Bounds on fluctuations for finite-time quantum Otto cycle

TL;DR

This paper establishes fundamental bounds on work fluctuations in finite-time quantum Otto engines, linking them to input heat fluctuations and efficiency, with implications for engine stability and performance.

Contribution

It derives lower bounds on work fluctuation ratios in finite-time quantum Otto cycles, highlighting conditions for bound saturation and scale-invariant energy spectra.

Findings

Work fluctuation exceeds input heat fluctuation in finite-time cycles.

Lower bound on work fluctuation ratio depends on average efficiency.

Bound saturation occurs in quasi-static limit for certain energy spectra.

Abstract

For finite-time quantum Otto heat engine with working fluid consisting of either a (i) qubit or (ii) a harmonic oscillator, we show that the relative fluctuation of output work is always greater than the corresponding relative fluctuation of input heat absorbed from the hot bath. As a result, the ratio between the work fluctuation and the input heat fluctuation receives a lower bound in terms of the square value of the average efficiency of the engine. The saturation of the lower bound is received in the quasi-static limit of the engine and can be shown for a class of working fluids that follow a scale-invariant energy eigenspectra under driving.