless, an arrow of time can be identified in many complex processes, such as the breaking of an egg. The irreversibility of such processes can also be used to keep track of the passage of time. Here, we investigate the implications of this insight for building quantum clocks from first principles.
Any system that can function as a clock needs an irreversible component whose dynamics indicate a clear directionality of time. However, typical irreversible processes found in nature, such as decaying atoms and cooling coffee cups, have no discernible regular temporal structure and therefore make for bad clocks by themselves. Instead, one relies on a combination of the internal, periodic dynamics of a clockwork with an irreversible, temporally unstructured process. The same is true when envisioning clocks at the quantum scale.
In this work, we identify and analyze the task performed by the clockwork, which we refer to as autonomous temporal probability concentration. That is, the clockwork generates a periodic structure that determines at which times the irreversible events—the clock’s ticks—can occur. We show that autonomous temporal probability concentration is intimately related to the complexity of the clockwork and can be performed arbitrarily well, as long as complexity is not constrained. However, the irreversible process itself sets a fundamental limit for the quality of clocks.
Thus, the second law of thermodynamics—the origin of irreversibility—limits the potential for any system to serve as a clock, while the complexity of the clockwork determines how well this can be achieved in practice.
