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Bound on Efficiency of Heat Engine from Uncertainty Relation Viewpoint.

Pritam Chattopadhyay1, Ayan Mitra2, Goutam Paul1

  • 1Cryptology and Security Research Unit, R.C. Bose Center for Cryptology and Security, Indian Statistical Institute, Kolkata 700108, India.

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This study connects quantum mechanics and thermodynamics in heat engines. We establish bounds for quantum heat engine efficiency using the uncertainty principle, linking quantum observables to measurable thermodynamic variables.

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Stirling cycleheat engineinfinite potential welluncertainty relation

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Area of Science:

  • Quantum mechanics
  • Thermodynamics
  • Quantum heat engines

Background:

  • Quantum systems can model heat engines, but the link between quantum observables and thermodynamic variables like efficiency is unclear.
  • Understanding this connection is crucial for advancing quantum thermodynamics.

Purpose of the Study:

  • To establish a clear link between quantum observables and thermodynamic variables in quantum heat engines.
  • To explore the role of the uncertainty principle in determining heat engine efficiency.

Main Methods:

  • Modeling quantum heat engines using quantum systems as working substances.
  • Analyzing the sum uncertainty relation of position and momentum operators.
  • Connecting quantum uncertainty relations to thermodynamic variables.

Main Results:

  • Established a connection between the sum uncertainty relation and thermodynamic variables in a quantum heat engine model.
  • Determined upper and lower bounds for the efficiency of quantum heat engines based on the uncertainty relation.

Conclusions:

  • The uncertainty principle provides a fundamental constraint on the efficiency of quantum heat engines.
  • This work bridges quantum mechanics and thermodynamics, offering a deeper understanding of quantum heat engine performance.