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Bounds on fluctuations for finite-time quantum Otto cycle
Sushant Saryal1, Bijay Kumar Agarwalla1
1Department of Physics, Indian Institute of Science Education and Research Pune, Dr. Homi Bhabha Road, Ward No. 8, NCL Colony, Pashan, Pune, Maharashtra 411008, India.
Physical Review. E
|July 17, 2021
Summary
We derived exact heat and work statistics for quantum Otto engines. Fluctuation ratios for work and heat are bounded by engine efficiency, especially in the quasistatic limit.
Area of Science:
- Quantum thermodynamics
- Statistical mechanics
- Quantum information
Background:
- Quantum Otto engines are theoretical models for quantum heat engines.
- Understanding heat and work fluctuations is crucial for analyzing engine performance and efficiency.
- Previous studies have focused on average quantities, with less emphasis on full statistical distributions.
Purpose of the Study:
- To provide exact full statistics of heat and work for quantum Otto engines.
- To derive universal expressions for cumulant ratios related to efficiency.
- To establish lower bounds for work and heat fluctuation ratios in non-adiabatic quantum Otto engines.
Main Methods:
- Analysis of scale-invariant energy eigenspectra under driving.
- Derivation of universal expressions for nth cumulant ratios.
- Investigation of quantum Otto engines with qubit and harmonic oscillator working fluids.
- Calculation of relative fluctuations of output work and input heat.
Main Results:
- Exact full statistics of heat and work derived for specific working fluids.
- Universal expression for the ratio of nth cumulant of work and heat established.
- Work fluctuation is consistently greater than heat fluctuation for non-adiabatic driving.
- A lower bound for the ratio of work to heat fluctuation is found in terms of average engine efficiency.
Conclusions:
- The quasistatic limit saturates the derived lower bound for fluctuation ratios.
- The findings offer insights into the fundamental limits of quantum heat engine performance.
- This work provides a theoretical framework for analyzing fluctuations in quantum thermodynamic devices.
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