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This study establishes a thermodynamic uncertainty relation for feedback cooling, revealing a trade-off between cooling efficiency and entropy reduction rate in classical systems. It shows ideal cooling is asymptotically possible using Kalman filter feedback control.

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Area of Science:

  • Thermodynamics
  • Statistical Mechanics
  • Control Theory

Background:

  • Feedback cooling utilizes measurement and control to reduce system temperatures.
  • Quantifying the thermodynamic cost for ideal cooling efficiency within finite time is a key challenge.

Purpose of the Study:

  • Establish a thermodynamic uncertainty relation (TUR) for feedback cooling in classical underdamped Langevin systems.
  • Derive the trade-off between cooling efficiency and entropy reduction rate.

Main Methods:

  • Theoretical derivation of a thermodynamic uncertainty relation.
  • Analysis of classical underdamped Langevin systems.
  • Application of feedback control based on the Kalman filter.

Main Results:

  • A novel TUR for feedback cooling was established.
  • A trade-off between cooling efficiency and entropy reduction rate was identified.
  • Asymptotic achievement of ideal cooling efficiency and finite entropy reduction rate is possible by diverging reversible local mean velocity fluctuations.

Conclusions:

  • The findings clarify the thermodynamic costs associated with achieving fundamental cooling limits in feedback control systems.
  • The study demonstrates the feasibility of optimal cooling using Kalman filter-based feedback.
  • Results provide insights into the fundamental limits of feedback cooling from a TUR perspective.