摘要翻译：
本文从基指数出发，给出了广义统计力学的一种可能形式。基指数是在基超几何级数框架下建立的指数函数的q变形形式。在q-非均匀格中，利用q-变分原理引入了与基指数有关的基熵。值得注意的是，这种分布在能谱中表现出一个自然截止。这一事实在广义统计力学的其他公式中已经遇到过，预计将与该理论在那些由长程相互作用控制的系统中的应用有关。利用q-微积分，证明了标准热力学函数关系是保留的，从而模拟了在q=1极限下恢复的一般热力学统计量的数学结构。
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英文标题：
《Basic-deformed thermostatistics》
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作者：
A. Lavagno, A.M. Scarfone and P. Narayana Swamy
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最新提交年份：
2007
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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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一级分类：Physics        物理学
二级分类：Mathematical Physics        数学物理
分类描述：Articles in this category focus on areas of research that illustrate the application of mathematics to problems in physics, develop mathematical methods for such applications, or provide mathematically rigorous formulations of existing physical theories. Submissions to math-ph should be of interest to both physically oriented mathematicians and mathematically oriented physicists; submissions which are primarily of interest to theoretical physicists or to mathematicians should probably be directed to the respective physics/math categories
这一类别的文章集中在说明数学在物理问题中的应用的研究领域，为这类应用开发数学方法，或提供现有物理理论的数学严格公式。提交的数学-PH应该对物理方向的数学家和数学方向的物理学家都感兴趣；主要对理论物理学家或数学家感兴趣的投稿可能应该指向各自的物理/数学类别
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一级分类：Mathematics        数学
二级分类：Mathematical Physics        数学物理
分类描述：math.MP is an alias for math-ph. Articles in this category focus on areas of research that illustrate the application of mathematics to problems in physics, develop mathematical methods for such applications, or provide mathematically rigorous formulations of existing physical theories. Submissions to math-ph should be of interest to both physically oriented mathematicians and mathematically oriented physicists; submissions which are primarily of interest to theoretical physicists or to mathematicians should probably be directed to the respective physics/math categories
math.mp是math-ph的别名。这一类别的文章集中在说明数学在物理问题中的应用的研究领域，为这类应用开发数学方法，或提供现有物理理论的数学严格公式。提交的数学-PH应该对物理方向的数学家和数学方向的物理学家都感兴趣；主要对理论物理学家或数学家感兴趣的投稿可能应该指向各自的物理/数学类别
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一级分类：Mathematics        数学
二级分类：Quantum Algebra        量子代数
分类描述：Quantum groups, skein theories, operadic and diagrammatic algebra, quantum field theory
量子群，skein理论，运算代数和图解代数，量子场论
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一级分类：Physics        物理学
二级分类：Nuclear Theory        核理论
分类描述：Nuclear Theory Theory of nuclear structure covering wide area from models of hadron structure to neutron stars. Nuclear equation of states at different external conditions. Theory of nuclear reactions including heavy-ion reactions at low and high energies. It does not include problems of data analysis, physics of nuclear reactors, problems of safety, reactor construction
核理论涵盖从强子结构模型到中子星等广泛领域的核结构理论。不同外部条件下的核状态方程。核反应理论，包括低能和高能的重离子反应。它不包括数据分析问题、核反应堆物理问题、安全问题、反应堆建设问题
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英文摘要：
  Starting from the basic-exponential, a q-deformed version of the exponential function established in the framework of the basic-hypergeometric series, we present a possible formulation of a generalized statistical mechanics. In a q-nonuniform lattice we introduce the basic-entropy related to the basic-exponential by means of a q-variational principle. Remarkably, this distribution exhibits a natural cut-off in the energy spectrum. This fact, already encountered in other formulations of generalized statistical mechanics, is expected to be relevant to the applications of the theory to those systems governed by long-range interactions. By employing the q-calculus, it is shown that the standard thermodynamic functional relationships are preserved, mimicking, in this way, the mathematical structure of the ordinary thermostatistics which is recovered in the q=1 limit.
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PDF链接：
https://arxiv.org/pdf/706.0426