摘要翻译:
本文把相空间中被微正则系综所包围的体积看作一个统计系综。这可以解释为微正则图像和正则图像之间的中间图像。通过维持该系综上的遍历假设,即其所有可达态的等概率,用几何论证的方法证明了该系综在热力学极限下与微正则系综和正则系综的等价性。由这种形式得到了Maxwellian分布和Boltzmann-Gibbs分布。在附录中,还从一个新的正则系综的微正则像导出了玻尔兹曼因子。
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英文标题:
《On the equivalence of the microcanonical and the canonical ensembles: a
geometrical approach》
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作者:
Ricardo Lopez-Ruiz, Jaime Sanudo and Xavier Calbet
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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:Chaotic Dynamics 混沌动力学
分类描述:Dynamical systems, chaos, quantum chaos, topological dynamics, cycle expansions, turbulence, propagation
动力系统,混沌,量子混沌,拓扑动力学,循环展开,湍流,传播
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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:Statistics 统计学
二级分类:Methodology 方法论
分类描述:Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计,调查,模型选择,多重检验,多元方法,信号和图像处理,时间序列,平滑,空间统计,生存分析,非参数和半参数方法
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英文摘要:
In this paper, we consider the volume enclosed by the microcanonical ensemble in phase space as a statistical ensemble. This can be interpreted as an intermediate image between the microcanonical and the canonical pictures. By maintaining the ergodic hypothesis over this ensemble, that is, the equiprobability of all its accessible states, the equivalence of this ensemble in the thermodynamic limit with the microcanonical and the canonical ensembles is suggested by means of geometrical arguments. The Maxwellian and the Boltzmann-Gibbs distributions are obtained from this formalism. In the appendix, the derivation of the Boltzmann factor from a new microcanonical image of the canonical ensemble is also given.
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PDF链接:
https://arxiv.org/pdf/708.1866