论文标题
迈向复杂性的普遍衡量
Towards a Universal Measure of Complexity
论文作者
论文摘要
最近有人认为，熵可以是对复杂性的直接度量，其中熵的较小值表明系统复杂性较低，而其较大的值表示较高的系统复杂性。我们对这种观点提出异议，并根据盖尔·曼（Gell-Mann）的复杂性提出了普遍的复杂性度量。我们对时间依赖性熵的非线性转换的普遍衡量底座的普遍度量，其中系统状态最高的系统状态与较小或没有复杂性系统的所有状态最远。我们已经表明，最复杂的是由纯状态组成的最佳混合状态，即给定系统的状态空间所允许的最规则和最无序的状态。证明最简单的最简单系统的范式范式示例显示，显示了这种方法。指出了这种通用度量的几个重要特征，尤其是其灵活性（即其对扩展的开放性），分析系统关键行为的能力以及研究动态复杂性的能力。
Recently it has been argued that entropy can be a direct measure of complexity, where the smaller value of entropy indicates lower system complexity, while its larger value indicates higher system complexity. We dispute this view and propose a universal measure of complexity based on the Gell-Mann's view of complexity. Our universal measure of complexity bases on a non-linear transformation of time-dependent entropy, where the system state with the highest complexity is the most distant from all the states of the system of lesser or no complexity. We have shown that the most complex is optimally mixed states consisting of pure states i.e., of the most regular and most disordered which the space of states of a given system allows. A parsimonious paradigmatic example of the simplest system with a small and a large number of degrees of freedom, is shown to support this methodology. Several important features of this universal measure are pointed out, especially its flexibility (i.e., its openness to extensions), ability to the analysis of a system critical behavior, and ability to study the dynamic complexity.
