Efficiency statistics of a quantum Otto cycle
arXiv:2109.12816 · doi:10.1103/PhysRevA.105.022609
Abstract
The stochastic efficiency [G. Verley et al., Nat. Commun. 5, 4721 (2014)] was introduced to evaluate the performance of energy-conversion machines in micro-scale. However, such an efficiency generally diverges when no heat is absorbed while work is produced in a thermodynamic cycle. As a result, any statistical moments of the efficiency do not exist. In this study, we come up with a different version of the definition for the stochastic efficiency which is always finite. Its mean value is equal to the conventional efficiency, and higher moments characterize the fluctuations of the cycle. In addition, the fluctuation theorems are re-expressed via the efficiency. For working substance satisfying the equipartition theorem, we clarify that the thermodynamic uncertainty relation for efficiency is valid in an Otto engine. To demonstrate our general discussions, the efficiency statistics of a quantum harmonic-oscillator Otto engine is systematically investigated. The probability that the stochastic efficiency surpasses the Carnot efficiency is explicitly obtained. This work may shed new insight for optimizing micro-machines with fluctuations.
References in corpus (41)
- Stochastic thermodynamics, fluctuation theorems, and molecular machines
- The Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences
- Nonequilibrium fluctuations, fluctuation theorems, and counting statistics in quantum systems
- Colloquium. Quantum Fluctuation Relations: Foundations and Applications
- Thermodynamic uncertainty relation for biomolecular processes
- Quantum Thermodynamic Cycles and quantum heat engines
- Single ion heat engine with maximum efficiency at maximum power
- Brownian Carnot engine
- Irreversible Performance of a Quantum Harmonic Heat Engine
- Universal trade-off relation between power and efficiency for heat engines
- Universal bounds on current fluctuations
- The unlikely Carnot efficiency
- Thermodynamic uncertainty relations from exchange fluctuation theorems
- Quantum Supremacy of Many-Particle Thermal Machines
- Nonequilibrium work distribution of a quantum harmonic oscillator
- Scaling-up quantum heat engines efficiently via shortcuts to adiabaticity
- Efficiency statistics at all times: Carnot limit at finite power
- Thermodynamic Geometry of Microscopic Heat Engines
- Efficiency of harmonic quantum Otto engines at maximal power
- Universal theory of efficiency fluctuations
- MBL-mobile: Quantum engine based on many-body localization
- Minimal work principle: proof and counterexamples
- Fluctuation Relation for Quantum Heat Engines and Refrigerators
- Quantum thermodynamic cycle with quantum phase transition
- Universal constraint for efficiency and power of a low-dissipation heat engine
- Efficiency fluctuations of a quantum Otto engine
- Shortcuts to adiabaticity from linear response theory
- Efficiency fluctuations in microscopic machines
- Experimental validation of the -scaling entropy generation in finite-time thermodynamics with dry air
- Work statistics across a quantum phase transition
- Fluctuation Relation for Heat Engines
- Optimal operating protocol to achieve efficiency at maximum power of heat engines
- Boosting the performance of the Quantum Otto heat engines
- Achieve Higher Efficiency at Maximum Power with Finite-time Quantum Otto Cycle
- Group-theoretical approach to the calculation of quantum work distribution
- Optimizing Thermodynamic Cycles with Two Finite-Sized Reservoirs
- Effect of finite-size heat source's heat capacity on the efficiency of heat engine
- Quantumness and thermodynamic uncertainty relation of finite-time Otto cycle
- The Bose-Fermi duality in quantum Otto heat engine with trapped repulsive Bosons
- Quantum refrigerators in finite-time cycle duration
- Efficiency large deviation function of quantum heat engines
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- Optimization of Asymmetric Quantum Otto Engine Cycles
- Quantum unital Otto heat engines: using Kirkwood-Dirac quasi-probability for the engine's coherence to stay alive