# Work and power fluctuations in a critical heat engine

## TL;DR

This paper studies how work output fluctuations in a critical heat engine scale with system size, revealing that large fluctuations persist near critical points, impacting engine performance.

## Contribution

It demonstrates the critical scaling of work fluctuations in Stirling engines near phase transitions, highlighting the dominance of fluctuations in macroscopic engine performance.

## Key findings

- Work variance scales with heat capacity's critical exponent.
- Relative work fluctuations diverge unless strict scaling conditions are met.
- Fluctuations do not vanish even in the infinite system size limit.

## Abstract

We investigate fluctuations of output work for a class of Stirling heat engines with working fluid composed of interacting units and compare these fluctuations to an average work output. In particular, we focus on engine performance close to a critical point where Carnot's efficiency may be attained at a finite power as reported in [M. Campisi and R. Fazio, Nat. Commun. 7, 11895 (2016)]. We show that the variance of work output per cycle scales with the same critical exponent as the heat capacity of the working fluid. As a consequence, the relative work fluctuation diverges unless the output work obeys a rather strict scaling condition, which would be very hard to fulfill in practice. Even under this condition, the fluctuations of work and power do not vanish in the infinite system size limit. Large fluctuations of output work thus constitute inseparable and dominant element in performance of the macroscopic heat engines close to a critical point.