Destructive effect of fluctuations on the performance of a Brownian gyrator

Abstract

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

6 pages +ESI 10 pages

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