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摘要翻译：
我们用多项式系数方法重新考虑热力学中的Boltzmann-Gibbs统计系综。我们证明了系综是由确定元素概率P_i$、构型概率P_j$、熵$S$和极值约束(EC)四个统计量来定义的。这种区别对于理解定义微正则系综、正则系综和宏正则系综的条件至关重要。这三个系综的特点是它们的大小守恒。系综大小的变化给四元组${p_i,P_j,S,Mt{EC}$的定义带来了困难，引起了玻尔兹曼-吉布斯形式的推广，如Tsallis所引入的。我们证明了广义热力学代表了普通热力学的一种变换，使得系统的能量保持守恒。从我们的结果可以明显看出，Tsallis的形式主义是一个非常具体的概括，然而，并不是唯一的概括。我们还重新讨论了Jaynes的最大熵原理，表明它通常会导致不正确的结果，并考虑适当的修正。
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英文标题：
《From Boltzmann-Gibbs ensemble to generalized ensembles》
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作者：
Thomas Oikonomou
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最新提交年份：
2011
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分类信息：
一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
We reconsider the Boltzmann-Gibbs statistical ensemble in thermodynamics using the multinomial coefficient approach. We show that an ensemble is defined by the determination of four statistical quantities, the element probabilities $p_i$, the configuration probabilities $P_j$, the entropy $S$ and the extremum constraints (EC). This distinction is of central importance for the understanding of the conditions under which a microcanonical, canonical and macrocanonical ensemble is defined. These three ensembles are characterized by the conservation of their sizes. A variation of the ensemble size creates difficulties in the definitions of the quadruplet $\{p_i, P_j, S, \mt{EC}\}$, giving rise for a generalization of the Boltzmann-Gibbs formalism, such one as introduced by Tsallis. We demonstrate that generalized thermodynamics represent a transformation of ordinary thermodynamics in such a way that the energy of the system remains conserved. From our results it becomes evident that Tsallis's formalism is a very specific generalization, however, not the only one. We also revisit the Jaynes's Maximum Entropy Principle, showing that in general it can lead to incorrect results and consider the appropriate corrections.
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PDF链接：
https://arxiv.org/pdf/712.231
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