复杂系统的统计力学和热力学
Statistical mechanics and thermodynamics of complex systems
摘要：
本文提出了一个基于广义Massieu-Planck热力学势的统一理论框架，建立了Boltzmann-Gibbs统计力学的新表述。根据这一理念的推广（经典）玻尔兹曼-吉布斯热统计学的建议，并连接到最近的非广泛的统计公式。这是通过定义一个方便的压缩函数来实现的，该压缩函数限制了完全平衡封闭的玻尔兹曼-吉布斯构型的集合。形式主义体现贝克-科恩超统计和直接连接的非线性动力学理论由于Kaniadakis提供，被提出的治疗完全符合它。作为一个例子Tsallis非广延统计完全重建到我们的制定增加新的见解（热力学第零定律，非特设定义的平均值的物理量，.）。我们将所有形式的发展与物理量和可测量量联系起来，并提出了一种建立任何基于温度测定的系统的相关统计的方法。
英文摘要：
An unified thermodynamical framework based in the use of a generalized Massieu-Planck thermodynamic potential is proposed and a new formulation of Boltzmann-Gibbs Statistical Mechanics is established. Under this philosophy a generalization of (classical) Boltzmann-Gibbs thermostatistics is suggested and connected to recent nonextensive statistics formulations. This is accomplished by defining a convenient squeezing function which restricts among the collections of Boltzmann-Gibbs configurations of the complete equilibrium closure. The formalism embodies Beck-Cohen superstatistics and a direct connection with the nonlinear kinetic theory due to Kaniadakis is provided, being the treatment presented fully consistent with it. As an example Tsallis nonextensive statistics is completely rebuilt into our formulation adding new insights (zeroth law of thermodynamics, non ad hoc definition of the mean value of a physical quantity,...). We relate all the formal development to physical and measurable quantities and suggest a way to establish the relevant statistics of any system based on determinations of temperature.
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