Optimal Efficiency of Heat Engines with Finite-Size Heat Baths

Abstract

The optimal efficiency of quantum (or classical) heat engines whose heat baths are $n$-particle systems is given by the information geometry and the strong large deviation. We give the optimal work extraction process as a concrete energy-preserving unitary time evolution among the heat baths and the work storage. We show that our optimal work extraction turns the disordered energy of the heat baths to the ordered energy of the work storage, by evaluating the ratio of the entropy difference to the energy difference in the heat baths and the work storage, respectively. By comparing the statistical mechanical optimal efficiency with the macroscopic thermodynamic bound, we evaluate the accuracy of the macroscopic thermodynamics with finite-size heat baths from the statistical mechanical viewpoint. We also evaluate the quantum coherence effect on the optimal efficiency of the cycle processes without restricting their cycle time, by comparing the classical and quantum optimal efficiencies.

Main: 16pages, 3figures Appendix: 21pages The second and third versions treat essentially the same topics as the first version, and give a substantial expansion of the first version. Because the first version has problems in the formulation, we gives a new formulation for quantum and classical heat engines in arXiv:1504.06150v2. The second and third versions are based on the new formulation

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Cited by in corpus (29)

• Stochastic thermodynamic interpretation of information geometry
• A Resource Theory for Work and Heat
• Energetic instability of passive states in thermodynamics
• Fundamental work cost of quantum processes
• Beyond the thermodynamic limit: finite-size corrections to state interconversion rates
• Efficiency versus Speed in Quantum Heat Engines: Rigorous Constraint from Lieb-Robinson Bound
• A quantum Otto engine with finite heat baths: energy, correlations, and degradation
• The maximum efficiency of nano heat engines depends on more than temperature
• Temperature dependent maximization of work and efficiency in a degeneracy assisted quantum Stirling heat engine
• Optimal performance of generalized heat engines with finite-size baths of arbitrary multiple conserved quantities beyond i.i.d. scaling
• Optimizing Thermodynamic Cycles with Two Finite-Sized Reservoirs
• Finite-bath corrections to the second law of thermodynamics
• Surpassing the Carnot Efficiency by extracting imperfect work
• Work and reversibility in quantum thermodynamics
• Effect of finite-size heat source's heat capacity on the efficiency of heat engine
• Fundamental relation between entropy production and heat current
• Attaining Carnot Efficiency with Quantum and Nanoscale Heat Engines
• Collective operations can extremely reduce work fluctuations
• Quantum work extraction efficiency for noisy quantum batteries: the role of coherence
• Efficiency of a cyclic quantum heat engine with finite-size baths
• Fluctuation-dissipation relations for thermodynamic distillation processes
• Moderate deviation analysis of majorisation-based resource interconversion
• Thermodynamics of a minimal algorithmic cooling refrigerator
• Two constructive proofs on d-majorization and thermo-majorization
• Correlated quantum machines beyond the standard second law
• A hierarchy of thermal processes collapses under catalysis
• Resource engines
• Optimal performance of a three stroke heat engine in the microscopic regime
• Asymptotic Convertibility of Entanglement: A General Approach to Entanglement Concentration and Dilution