论文标题
对规模依赖性复杂性的正式定义和必要多样性的多尺度定律
A Formal Definition of Scale-dependent Complexity and the Multi-scale Law of Requisite Variety
论文作者
论文摘要
阿什比（Ashby）的必要品种定律允许将系统与其环境进行比较，从而提供了系统功效的必要条件（但不够）：系统必须具有至少与任何需要从系统中不同响应的环境行为的复杂性。但是，为了说明系统的复杂性对其描述的细节或规模级别的依赖性，需要对Ashby定律进行多尺度的概括。据我们所知，我们定义了一系列复杂性概况（复杂性作为规模的函数），它首先展示了必要多样性的多尺度定律。这种形式主义提供了多尺度复杂性的特征，并将必要品种对系统行为的单一限制定律概括为一类多尺度约束。我们表明，这些复杂性概况满足了一个总规则，这反映了较小和较大规模的自由度之间的权衡，我们将结果扩展到具有连续组件的细分系统和系统。
Ashby's law of requisite variety allows a comparison of systems with their environments, providing a necessary (but not sufficient) condition for system efficacy: a system must possess at least as much complexity as any set of environmental behaviors that require distinct responses from the system. However, to account for the dependence of a system's complexity on the level of detail -- or scale -- of its description, a multi-scale generalization of Ashby's law is needed. We define a class of complexity profiles (complexity as a function of scale) that is the first, to our knowledge, to exhibit a multi-scale law of requisite variety. This formalism provides a characterization of multi-scale complexity and generalizes the law of requisite variety's single constraint on system behaviors to a class of multi-scale constraints. We show that these complexity profiles satisfy a sum rule, which reflects a tradeoff between smaller- and larger-scale degrees of freedom, and we extend our results to subdivided systems and systems with a continuum of components.
