研究以效率衡量为工具，将最小努力原则应用于推导齐普夫定律和帕累托定律
Study of a measure of efficiency as a tool for applying the principle of least effort to the derivation of the Zipf and the Pareto laws
摘要：
最小努力原则被认为是生命系统的普遍规则。将其应用于推导生命系统的幂律概率分布一直是一个挑战。最近，一个衡量效率的工具，提出了直接从最小努力的原则推导齐普夫和帕累托定律。目前的工作是从数学的角度进一步研究这种效率措施。其目的是进一步了解其属性和有用性作为性能指标。我们解决了一些关键的数学性质，这种效率，如它的符号，唯一性和鲁棒性。我们也看看这个措施和其他属性的系统，如不平等和不确定性之间的关系，通过引入一种新的方法来计算非负连续熵。
英文摘要：
The principle of least effort is believed to be a universal rule for living systems. Its application to the derivation of the power law probability distributions of living systems has long been challenging. Recently, a measure of efficiency was proposed as a tool of deriving Zipf s and Pareto s laws directly from the principle of least effort. The present work is a further investigation of this efficiency measure from a mathematical point of view. The aim is to get further insight into its properties and usefulness as a metric of performance. We address some key mathematical properties of this efficiency such as its sign, uniqueness and robustness. We also look at the relationship between this measure and other properties of the system of interest such as inequality and uncertainty, by introducing a new method for calculating non-negative continuous entropy.
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