Thermodynamic Uncertainty Relations for Bosonic Otto Engines

TL;DR

This paper investigates the thermodynamic uncertainty relations in two-mode bosonic Otto engines, deriving exact fluctuation expressions and exploring the interdependence of work, heat, and efficiency in quantum thermodynamic cycles.

Contribution

It provides the first exact fluctuation formulas and thermodynamic uncertainty relations for bosonic Otto engines with tunable bilinear interactions.

Findings

Derived exact expressions for work and heat fluctuations.

Established thermodynamic uncertainty relations linking work, heat, and entropy production.

Outlined applicability to other quantum Otto engine configurations.

Abstract

We study two-mode bosonic engines undergoing an Otto cycle. The energy exchange between the two bosonic systems is provided by a tunable unitary bilinear interaction in the mode operators modeling frequency conversion, whereas the cyclic operation is guaranteed by relaxation to two baths at different temperature after each interacting stage. By means of a two-point-measurement approach we provide the joint probability of the stochastic work and heat. We derive exact expressions for work and heat fluctuations, identities showing the interdependence among average extracted work, fluctuations and efficiency, along with thermodynamic uncertainty relations between the signal-to-noise ratio of observed work and heat and the entropy production. We outline how the presented approach can be suitably applied to derive thermodynamic uncertainty relations for quantum Otto engines with alternative unitary strokes.