Synchronization among arrays of beating cilia is one of the emergent phenomena in biological processes at meso-scopic scales. Strong inter-ciliary couplings modify the natural beating frequencies, $\omega$, of individual cilia to produce a collective motion that moves around a group frequency $\omega_m$. Here we study the thermodynamic cost of synchronizing cilia arrays by mapping their dynamics onto a generic phase oscillator model. The model suggests that upon synchronization the mean heat dissipation rate is decomposed into two contributions, dissipation from each cilium's own natural driving force and dissipation arising from the interaction with other cilia, the latter of which can be interpreted as the one produced by a potential with a time-dependent protocol in the framework of our model. The spontaneous phase-synchronization of beating dynamics of cilia induced by strong inter-ciliary coupling is always accompanied with a significant reduction of dissipation for the cilia population, suggesting that organisms as a whole expend less energy by attaining a temporal order. At the level of individual cilia, however, a population of cilia with $|\omega|< \omega_m$ expend more amount of energy upon synchronization.

中文翻译：

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使一群跳动的纤毛同步的热力学成本

跳动纤毛阵列之间的同步是细观尺度生物过程中的新兴现象之一。强大的纤毛间耦合改变了个体纤毛的自然跳动频率 $\omega_ 以产生围绕群频率 $\omega_m$ 移动的集体运动。在这里，我们通过将纤毛阵列的动力学映射到通用相位振荡器模型来研究同步纤毛阵列的热力学成本。该模型表明，在同步时，平均散热率分解为两个贡献，来自每个纤毛自身自然驱动力的耗散和来自与其他纤毛相互作用的耗散，后者可以解释为由具有我们模型框架中的时间相关协议。由强烈的纤毛间耦合引起的纤毛搏动动力学的自发相位同步总是伴随着纤毛种群耗散的显着减少，这表明生物体作为一个整体通过获得时间顺序消耗更少的能量。然而，在单个纤毛的水平上，$|\omega|< \omega_m$ 的纤毛种群在同步时消耗更多的能量。