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arXiv:2605.21833

Comment on "Entropic Costs of Extracting Classical Ticks from a Quantum Clock"

Longyan Gong

cond-mat.mes-hallquant-phSubmitted May 20, 2026• Announced May 22, 2026• 0 citations
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Abstract

A recent Letter by Wadhia et al. reports a realization of a quantum clock using a double quantum dot (DQD) [Phys. Rev. Lett. 135, 200407 (2005)]. This Comment identifies two fundamental issues: (I) the claimed ``quantum clock" exhibits only classical behavior and lacks intrinsic temporal correlations between ticks; it is not sufficient for accurate time as a good clock. (II) the thermodynamic analysis misassigns entropy production and conflates amplification with measurement; the reported combined entropy is an engineering dissipation, not a fundamental cost of quantum timekeeping.

Comments
Comment on arXiv:2502.00096 (published journal version at https://doi.org/10.1103/5rtj-djfk)

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Entropic Costs of Extracting Classical Ticks from a Quantum Clock.

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We experimentally realize a quantum clock by using a charge sensor to count charges tunneling through a double quantum dot (DQD). Individual tunneling events are used as the clock's ticks. We quantify the clock's precision while measuring the power dissipated by the DQD and, separately, the charge sensor in both direct-current and radio-frequency readout modes. This allows us to probe the thermodynamic cost of creating ticks microscopically and recording them macroscopically. Our experiment is the first to explore the interplay between the entropy produced by a microscopic clockwork and its macroscopic measurement apparatus. We show that the latter contribution not only dwarfs the former but also unlocks greatly increased precision, because the measurement record can be exploited to optimally estimate time even when the DQD is at equilibrium. Our results suggest that the entropy produced by the amplification and measurement of a clock's ticks, which has often been ignored in the literature, is the most important and fundamental thermodynamic cost of timekeeping at the quantum scale.

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A recent Letter by Wadhia et al. reports a realization of a quantum clock using a double quantum dot (DQD) [Phys. Rev. Lett. 135, 200407 (2005)]. This Comment identifies two fundamental issues: (I) the claimed ``quantum clock" exhibits only classical behavior and lacks intrinsic temporal correlations between ticks; it is not sufficient for accurate time as a good clock. (II) the thermodynamic analysis misassigns entropy production and conflates amplification with measurement; the reported combined entropy is an engineering dissipation, not a fundamental cost of quantum timekeeping.
We experimentally realize a quantum clock by using a charge sensor to count charges tunneling through a double quantum dot (DQD). Individual tunneling events are used as the clock's ticks. We quantify the clock's precision while measuring the power dissipated by the DQD and, separately, the charge sensor in both direct-current and radio-frequency readout modes. This allows us to probe the thermodynamic cost of creating ticks microscopically and recording them macroscopically. Our experiment is the first to explore the interplay between the entropy produced by a microscopic clockwork and its macroscopic measurement apparatus. We show that the latter contribution not only dwarfs the former but also unlocks greatly increased precision, because the measurement record can be exploited to optimally estimate time even when the DQD is at equilibrium. Our results suggest that the entropy produced by the amplification and measurement of a clock's ticks, which has often been ignored in the literature, is the most important and fundamental thermodynamic cost of timekeeping at the quantum scale.
We experimentally realize a quantum clock by using a charge sensor to count charges tunneling through a double quantum dot (DQD). Individual tunneling events are used as the clock's ticks. We quantify the clock's precision while measuring the power dissipated by the DQD and, separately, the charge sensor in both direct-current and radio-frequency readout modes. This allows us to probe the thermodynamic cost of creating ticks microscopically and recording them macroscopically. Our experiment is the first to explore the interplay between the entropy produced by a microscopic clockwork and its macroscopic measurement apparatus. We show that the latter contribution not only dwarfs the former but also unlocks greatly increased precision, because the measurement record can be exploited to optimally estimate time even when the DQD is at equilibrium. Our results suggest that the entropy produced by the amplification and measurement of a clock's ticks, which has often been ignored in the literature, is the most important and fundamental thermodynamic cost of timekeeping at the quantum scale.
We experimentally realize a quantum clock by using a charge sensor to count charges tunneling through a double quantum dot (DQD). Individual tunneling events are used as the clock’s ticks. We quantify the clock’s precision while measuring the power dissipated by the DQD and, separately, the charge sensor in both direct-current and radio-frequency readout modes. This allows us to probe the thermodynamic cost of creating ticks microscopically and recording them macroscopically. Our experiment is the first to explore the interplay between the entropy produced by a microscopic clockwork and its macroscopic measurement apparatus. We show that the latter contribution not only dwarfs the former but also unlocks greatly increased precision, because the measurement record can be exploited to optimally estimate time even when the DQD is at equilibrium. Our results suggest that the entropy produced by the amplification and measurement of a clock’s ticks, which has often been ignored in the literature, is the most important and fundamental thermodynamic cost of timekeeping at the quantum scale.
Even though our microscopic physical theories, such as classical or quantum mechanics, are time-reversal invariant, time appears to march forward irreversibly. It is widely believed that effective entropy increase due to the second law of thermodynamics is at the origin of this emergent arrow of time. Any system that is out of thermal equilibrium and produces entropy can thus be used as a clock, be it a melting ice cube or a sophisticated atomic clock. The understanding of entropy in physics has significantly advanced with the advent of information theory in the last century. It has also led to the insight that the amount of entropy a clock produces is linked to how precisely the clock works, and thereby, how much information the clock reveals about the passage of time. In this thesis, we ask: what fundamental limits does the underlying physical theory impose on the precision of clocks within that theory? To rigorously answer this question, we devise a minimal clock model within quantum theory. By consistently modeling all clock constituents as quantum systems, we can ensure we account for all the resources used by the clock. This includes, in particular, the readout. Classically, one can obtain this for free, but quantum mechanically, this has a resource cost associated with it. To this end, we consolidate existing frameworks that describe clocks in both classical and quantum theory. Revising fluctuation theorems from quantum thermodynamics, we demonstrate how such theorems impose limits on the attainable precision of clocks. These precision bounds turn out to be more stringent for classical systems than for quantum ones. Quantum clocks can harness coherence and correlations to suppress fluctuations, allowing them to exponentially surpass precision bounds that hold for classical clocks. We show this separation between classical and quantum clocks by constructing an explicit example that uses quantum dynamics to saturate the quantum precision bounds. Finally, we close the thesis by exploring implications of these timekeeping bounds beyond fundamental science in quantum technologies. We show how quantum clocks can be used to quantify the energetic cost of quantum computation by linking computational fidelity to thermodynamic entropy production.
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.