Equivalence between four versions of thermostatistics based on strongly pseudoadditive entropies
Equivalence between four versions of thermostatistics based on strongly pseudoadditive entropies
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DOI：
10.1103/physreve.100.062135
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发表时间：
2019-12-26
影响因子：
2.4
通讯作者：
Wada, Tatsuaki
中科院分区：
文献类型：
--
作者：
Ilic, Velimir M.;Scarfone, Antonio Maria;Wada, Tatsuaki
强伪加性熵（SPA）可以表示为Shannon熵和Renyi熵的一个递增的连续变换，这类熵在过去几十年中得到了广泛的研究。虽然它们的数学结构已经被广泛的Shannon-Khinchin公理所探索和建立，但它们的热统计性质的分析大多局限于属于双参数Sharma-Mittal熵类的特殊情况，如Tsallis、Renyi和高斯熵。在本文中，我们提出了一个一般的分析强伪加性熵热统计考虑了线性和护航约束的内能。我们发展了热统计形式之间的两种对偶性。将Renyi熵的形式转化为一般能量约束下的SPA熵的形式，将线性约束下的广义热统计量转化为护航约束下的广义热统计量。因此，我们建立了基于Renyi熵和SPA熵耦合线性约束和护航约束的四种不同热统计形式之间的等价性，并提供了转换公式。通过这种方式，我们得到了一个一般的框架，它适用于以前文献中讨论过的广泛的熵和约束类。作为一个例子，我们重新推导了Sharma-Mittal熵的最大熵分布，并建立了相应的热力学势之间的新关系。作为特殊情况，我们获得了以前开发的最大熵分布和Tsallis， Renyi和高斯熵的热力学量的表达式。此外，该结果还应用于推导超广义熵的热统计关系，这是以前没有考虑过的。
The class of strongly pseudoadditive (SPA) entropies, which can be represented as an increasing continuous transformation of Shannon and Renyi entropies, have intensively been studied in previous decades. Although their mathematical structure has thoroughly been explored and established by generalized Shannon-Khinchin axioms, the analysis of their thermostatistical properties have mostly been limited to special cases which belong to two parameter Sharma-Mittal entropy class, such as Tsallis, Renyi and Gaussian entropies. In this paper we present a general analysis of the strongly pseudoadditive entropies thermostatistics by taking into account both linear and escort constraints on internal energy. We develop two types of dualities between the thermostatistics formalisms. By the first one, the formalism of Renyi entropy is transformed in the formalism of SPA entropy under general energy constraint and, by the second one, the generalized thermostatistics which corresponds to the linear constraint is transformed into the one which corresponds to the escort constraint. Thus, we establish the equivalence between four different thermostatistics formalisms based on Renyi and SPA entropies coupled with linear and escort constraints and we provide the transformation formulas. In this way we obtain a general framework which is applicable to the wide class of entropies and constraints previously discussed in the literature. As an example, we rederive maximum entropy distributions for Sharma-Mittal entropy and we establish new relationships between the corresponding thermodynamic potentials. We obtain, as special cases, previously developed expressions for maximum entropy distributions and thermodynamic quantities for Tsallis, Renyi, and Gaussian entropies. In addition, the results are applied for derivation of thermostatistical relationships for supraextensive entropy, which has not previously been considered.