The efficiency fluctuations of microscopic heat engines with a finite state space were recently discovered to follow a universal distribution in the long-time limit [Nat. Commun. 5, 4721 (2014)], i.e. the efficiency large deviation function (LDF) was found to have a universal shape. I will derive an expression for the efficiency LDF of the Brownian gyrator, a two-dimensional Brownian particle interacting with two heat baths at different temperatures, which can act as a nanoscale heat engine. Having an infinite, unbounded state space, this system is not covered by the aforementioned theory, but bears some resemblance to it nonetheless. I will describe these similarities, compare the result to other recent findings, and discuss deviations.
