基于q-变形微积分的广义统计变分摄动逼近
Generalized Statistics Variational Perturbation Approximation using q-Deformed Calculus
摘要：
介绍了一个在Tsallis统计量的非加性统计范围内推广变分扰动近似（VPA）的原则框架。这是通过使用\emph{q-deformed calculus}制定的变分程序的广义自由能（GFE）的微扰展开的条款构成的操作。借助于Hellmann-Feynman定理，导出了一个候选的\textit{q-deformed}广义VPA（GVPA）.在正则概率密度最大化Tsallis熵的情况下，得到了近似广义有限单元的广义Bogoliubov不等式。数值例子表明应用的\textit{q-deformed} GVPA。强调了\textit{q-deformed} GVPA模型与\textit{vis-á-vis}先前GVPA模型之间的定性区别。
英文摘要：
A principled framework to generalize variational perturbation approximations (VPA's) formulated within the ambit of the nonadditive statistics of Tsallis statistics, is introduced. This is accomplished by operating on the terms constituting the perturbation expansion of the generalized free energy (GFE) with a variational procedure formulated using \emph{q-deformed calculus}. A candidate \textit{q-deformed} generalized VPA (GVPA) is derived with the aid of the Hellmann-Feynman theorem. The generalized Bogoliubov inequality for the approximate GFE are derived for the case of canonical probability densities that maximize the Tsallis entropy. Numerical examples demonstrating the application of the \textit{q-deformed} GVPA are presented. The qualitative distinctions between the \textit{q-deformed} GVPA model \textit{vis-á-vis} prior GVPA models are highlighted.
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