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 that is based on Gell-Mann’s view of complexity. Our universal measure of complexity is based 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 the optimally mixed state 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), suitability to the analysis of system critical behaviour, and suitability to study the dynamic complexity.

中文翻译：

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迈向复杂性的通用度量

最近，有人认为熵可以作为复杂度的直接度量，熵值越小表示系统复杂度越低，而熵值越大表示系统复杂度越高。我们对这一观点提出异议，并基于盖尔曼的复杂性观点提出了一种通用的复杂性衡量标准。我们对复杂性的通用度量基于与时间相关的熵的非线性变换，其中具有最高复杂性的系统状态与具有较小复杂性或没有复杂性的系统的所有状态最远。我们已经证明，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允许的最规则和最无序的状态。显示了具有少量和大量自由度的最简单系统的简约范式示例支持这种方法。指出了这种通用度量的几个重要特征，特别是它的灵活性（即对扩展的开放性）、对系统关键行为分析的适用性以及对动态复杂性研究的适用性。