关于广义熵测度和途径
On generalized entropy measures and pathways
摘要：
产品的概率属性，在文献中称为统计独立性，首先检查。然后引入了广义熵，它们都是香农熵的推广。结果表明，递归性假设的性质自动确定香农熵的对数函数形式。由于对数性质，当应用于具有乘积概率性质的情况时，香农熵自然会产生可加性。有人认为，自然的过程是非加性，重要的，例如，在统计力学，甚至在产品的概率属性的情况下和加性可以举行由于参与递归假设导致一个对数函数。推广，包括Mathai的广义熵的介绍和一些属性进行了检查。情况下检查Mathai的熵导致通路模型，指数和幂律行为和相关的微分方程。马泰的熵Kerridge的措施的“不准确性”的连接也进行了探讨。
英文摘要：
Product probability property, known in the literature as statistical independence, is examined first. Then generalized entropies are introduced, all of which give generalizations to Shannon entropy. It is shown that the nature of the recursivity postulate automatically determines the logarithmic functional form for Shannon entropy. Due to the logarithmic nature, Shannon entropy naturally gives rise to additivity, when applied to situations having product probability property. It is argued that the natural process is non-additivity, important, for example, in statistical mechanics, even in product probability property situations and additivity can hold due to the involvement of a recursivity postulate leading to a logarithmic function. Generalizations, including Mathai's generalized entropy are introduced and some of the properties are examined. Situations are examined where Mathai's entropy leads to pathway models, exponential and power law behavior and related differential equations. Connection of Mathai's entropy to Kerridge's measure of "inaccuracy" is also explored.
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