Destructive effect of fluctuations on the performance of a Brownian gyrator
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866914245931696128 |
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| author | Viot, Pascal Argun, Aykut Volpe, Giovanni Imparato, Alberto Rondoni, Lamberto Oshanin, Gleb |
| author_facet | Viot, Pascal Argun, Aykut Volpe, Giovanni Imparato, Alberto Rondoni, Lamberto Oshanin, Gleb |
| contents | 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 ${\cal L}$ and angular velocity $\cal W$ 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 ${\cal L}$ and $\cal W$. For finite time-step $δt$, the PDF of ${\cal L}$ has exponential tails and all moments are therefore well-defined, but the noise-to-signal ratio can attain big values for small $δt$. Conversely, the PDF of ${\cal W}$ exhibits heavy power-law tails and its mean ${\cal W}$ 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 |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2307_05248 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Destructive effect of fluctuations on the performance of a Brownian gyrator Viot, Pascal Argun, Aykut Volpe, Giovanni Imparato, Alberto Rondoni, Lamberto Oshanin, Gleb Statistical Mechanics 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 ${\cal L}$ and angular velocity $\cal W$ 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 ${\cal L}$ and $\cal W$. For finite time-step $δt$, the PDF of ${\cal L}$ has exponential tails and all moments are therefore well-defined, but the noise-to-signal ratio can attain big values for small $δt$. Conversely, the PDF of ${\cal W}$ exhibits heavy power-law tails and its mean ${\cal W}$ 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 |
| title | Destructive effect of fluctuations on the performance of a Brownian gyrator |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2307.05248 |