Being able to measure time, whether directly or indirectly, is a significant advantage for an organism. It allows for timely reaction to regular or predicted events, reducing the pressure for fast processing of sensory input. Thus, clocks are ubiquitous in biology. In the present article, we consider minimal abstract pure clocks in different configurations and investigate their characteristic dynamics. We are especially interested in optimally time-resolving clocks. Among these, we find fundamentally diametral clock characteristics, such as oscillatory behavior for purely local time measurement or decay-based clocks measuring time periods on a scale global to the problem. We include also sets of independent clocks (clock bags), sequential cascades of clocks, and composite clocks with controlled dependence. Clock cascades show a condensation effect, and the composite clock shows various regimes of markedly different dynamics.

中文翻译：

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用最少的时钟测量时间

能够直接或间接测量时间对于生物体来说是一个重要的优势。它允许对常规或预测事件做出及时反应，减少对感官输入进行快速处理的压力。因此，时钟在生物学中无处不在。在本文中，我们考虑不同配置的最小抽象纯时钟并研究它们的特征动力学。我们对最佳时间分辨时钟特别感兴趣。其中，我们发现了基本的直径时钟特性，例如纯本地时间测量的振荡行为或基于衰减的时钟在全球范围内测量时间周期的问题。我们还包括独立时钟集（时钟包）、时钟的顺序级联和具有受控依赖性的复合时钟。时钟级联显示出凝聚效应，