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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Superstatistics ： ウィキペディア英語版 Superstatistics Superstatistics is a branch of statistical mechanics or statistical physics devoted to the study of non-linear and non-equilibrium systems. It is characterized by using the superposition of multiple differing statistical models to achieve the desired non-linearity. In terms of ordinary statistical ideas, this is equivalent to compounding the distributions of random variables and it may be considered a simple case of a doubly stochastic model. Consider an extended thermodynamical system which is locally in equilibrium and has a Boltzmann distribution, that is the probability of finding the system in a state with energy $E$ is proportional to $\backslash exp(-\backslash beta\; E)$. Here $\backslash beta$ is the local inverse temperature. A non-equilibrium thermodynamical system is modeled by considering macroscopic fluctuations of the local inverse temperature. These fluctuations happen on time scales which are much larger than the microscopic relaxation times to the Boltzmann distribution. If the fluctuations of $\backslash beta$ are characterized by a distribution $f(\backslash beta)$, the ''superstatistical Boltzmann factor'' of the system is given by :$$ B(E)=\int_0^\infty d\beta f(\beta)\exp(-\beta E). This defines the superstatistical partition function :$$ Z = \sum_^W B(E_i), where the system can assume discrete energy states $\backslash \_^W$. The probability of finding the system in state $E\_i$ is then given by :$$ p_i=\fracB(E_i). Modeling the fluctuations of $\backslash beta$ leads to a description in terms of statistics of Boltzmann statistics, or "superstatistics". One needs to note here that the word super here is short for superposition of the statistics. ==See also== * Maxwell–Boltzmann statistics 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Superstatistics」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.