大学化学 >> 2015, Vol. 30 >> Issue (6): 83-88.doi: 10.3866/pku.DXHX20150683

自学之友 上一篇    

平衡分布与最概然分布

刘国杰, 黑恩成   

  1. 华东理工大学化学系 上海 200237
  • 发布日期:2015-12-25
  • 通讯作者: 黑恩成 E-mail:heiec@ecust.edu.cn
  • 基金资助:

    教育部教育质量工程建设项目(No.YJ0136104);国家精品资源共享课建设项目(No.YJ0125206)

Equilibrium Distribution and the Most Probable Distribution

Liu Guojie, Hei Encheng   

  1. School of Chemistry, East China University of Science and Technology, Shanghai, 200237, China
  • Published:2015-12-25

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摘要：

以二项分布为例,阐述了平衡分布与最概然分布间的关系。通过子数很多时,二项分布可以变为正态分布以及它的相对涨落与子数的平方根成反比的统计力学原理,阐明了热力学系统的平衡分布可用其最概然分布来代表。

关键词: 平衡分布, 最概然分布, 热力学系统的相对涨落

Abstract:

Taking binomial distribution as an illustration, we elaborated the relationship between equilibrium distribution and the most probable distribution. According to the statistical mechanics, the binomial distribution approximates to the normal distribution when the number is large enough, and the relative fluctuation is inversely proportional to the square root of the number, we illustrated that the equilibrium distribution of a thermodynamic system could be described by the most probable distribution.

Key words: Equilibrium distribution, Most probable distribution, Relative fluctuation of thermodynamic system