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The Brownian gyrator (BG) is often called a minimal model of a nano-engineperforming a rotational motion, judging solely upon the fact that innon-equilibrium conditions its torque, angular momentum ${\cal L}$ and angularvelocity $\cal W$ have non-zero mean values. For a time-discretized model,which is most adapted for the analysis of an essentially discrete-time datagarnered in experiments or numerical simulations, we calculate the previouslyunknown probability density functions (PDFs) of ${\cal L}$ and $\cal W$. Forfinite time-step $\delta t$, the PDF of ${\cal L}$ has exponential tails andall moments are therefore well-defined, but the noise-to-signal ratio canattain big values for small $\delta t$. Conversely, the PDF of ${\cal W}$exhibits heavy power-law tails and its mean ${\cal W}$ is the only existingmoment. The BG is therefore not an engine in the common sense: it does notexhibit regular rotations on each run and its fluctuations are not only a minornuisance -- on contrary, their effect is completely destructive for theperformance. Our theoretical predictions are confirmed by numerical simulationsand experimental data. We discuss some plausible improvements

Destructive effect of fluctuations on the performance of a Brownian gyrator