Universal efficiency at optimal work with Bayesian statistics

Abstract

If the work per cycle of a quantum heat engine is averaged over an appropriate prior distribution for an external parameter $a$, the work becomes optimal at Curzon-Ahlborn efficiency. More general priors of the form $\Pi (a)\propto 1/a^{\gamma }$ yield optimal work at an efficiency which stays close to CA value, in particular near equilibrium the efficiency scales as one-half of the Carnot value. This feature is analogous to the one recently observed in literature for certain models of finite-time thermodynamics. Further, the use of Bayes' theorem implies that the work estimated with posterior probabilities also bears close analogy with the classical formula. These findings suggest that the notion of prior information can be used to reveal thermodynamic features in quantum systems, thus pointing to a new connection between thermodynamic behavior and the concept of information.

revtex4, 5 pages, abstract changed and presentation improved; results unchanged. New result with Bayes Theorem added

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Cited by in corpus (8)

• Optimal Performance of a Three-level Quantum Refrigerator
• Expected Behavior of Quantum Thermodynamic Machines with Prior Information
• Efficiencies of power plants, quasi-static models and the geometric-mean temperature
• Estimating performance of Feynman's ratchet with limited information
• Efficiency at optimal work from finite reservoirs: a probabilistic perspective
• Ignorance based inference of optimality in thermodynamic processes
• Informative priors and the analogy between quantum and classical heat engines
• The many avatars of Curzon-Ahlborn efficiency