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arXiv:2407.07948 · Nature Physics

Precision is not limited by the second law of thermodynamics

Florian Meier, Y. Minoguchi, Simon Sundelin, Tony J. G. Apollaro, Paul Erker, Simone Gasparinetti, Marcus Huber

Published Jun 2, 2025• 17 citations
arXivHTMLPDF

Abstract

Physical devices operating out of equilibrium are affected by thermal fluctuations, limiting their operational precision. This issue is particularly pronounced at microscopic and quantum scales, where its mitigation requires additional entropy dissipation. Understanding this constraint is important for both fundamental physics and technological design. Clocks, for example, need a thermodynamic flux towards equilibrium to measure time, resulting in a minimum entropy dissipation per clock tick. Although classical and quantum models often show a linear relationship between precision and dissipation, the ultimate bounds on this relationship remain unclear. Here we present an autonomous quantum many-body clock model that achieves clock precision that scales exponentially with entropy dissipation. This is enabled by coherent transport in a spin chain with tailored couplings, where dissipation is confined to a single link. The result demonstrates that coherent quantum dynamics can surpass the traditional thermodynamic precision limits, potentially guiding the development of future high-precision, low-dissipation quantum devices.

DOI
10.1038/s41567-025-02929-2

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Physical devices operating out of equilibrium are affected by thermal fluctuations, limiting their operational precision. This issue is particularly pronounced at microscopic and quantum scales, where its mitigation requires additional entropy dissipation. Understanding this constraint is important for both fundamental physics and technological design. Clocks, for example, need a thermodynamic flux towards equilibrium to measure time, resulting in a minimum entropy dissipation per clock tick. Although classical and quantum models often show a linear relationship between precision and dissipation, the ultimate bounds on this relationship remain unclear. Here we present an autonomous quantum many-body clock model that achieves clock precision that scales exponentially with entropy dissipation. This is enabled by coherent transport in a spin chain with tailored couplings, where dissipation is confined to a single link. The result demonstrates that coherent quantum dynamics can surpass the traditional thermodynamic precision limits, potentially guiding the development of future high-precision, low-dissipation quantum devices.
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Precision in nonequilibrium processes comes at a thermodynamic cost: suppressing fluctuations generally requires increased dissipation. Thermodynamic uncertainty relations (TURs) make this trade-off quantitative by linking current fluctuations to entropy production in classical stochastic dynamics. In the decade since its discovery, the canonical steady-state TUR and its finite-time generalizations have become a cornerstone of non-equilibrium thermodynamics, constraining the performance of molecular machines and allowing heat dissipation to be inferred from observable fluctuations. Whether the canonical TUR can be violated in a controlled quantum device remains an outstanding experimental question, in part because doing so requires resolving extremely small steady-state currents as well as their fluctuations. Here we experimentally show that steady-state quantum transport can surpass the precision permitted by the canonical TUR. We observe this violation in a superconducting quantum thermal machine coupled to a microwave waveguide acting as a cold bath and to a classical noise source providing an effective infinite-temperature bath. We observe a TUR ratio Q=1.71±0.17Q = 1.71 \pm 0.17Q=1.71±0.17, in violation of the classical bound Q≥2Q \geq 2Q≥2. Our results demonstrate a fundamental distinction between classical and quantum thermodynamics, paving the way for quantum thermal devices that achieve enhanced precision at reduced energy cost.
Precise and autonomous clocks are of fundamental interest and central importance to both foundational studies and practical applications. Here, we construct a blueprint for a quantum clock governed by time-independent interactions. By carefully-engineered coherent transport in dissipative spin chains, we achieve a scaling exponent at the precision-resolution trade-off fundamental bound, bringing this within reach of physically realistic and experimentally accessible systems. We further introduce a sudden-quench protocol that enables repeated operation through a simple initialization and detachment mechanism. Remarkably, the protocol is robust to imprecise detachment timing, implying that high-precision timekeeping can be achieved even when driven by a clock with much lower precision.
Creating precise timing devices at ultra-short time scales is not just an important technological challenge, but confronts us with foundational questions about timekeeping's ultimate precision limits. Research on clocks has either focused on long-term stability using an oscillator stabilized by a level transition, limiting precision at short timescales, or on making individual stochastic ticks as precise as possible. Here, we prove the viability of a conceptually different avenue: the autonomous self-correction of consecutive ticks by quantum correlations. This provides a new paradigm that integrates the advantages and insights from quantum transport theory to operate clocks at ultra-short timescales. We fully solve a model of coupled quantum systems and show how the emergent Pauli exclusion principle correlates the clock at the quantum level yielding an exponential advantage in precision. We furthermore demonstrate through simulations with realistic imperfections that this remarkable gain in precision remains stable providing a roadmap for implementation with contemporary quantum technologies.
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.
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.