Journal
PHYSICAL REVIEW X
Volume 11, Issue 2, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevX.11.021029
Keywords
Condensed Matter Physics; Statistical Physics
Categories
Funding
- Royal Society
- EPSRC Platform Grant [EP/R029229/1]
- Foundational Questions Institute Fund, a donor advised fund of Silicon Valley Community Foundation [FQXi-IAF19-01]
- European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme [818751, 948932]
- Templeton World Charity Foundation
- Austrian Science Fund (FWF) through the START project [Y879-N27]
- FQXi Grant [FQXiIAF19-03-S2]
- ESQ Discovery Grant Emergent time-operationalism, quantum clocks and thermodynamics of the Austrian Academy of Sciences (OAW)
- Austrian Science Fund (FWF) through the Zukunftskolleg [ZK03]
- EPSRC [EP/R029229/1] Funding Source: UKRI
- European Research Council (ERC) [818751, 948932] Funding Source: European Research Council (ERC)
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Research demonstrates that there is a linear relationship between the accuracy of clocks and entropy, with experimental measurements showing this relationship exists in nanoscale clocks and operates within an order of magnitude of the theoretical limit.
All clocks, in some form or another, use the evolution of nature toward higher entropy states to quantify the passage of time. Because of the statistical nature of the second law and corresponding entropy flows, fluctuations fundamentally limit the performance of any clock. This suggests a deep relation between the increase in entropy and the quality of clock ticks. Indeed, minimal models for autonomous clocks in the quantum realm revealed that a linear relation can be derived, where for a limited regime every bit of entropy linearly increases the accuracy of quantum clocks. But can such a linear relation persist as we move toward a more classical system? We answer this in the affirmative by presenting the first experimental investigation of this thermodynamic relation in a nanoscale clock. We stochastically drive a nanometer-thick membrane and read out its displacement with a radio-frequency cavity, allowing us to identify the ticks of a clock. We show theoretically that the maximum possible accuracy for this classical clock is proportional to the entropy created per tick, similar to the known limit for a weakly coupled quantum clock but with a different proportionality constant. We measure both the accuracy and the entropy. Once nonthermal noise is accounted for, we find that there is a linear relation between accuracy and entropy and that the clock operates within an order of magnitude of the theoretical bound.
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