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Entropy02:39

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Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
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A pure, perfectly crystalline solid possessing no kinetic energy (that is, at a temperature of absolute zero, 0 K) may be described by a single microstate, as its purity, perfect crystallinity,and complete lack of motion means there is but one possible location for each identical atom or molecule comprising the crystal (W = 1). According to the Boltzmann equation, the entropy of this system is zero.
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The second law of thermodynamics can be stated quantitatively using the concept of entropy. Entropy is the measure of disorder of the system.
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第一个数字的Shannon Entropy.

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  • 1Faculty of Natural Sciences, University of Ulm, Einsteinallee 11, D-89069 Ulm, Germany.

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概括

该研究探讨了数字数据中的Shannon,发现第一位数分布偏离了Newcomb-Benford定律. 这种偏差会影响计算,揭示非标准分布的较低值.

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科学领域:

  • 信息理论 信息理论
  • 统计分析 统计分析
  • 数据科学数据科学数据科学

背景情况:

  • 值量化信息,测量字符传输的平均二进制数字.
  • 纽科姆-本福德定律 (NB定律) 描述了数字数据集中首位数字的典型频率分布.
  • 从NB法规中可以出现偏差,首位数字"1"的出现比预测的频率要高得多.

研究的目的:

  • 计算和比较各种第一位数分布的香农 (H).
  • 调查从Newcomb-Benford定律的偏差如何影响值.
  • 在各种数据集中分析,包括那些不遵循NB法的人.

主要方法:

  • 根据第一位数发生的概率计算Shannon (H).
  • 分析显示标准NB法分布的数据集.
  • 分析具有非标准第一位数分布的数据集,包括来自功率函数的数据集.
  • 在不同的数据分布中比较值.

主要成果:

  • 按照NB分布的第一个数字的Shannon是每位数字的H = 2.88位.
  • 偏离NB定律的数据集显示出较低的值,例如每位2.76比特 (金星坑直径) 和每位2.04比特 (矿物碎片重量).
  • 特定分布,其中"1"的频率是"9"的40倍以上,可以通过负指数 (p > 1) 的功率函数来建模.

结论:

  • 香农提供了第一位数分布中的信息内容的度量.
  • 偏离Newcomb-Benford定律导致的减少.
  • 分析揭示了数据集中的不同信息特征,超出了NB法通常描述的信息特征.