Efficiency fluctuations of stochastic machines undergoing a phase transition

TL;DR

This paper investigates how phase transitions in a stochastic heat engine with many interacting components influence the fluctuations of its efficiency, revealing distinct behaviors in ergodic and nonergodic regimes.

Contribution

It introduces a model of a stochastic heat engine with phase transition behavior and analyzes how efficiency fluctuations depend on system size and observation time.

Findings

Efficiency fluctuates widely in the ergodic case.

Efficiency concentrates near specific values in the nonergodic case.

Decay rate at reversible efficiency remains dominant despite phase transition.

Abstract

We study the efficiency fluctuations of a stochastic heat engine made of $N$ interacting unicyclic machines and undergoing a phase transition in the macroscopic limit. Depending on $N$ and on the observation time, the machine can explore its whole phase space or not. This affects the engine efficiency that either strongly fluctuates on a large interval of equiprobable efficiencies (ergodic case) or fluctuates close to several most likely values (nonergodic case). We also provide a proof that despite the phase transition, the decay rate of the efficiency distribution at the reversible efficiency remains largest one although other efficiencies can now decay equally fast.