The role of constraints within generalized nonextensive statistics
The role of constraints within generalized nonextensive statistics
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DOI：
10.1016/s0378-4371(98)00437-3
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发表时间：
1998-12-15
影响因子：
3.3
通讯作者：
Plastino, AR
中科院分区：
文献类型：
--
作者：
Tsallis, C;Mendes, RS;Plastino, AR
吉布斯-杰恩斯引入统计力学的途径是基于采用物理上适当的约束的特定熵形式。例如，对于通常的正则系综，采用(i) S-1 = -k Sigma(i) p(i) ln p(i), (ii) Sigma(i) p(i) = 1, (iii) Sigma(i) p(i) epsilon(i) = U-1 （{epsilon(i)}）降特征值的哈密顿量；U-1下降内能)。平衡包括在存在约束（ii）和（iii）的情况下，对{p(i)}进行SI优化。在最近引入的非广泛统计中，(i)被推广为S-q = k[1 - Sigma(i) p(i)(q)]/[q -1] (q—> 1再现S-1), （ii）被维持，（iii）以可能涉及p(i)(q)的方式被推广。在目前的努力中，我们分析了（iii）的一些特殊选择的后果，以及它们对文献中研究的各种物理系统的形式和实际含义。为了说明一些数学上相关的问题，我们分别计算了与非简并二能级系统以及经典谐振子和量子谐振子相关的比热。(C) 1998 Elsevier Science B.V.版权所有
The Gibbs-Jaynes path for introducing statistical mechanics is based on the adoption of a specific entropic form S ann of physically appropriate constraints. For instance, for the usual canonical ensemble, one adopts (i) S-1 = -k Sigma(i) p(i) ln p(i), (ii) Sigma(i) p(i) = 1 and (iii) Sigma(i) p(i) epsilon(i) = U-1 ({epsilon(i)} drop eigenvalues of the Hamiltonian; U-1 drop internal energy). Equilibrium consists in optimizing SI with regard to {p(i)} in the presence of constraints (ii) and (iii). Within the recently introduced nonextensive statistics, (i) is generalized into S-q = k[1 - Sigma(i) p(i)(q)]/[q - 1] (q --> 1 reproduces S-1), (ii) is maintained, and (iii) is generalized in a manner which might involve p(i)(q). In the present effort, we analyze the consequences of some special choices for (iii), and their formal and practical implications for the various physical systems that have been studied in the literature. To illustrate some mathematically relevant points, we calculate the specific heat respectively associated with a nondegenerate two-level system as well as with the classical and quantum harmonic oscillators. (C) 1998 Elsevier Science B.V. All rights reserved.