最大熵定理及其在生物多样性度量中的应用
A maximum entropy theorem with applications to the measurement of biodiversity
摘要：
这是一个初步的文章陈述和证明一个新的最大熵定理。我们认为熵可以用来衡量生物多样性。在这种情况下，问题是：对于给定的物种集合，哪种频率分布最大化了多样性？这个定理给出了答案。最令人惊讶的是，虽然我们处理的不仅仅是一个熵，而是一个单参数熵族，但存在一个同时使所有熵最大化的分布。
英文摘要：
This is a preliminary article stating and proving a new maximum entropy theorem. The entropies that we consider can be used as measures of biodiversity. In that context, the question is: for a given collection of species, which frequency distribution(s) maximize the diversity? The theorem provides the answer. The chief surprise is that although we are dealing with not just a single entropy, but a one-parameter family of entropies, there is a single distribution maximizing all of them simultaneously.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
