Inspired by recent experiments on fluctuations of flagellar beating in sperm and C. reinhardtii, we investigate the precision of phase fluctuations in a system of nearest-neighbor-coupled molecular motors. We model the system as a Kuramoto chain of oscillators with a coupling constant k and noisy driving. The precision p is a Fano-factor-like observable, which obeys the thermodynamic uncertainty relation (TUR), which is an upper bound related to dissipation. We first consider independent motor noises with diffusivity D: in this case, the precision goes as k/D , coherently with the behavior of spatial order. The minimum observed precision is that of the uncoupled oscillator punc ; the maximum observed precision is Npunc , saturating the TUR bound. Then we consider driving noises which are spatially correlated, as may happen in the presence of some direct coupling between adjacent motors. Such a spatial correlation in the noise does not evidently reduce the degree of spatial correlation in the chain, but sensibly reduces the maximum attainable precision p, coherently with experimental observations. The limiting behavior of the precision, in the two opposite cases of negligible interaction and strong interaction, is well reproduced by the precision of the single chain site punc and the precision of the center of mass of the chain Neffpunc with Neff<N : both do not depend on the degree of interaction in the chain, but Neff decreases with the correlation length of the motor noises.

中文翻译：

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电机链的热力学精度：相位差和噪声相关性

受到最近关于精子鞭毛跳动波动的实验的启发莱茵衣藻，我们研究了最近邻耦合分子马达系统中相位波动的精度。我们将系统建模为具有耦合常数的 Kuramoto 振荡器链k和嘈杂的驾驶。精度p是一个类似 Fano 因子的可观测量，它遵循热力学不确定性关系 (TUR)，这是与耗散相关的上限。我们首先考虑具有扩散性的独立电机噪声D：在这种情况下，精度为 k/D ，与空间秩序的行为一致。最小观测精度是非耦合振荡器的精度 p你nC ;最大观测精度为 氮p你nC ，使 TUR 界限饱和。然后我们考虑空间相关的驱动噪声，这可能发生在相邻电机之间存在某种直接耦合的情况下。噪声中的这种空间相关性并没有明显降低链中的空间相关性程度，但明显降低了可达到的最大精度p，与实验观察一致。在可忽略的相互作用和强相互作用的两种相反情况下，精度的限制行为可以通过单链位点的精度很好地再现 p你nC 以及链条质心的精度 氮eFFp你nC 和 氮eFF<氮 : 两者都可以不是取决于链中相互作用的程度，但是 氮eFF 随着电机噪声的相关长度的增加而减小。