Surpassing the Carnot efficiency by extracting imperfect work

Nelly Huei Ying Ng*, Mischa Prebin Woods, Stephanie Wehner

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

25 Citations (Scopus)
74 Downloads (Pure)


A suitable way of quantifying work for microscopic quantum systems has been constantly debated in the field of quantum thermodynamics. One natural approach is to measure the average increase in energy of an ancillary system, called the battery, after a work extraction protocol. The quality of energy extracted is usually argued to be good by quantifying higher moments of the energy distribution, or by restricting the amount of entropy to be low. This limits the amount of heat contribution to the energy extracted, but does not completely prevent it. We show that the definition of 'work' is crucial. If one allows for a definition of work that tolerates a non-negligible entropy increase in the battery, then a small scale heat engine can possibly exceed the Carnot efficiency. This can be done without using any additional resources such as coherence or correlations, and furthermore can be achieved even when one of the heat baths is finite in size.

Original languageEnglish
Article number113005
JournalNew Journal of Physics
Issue number11
Publication statusPublished - 2017


  • quantum heat engines
  • quantum thermodynamics
  • single-shot work extraction
  • thermodynamic resource theories


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