# Efficiency fluctuations in microscopic machines

## TL;DR

This paper extends a universal theory of efficiency fluctuations in microscopic machines to systems with arbitrary state spaces, providing detailed conditions for universal behavior and illustrating results with colloidal engine models.

## Contribution

It generalizes the existing theory to more complex systems and clarifies when universal efficiency fluctuation features hold.

## Key findings

- Extended the theory to arbitrary state space machines.
- Identified conditions for deviations from universal features.
- Provided exact results for colloidal engine models.

## Abstract

Nanoscale machines are strongly influenced by thermal fluctuations, contrary to their macroscopic counterparts. As a consequence, even the efficiency of such microscopic machines becomes a fluctuating random variable. Using geometric properties and the fluctuation theorem for the total entropy production, a `universal theory of efficiency fluctuations' at long times, for machines with a finite state space, was developed in [Verley \textit{et al.}, Nat.~Commun.~\textbf{5}, 4721 (2014); Phys.~Rev.~E~\textbf{90}, 052145 (2014)]. We extend this theory to machines with an arbitrary state space. Thereby, we work out more detailed prerequisites for the `universal features' and explain under which circumstances deviations can occur. We also illustrate our findings with exact results for two non-trivial models of colloidal engines.