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.1 MoreReceived 13 July 2020Revised 26 November 2020Accepted 24 December 2020DOI:https://doi.org/10.1103/PhysRevX.11.011046Published 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 SocietyPhysics Subject Headings (PhySH)Research AreasAtomic, optical & lattice clocksQuantum thermodynamicsPhysical SystemsQuantum heat engines & refrigeratorsQuantum InformationStatistical Physics
Highlights
Time plays a special role in quantum physics
Our work provides a concrete physical realization of the maps that effect the transfer of ticks to the register
The conceptual split of any such task into a clockwork, which creates a temporally concentrated probability distribution and a mechanism for irreversibility, allowed us to derive an analytic formula for the achievable temporal probability concentration of the clockwork
Summary
Time plays a special role in quantum physics. While other physical quantities of interest are represented as Hermitian operators, there is no observable corresponding to time itself. Time plays the role of a parameter in the equations of motion. The passage of time is estimated via the evolution of a reference system—a clock. By tracking the dynamical evolution of (observable quantities related to) such a clock system, it is possible to extract information about the flow of time; see, e.g., Refs. We consider time to be a continuously elapsing parameter t (“Schrödinger time”) whose value is estimated by a clock in terms of discrete increments (“ticks”). The evolution of any closed system is time-reversal symmetric, and, any complete description of an instrument
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