Abstract
The efficiency of small thermal machines is typically a fluctuating quantity. We here study the efficiency large deviation properties of two exemplary quantum heat engines, the harmonic oscillator and the two-level Otto motors. To this end, we analytically compute their joint characteristic functions for heat and work based on the two-projective-measurement approach. We investigate work–heat correlations within the respective engine cycles and find, for generic scale-invariant quantum heat engines, that work and heat are perfectly anticorrelated for adiabatic driving. In this limit, the effects of thermal as well as quantum fluctuations are suppressed, the large deviation functions are singular and the stochastic efficiency is equal to the macroscopic efficiency.
Highlights
The efficiency of small thermal machines is typically a fluctuating quantity
Work output and heat input are perfectly anticorrelated for adiabatic cycles, in agreement with the result obtained for scaleinvariant engines
We have investigated the work-heat correlations and the efficiency statistics of the quantum Otto cycle with a working medium consisting of a two-level system or a harmonic oscillator
Summary
We begin by analyzing the work-heat correlations within the quantum Otto cycle using the Pearson coefficient. Work output and heat input are perfectly anticorrelated for adiabatic cycles, in agreement with the result obtained for scaleinvariant engines. For adiabatic driving (Fig. 2b), when work output and heat input are perfectly anticorrelated, the rate function of both systems noticeably departs from that general form: it is zero at the thermodynamic efficiency ηth and infinite everywhere else, confirming that the efficiency behaves deterministically. A deeper understanding of the stark differences between adiabatic and nonadiabatic driving in the quantum Otto cycle may be gained by applying the geometric approach of Ref. [7, 8] only applies when there is a unique minimum This is the case for nonadiabatic driving, as can be seen from the contour plot of φ(γ1, γ2) for the two-level quantum motor (Fig. 3a). A similar behavior is observed for the example of the harmonic quantum heat engine [54]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
