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In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate errors. Despite the cares we take, the presence of random errors means that repeated measurements almost never have exactly the same magnitude. The collective difference between these measurements - observed values - and the estimated or expected value is called uncertainty. Uncertainty is conventionally written after the estimated or expected value.
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Scientists typically make repeated measurements of a quantity to ensure the quality of their findings and to evaluate both the precision and the accuracy of their results. Measurements are said to be precise if they yield very similar results when repeated in the same manner. A measurement is considered accurate if it yields a result that is very close to the true or the accepted value. Precise values agree with each other; accurate values agree with a true value. 
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Thermodynamic uncertainty relations including measurement and feedback.

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Any fluctuation relation implies a thermodynamic uncertainty relation, extending its use to feedback and measurement. This allows for potentially unlimited signal-to-noise ratios by compensating with backward experiments.

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Area of Science:

  • Thermodynamics
  • Statistical Mechanics
  • Information Theory

Background:

  • Thermodynamic uncertainty relations link signal-to-noise ratio to dissipation.
  • Fluctuation relations generalize the second law of thermodynamics for stochastic processes.

Purpose of the Study:

  • To demonstrate that fluctuation relations imply thermodynamic uncertainty relations.
  • To extend thermodynamic uncertainty relations to systems with measurement and feedback.

Main Methods:

  • Derivation of thermodynamic uncertainty relations from fluctuation relations.
  • Analysis of systems with feedback, considering time-reversal invariance.

Main Results:

  • Any fluctuation relation directly implies a thermodynamic uncertainty relation.
  • Extension of uncertainty relations to scenarios involving measurement and feedback.
  • Demonstration that signal-to-noise ratio can be arbitrarily large if the backward experiment compensates.

Conclusions:

  • The connection between fluctuation and uncertainty relations broadens their applicability.
  • Feedback control can lead to enhanced signal-to-noise ratios under specific conditions.
  • Illustrative examples include the Szilard engine and quantum dot work extraction.