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Fluctuation-dissipation relations for thermodynamic distillation processes.

Tanmoy Biswas1, A de Oliveira Junior2, Michał Horodecki1

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Summary
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We derived a quantum version of the fluctuation-dissipation theorem within a resource theory framework. This connects energy dissipation in quantum systems to their equilibrium fluctuations, optimizing thermodynamic processes.

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Area of Science:

  • Quantum Thermodynamics
  • Statistical Physics
  • Resource Theory

Background:

  • The fluctuation-dissipation theorem connects system response to equilibrium fluctuations.
  • Resource theory provides a framework for analyzing optimal quantum state transitions under thermodynamic constraints.

Purpose of the Study:

  • To derive a quantum version of the fluctuation-dissipation theorem within a resource-theoretic framework.
  • To characterize optimal thermodynamic distillation processes and relate dissipated free energy to initial state fluctuations.

Main Methods:

  • Derivation of fluctuation-dissipation relations within a resource-theoretic framework.
  • Characterization of optimal thermodynamic distillation processes.
  • Analysis of quantum state transitions under thermodynamic constraints.

Main Results:

  • A novel fluctuation-dissipation relation is established for quantum systems.
  • The relation connects dissipated free energy to free-energy fluctuations of initial states.
  • Optimal performance of quantum thermodynamic protocols (work extraction, information erasure, communication) is analyzed up to second-order asymptotics for large N systems.

Conclusions:

  • The derived fluctuation-dissipation relations offer a rigorous analysis of quantum thermodynamic protocols for states with coherence.
  • This work provides insights into the intermediate regime of large but finite quantum systems.
  • The findings advance the understanding of thermodynamics in quantum information processing.