Favretti Marco
Dipartimento di Matematica "Tullio Levi-Civita", Università degli Studi di Padova, 35122 Padova, Italy.
Entropy (Basel). 2017 Dec 27;20(1):11. doi: 10.3390/e20010011.
In the first part of the paper we work out the consequences of the fact that Jaynes' Maximum Entropy Principle, when translated in mathematical terms, is a for an entropy function H ( p ) expressing the uncertainty associated with the probability distribution . Consequently, if two observers use different independent variables or g ( p ) , the associated entropy functions have to be defined accordingly and they are different in the general case. In the second part we apply our findings to an analysis of the foundations of the Maximum Entropy Theory of Ecology (M.E.T.E.) a purely statistical model of an ecological community. Since the theory has received considerable attention by the scientific community, we hope to give a useful contribution to the same community by showing that the procedure of application of MEP, in the light of the theory developed in the first part, suffers from some incongruences. We exhibit an alternative formulation which is free from these limitations and that gives different results.
在本文的第一部分，我们阐述了这样一个事实的结果：当用数学术语表述时，杰恩斯的最大熵原理是一个关于熵函数(H(p))的[具体内容缺失]，该熵函数表示与概率分布相关的不确定性。因此，如果两个观察者使用不同的独立变量(f(p))或(g(p))，则相关的熵函数必须相应地定义，并且在一般情况下它们是不同的。在第二部分中，我们将我们的发现应用于对生态最大熵理论（M.E.T.E.）基础的分析，这是一个生态群落的纯统计模型。由于该理论已受到科学界的相当关注，我们希望通过表明根据第一部分所发展的理论，最大熵原理的应用过程存在一些不一致之处，从而为同一科学界做出有益贡献。我们展示了一种没有这些局限性且能给出不同结果的替代表述。
