Efficiency fluctuations of a quantum heat engine

Tobias Denzler,Eric Lutz

doi:10.1103/physrevresearch.2.032062

Abstract

We derive the probability distribution of the efficiency of a quantum Otto engine. We explicitly compute the quantum efficiency statistics for an analytically solvable two-level engine. We analyze the occurrence of values of the stochastic efficiency above unity, in particular at infinity, in the nonadiabatic regime and further determine mean and variance in the case of adiabatic driving. We finally investigate the classical-to-quantum transition as the temperature is lowered.

Highlights

Efficiency is a key performance measure of thermal machines
We find that the stochastic efficiency is equal to the deterministic macroscopic efficiency for adiabatic driving, while efficiency values at infinity appear for nonadiabatic driving, when no heat is absorbed nonzero work is produced
We investigate the transition of the nonadiabatic distribution from a regime dominated by thermal fluctuations at high temperatures to a domain characterized by quantum fluctuations at low temperatures

Summary

INTRODUCTION

Efficiency is a key performance measure of thermal machines. For heat engines that cyclically convert heat into useful work, it is defined as the ratio of work output and heat input [1]. The stochastic efficiency of a Carnot engine has been shown to admit values larger than the Carnot bound [6] The latter quantity has been found to be the least likely in the long-time limit [6]. We determine the respective work and heat probability densities of the different branches of the engine cycle by extending the two-projective-measurement scheme [42] to thermal machines. We use these correlated distributions to derive a general formula for the quantum efficiency statistics and first examine its generic properties for scale-invariant driving Hamiltonians [43,44,45,46,47]. We investigate the transition of the nonadiabatic distribution from a regime dominated by thermal fluctuations at high temperatures to a domain characterized by quantum fluctuations at low temperatures

QUANTUM OTTO ENGINE

QUANTUM EFFICIENCY DISTRIBUTION

EXAMPLE OF A SPIN HEAT ENGINE

HIGH-TEMPERATURE AND LOW-TEMPERATURE DISTRIBUTIONS