Abstract
Time remains one of the least well-understood concepts in physics, most notably in quantum mechanics. A central goal is to find the fundamental limits of measuring time. One of the main obstacles is the fact that time is not an observable and thus has to be measured indirectly. Here, we explore these questions by introducing a model of time measurements that is complete and autonomous. Specifically, our autonomous quantum clock consists of a system out of thermal equilibrium—a prerequisite for any system to function as a clock—powered by minimal resources, namely, two thermal baths at different temperatures. Through a detailed analysis of this specific clock model, we find that the laws of thermodynamics dictate a trade-off between the amount of dissipated heat and the clock’s performance in terms of its accuracy and resolution. Our results furthermore imply that a fundamental entropy production is associated with the operation of any autonomous quantum clock, assuming that quantum machines cannot achieve perfect efficiency at finite power. More generally, autonomous clocks provide a natural framework for the exploration of fundamental questions about time in quantum theory and beyond.
- Received 7 November 2016
DOI:https://doi.org/10.1103/PhysRevX.7.031022
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)
Viewpoint
The Thermodynamic Cost of Measuring Time
Published 2 August 2017
A simple model of an autonomous quantum clock yields a quantitative connection between the clock’s thermodynamic cost and its accuracy and resolution.
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Popular Summary
Time is arguably one of the most prominent concepts in physics, yet it still holds a significant number of mysteries, particularly in the context of quantum physics. Quantum theory fails to provide a clear description of what time actually is and treats it simply as a classical external variable. It is often argued that this failure represents one of the obstacles to unifying quantum theory with general relativity. Here, we theoretically explore the ultimate limitation of measuring time based only on the laws of quantum physics.
We introduce the concept of an autonomous quantum clock, which represents a minimal model of a quantum clock that is both complete and self-contained. It allows us to elucidate the fundamental limitations in the process of timekeeping without implicitly assuming unaccounted-for resources through external control. We consider that our out-of-thermal-equilibrium clock is powered by two thermal baths held at different temperatures. We show that the clock’s accuracy and resolution—its performance—are intimately related to the power the clock dissipates. In other words, measuring time results in an increase in entropy. This finding provides a quantitative basis for the intuitive connection between the second law of thermodynamics and the arrow of time.
We expect that the concepts and tools we have developed will enable other researchers to explore novel questions about time in quantum theory and beyond.