Bosonic two-stroke heat engines with polynomial nonlinear coupling

TL;DR

This paper investigates the thermodynamics of bosonic two-stroke heat engines with nonlinear coupling, analyzing work fluctuations, optimizing performance, and exploring thermodynamic uncertainty relations for specific interaction cases.

Contribution

It introduces a general nonlinear interaction model for bosonic heat engines, derives work fluctuation distributions, and optimizes engine performance considering specific nonlinear cases.

Findings

Identified optimal interactions for large average work with small fluctuations.

Derived work fluctuation distributions using the two-point measurement scheme.

Optimized work and signal-to-noise ratio for specific nonlinear interactions.

Abstract

We study the thermodynamics of two-stroke heat engines where two bosonic modes $a$ and $b$ are coupled by the general nonlinear interaction $V_{\theta} = \exp {(\theta a^{\dagger n}b^m -\theta^* a^n b^{\dagger m})}$. By adopting the two-point measurement scheme we retrieve the distribution of the stochastic work, and hence the relative fluctuations of the extracted work up to the second order in the coupling $\theta$. We identify the optimal interactions providing large average work with small fluctuations in the operational regime of the heat engine. Then, we consider the specific cases $n=2$, $m=1$ and $n=1$, $m=2$ up to the fourth order in $\theta$. We optimize the average work and the signal-to-noise ratio over the frequencies of the bosonic modes and the temperatures of the reservoirs. Finally, we determine the thermodynamic uncertainty relations for these processes in relation with the order of the expansion of the unitary interaction $V_{\theta}$.