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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 Tsallis entropy ： ウィキペディア英語版 Tsallis entropy In physics, the Tsallis entropy is a generalization of the standard Boltzmann–Gibbs entropy. It was introduced in 1988 by Constantino Tsallis as a basis for generalizing the standard statistical mechanics. In the scientific literature, the physical relevance of the Tsallis entropy was occasionally debated. However, from the years 2000 on, an increasingly wide spectrum of natural, artificial and social complex systems have been identified which confirm the predictions and consequences that are derived from this nonadditive entropy, such as nonextensive statistical mechanics, which generalizes the Boltzmann–Gibbs theory. Among the various experimental verifications and applications presently available in the literature, the following ones deserve a special mention: # The distribution characterizing the motion of cold atoms in dissipative optical lattices, predicted in 2003 and observed in 2006. # The fluctuations of the magnetic field in the solar wind enabled the calculation of the q-triplet (or Tsallis triplet). # The velocity distributions in driven dissipative dusty plasma. # Spin glass relaxation. # Trapped ion interacting with a classical buffer gas. # High energy collisional experiments at LHC/CERN (CMS, ATLAS and ALICE detectors) and RHIC/Brookhaven (STAR and PHENIX detectors). Among the various available theoretical results which clarify the physical conditions under which Tsallis entropy and associated statistics apply, the following ones can be selected: # Anomalous diffusion. # Uniqueness theorem. # Sensitivity to initial conditions and entropy production at the edge of chaos. # Probability sets which make the nonadditive Tsallis entropy to be extensive in the thermodynamical sense. # Strongly quantum entangled systems and thermodynamics. # Thermostatistics of overdamped motion of interacting particles. # Nonlinear generalizations of the Schroedinger, Klein-Gordon and Dirac equations. For further details a bibliography is available at http://tsallis.cat.cbpf.br/biblio.htm Given a discrete set of probabilities $\backslash$ with the condition $\backslash sum\_i\; p\_i=1$, and $q$ any real number, the Tsallis entropy is defined as :$S\_q()\; =\; \backslash left(\; 1\; -\; \backslash sum\_i\; p\_i^q\; \backslash right),$ where $q$ is a real parameter sometimes called ''entropic-index''. In the limit as $q\; \backslash to\; 1$, the usual Boltzmann–Gibbs entropy is recovered, namely :$S\_\; =\; S\_1(p)\; =\; -k\; \backslash sum\_i\; p\_i\; \backslash ln\; p\_i\; .$ For continuous probability distributions, we define the entropy as :$S\_q()\; =\; \backslash left(\; 1\; -\; \backslash int\; (p(x))^q\backslash ,\; dx\; \backslash right),$ where $p(x)$ is a probability density function. The Tsallis Entropy has been used along with the Principle of maximum entropy to derive the Tsallis distribution. == Various relationships == The discrete Tsallis entropy satisfies :$S\_q\; =\; -\backslash lim\_D\_q\; \backslash sum\_i\; p\_i^x$ where ''D''''q'' is the q-derivative with respect to ''x''. This may be compared to the standard entropy formula: :$S\; =\; -\backslash lim\_\backslash frac\; \backslash sum\_i\; p\_i^x$ 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「Tsallis entropy」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.