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

arXiv comment6 pages +ESI 10 pages

References in corpus (23)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Active Particles in Complex and Crowded Environments
• Brownian motors: noisy transport far from equilibrium
• Artificial Brownian motors: Controlling transport on the nanoscale
• On the heat flux and entropy produced by thermal fluctuations
• The Brownian gyrator: a minimal heat engine on the nano-scale
• Non-equilibrium and information: the role of cross-correlations
• Experimental Realization of a Minimal Microscopic Heat Engine
• Two-temperature Langevin dynamics in a parabolic potential
• Statistical properties of the energy exchanged between two heat baths coupled by thermal fluctuations
• Two-temperature Brownian dynamics of a particle in a confining potential
• Asymmetry relations and effective temperatures for biased Brownian gyrators
• Inference in non-equilibrium systems from incomplete information: the case of linear systems and its pitfalls
• Dynamical large deviations of linear diffusions
• A simple system with two temperatures
• Inertial effects on the Brownian gyrator
• Nonequilibrium diffusion processes via non-Hermitian electromagnetic quantum mechanics with application to the statistics of entropy production in the Brownian gyrator
• Autonomous quantum rotator
• Autonomous Brownian gyrators: a study on gyrating characteristics
• Information-theoretic analysis of the directional influence between cellular processes
• Fractional Brownian Gyrator
• Cooperative dynamics in two-component out-of-equilibrium systems: Molecular "spinning tops"
• Irregular gyration of a two-dimensional random-acceleration process in a confining potential

Cited by in corpus (2)

• Interrogating the Ballistic Regime in Liquids with Rotational Optical Tweezers
• Charging capacitors using diodes at different temperatures. I Theor