Plastino Angel R, Tsallis Constantino, Wedemann Roseli S, Haubold Hans J
CeBio y Departamento de Ciencias Básicas, Universidad Nacional del Noroeste de la Província de Buenos Aires, UNNOBA, CONICET, Roque Saenz Peña 456, Junin B6000, Argentina.
Centro Brasileiro de Pesquisas Físicas and National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, Rio de Janeiro 22290-180, RJ, Brazil.
Entropy (Basel). 2022 Nov 25;24(12):1723. doi: 10.3390/e24121723.
Several generalizations or extensions of the Boltzmann-Gibbs thermostatistics, based on non-standard entropies, have been the focus of considerable research activity in recent years. Among these, the power-law, non-additive entropies Sq≡k1-∑ipiqq-1(q∈R;S1=SBG≡-k∑ipilnpi) have harvested the largest number of successful applications. The specific structural features of the Sq thermostatistics, therefore, are worthy of close scrutiny. In the present work, we analyze one of these features, according to which the -logarithm function lnqx≡x1-q-11-q(ln1x=lnx) associated with the Sq entropy is linked, via a duality relation, to the -exponential function characterizing the maximum-entropy probability distributions. We enquire into which entropic functionals lead to this or similar structures, and investigate the corresponding duality relations.
近年来，基于非标准熵的玻尔兹曼 - 吉布斯统计力学的若干推广或扩展一直是大量研究活动的焦点。其中，幂律非加性熵(S_q\equiv k\frac{1 - \sum_ip_i^q}{q - 1}(q\in R; S_1 = S_{BG}\equiv -k\sum_ip_i\ln p_i))获得了最多的成功应用。因此，(S_q)统计力学的具体结构特征值得仔细研究。在本工作中，我们分析这些特征之一，即与(S_q)熵相关的(-)对数函数(\ln_qx\equiv\frac{x^{1 - q} - 1}{1 - q}(\ln_1x = \ln x))通过对偶关系与表征最大熵概率分布的(-)指数函数相关联。我们探究哪些熵泛函会导致这种或类似结构，并研究相应的对偶关系。
