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Work fluctuations due to partial thermalizations in two-level systems.

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Finite-time work extraction from two-level systems involves fluctuations due to partial thermalization. Analytic work distributions and bounds reveal inherent unpredictability in these energy processes.

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Area of Science:

  • Thermodynamics
  • Quantum Mechanics
  • Statistical Physics

Background:

  • Work extraction from quantum systems is crucial for energy harvesting.
  • Finite-time processes introduce fluctuations and irreversibility.
  • Partial thermalization affects work extraction efficiency.

Purpose of the Study:

  • To analyze work extraction in two-level systems undergoing partial thermalization.
  • To characterize work fluctuations and their dependence on driving and thermalization rates.
  • To investigate modified Carnot cycles for finite-time work extraction.

Main Methods:

  • Modeling work extraction as continuous-time Markov processes.
  • Analyzing work distribution for a constant energy gap driving rate.
  • Deriving analytic expressions for average work and work variance bounds.
  • Applying Jarzynski's fluctuation-dissipation relation.
  • Modifying the Carnot cycle to include partial thermalization.

Main Results:

  • Work extraction processes are generally not fluctuation-free.
  • Analytic expressions for average work and a lower bound for work variance were derived.
  • An upper bound for Monte Carlo estimates of work variance was obtained.
  • Modified Carnot cycles with partial thermalization were analyzed.
  • Efficiency at maximum power was determined for finite-time cycles.

Conclusions:

  • Partial thermalization in finite-time work extraction leads to inherent fluctuations.
  • The derived bounds provide insights into the limits of work extraction predictability.
  • Modified thermodynamic cycles can be optimized for efficiency at maximum power under realistic constraints.