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In information theory and statistics, negentropy is used as a measure of distance to normality.  The concept and phrase "negative entropy" was introduced by Erwin Schrödinger in his 1944 popular-science book What is Life? Later, Léon Brillouin shortened the phrase to negentropy. In 1974, Albert Szent-Györgyi proposed replacing the term negentropy with syntropy. That term may have originated in the 1940s with the Italian mathematician Luigi Fantappiè, who tried to construct a unified theory of biology and physics. Buckminster Fuller tried to popularize this usage, but negentropy remains common.

In information theory and statistics, negentropy is used as a measure of distance to normality.  The concept and phrase "negative entropy" was introduced by Erwin Schrödinger in his 1944 popular-science book What is Life? Later, Léon Brillouin shortened the phrase to negentropy. In 1974, Albert Szent-Györgyi proposed replacing the term negentropy with syntropy. That term may have originated in the 1940s with the Italian mathematician Luigi Fantappiè, who tried to construct a unified theory of biology and physics. Buckminster Fuller tried to popularize this usage, but negentropy remains common.

在信息论和统计学中，负熵被用来度量与正态分布之间的距离。“负的熵”这个概念和短语是由埃尔温·薛定谔在他1944年的科普著作《生命是什么？》引入，后来莱昂·布里渊 把这个短语缩写为“负熵”。1974年， 阿尔伯特·圣捷尔吉提出用短语“同向”代替“负熵”。这个术语可能起源于20世纪40年代意大利数学家 Luigi fantappi，他试图建立一个生物学和物理学的统一理论。巴克敏斯特·福乐试图推广这种用法，但是负熵仍然很常用。

在<font color="#ff8000">信息论 information theory</font>和<font color="#ff8000">统计学 statistics</font>中，<font color="#ff8000">负熵 negentropy</font>被用来度量与正态分布之间的距离。“负的熵”这个概念和短语是由埃尔温·薛定谔在他1944年的科普著作<font color="#ff8000">《生命是什么？》 What is Life?</font>引入，后来莱昂·布里渊 把这个短语缩写为“负熵”。1974年， 阿尔伯特·圣捷尔吉提出用短语“同向”代替“负熵”。这个术语可能起源于20世纪40年代意大利数学家 Luigi fantappi，他试图建立一个生物学和物理学的统一理论。巴克敏斯特·福乐试图推广这种用法，但是负熵仍然很常用。

{{cquote|... if I had been catering for them [physicists] alone I should have let the discussion turn on ''[[Thermodynamic free energy|free energy]]'' instead. It is the more familiar notion in this context. But this highly technical term seemed linguistically too near to ''[[energy]]'' for making the average reader alive to the contrast between the two things.}}

{{cquote|... if I had been catering for them [physicists] alone I should have let the discussion turn on ''[[Thermodynamic free energy|free energy]]'' instead. It is the more familiar notion in this context. But this highly technical term seemed linguistically too near to ''[[energy]]'' for making the average reader alive to the contrast between the two things.}}

如果我只是迎合他们物理学家，我应该让讨论转向“[[热力学自由能|自由能]]”。在这个语境中，自由能是更熟悉的概念。但是，这个高度专业的术语在语言学上似乎太接近于“[[能量]]”，无法让普通读者生动地看到两者之间的区别。

如果我只是迎合他们物理学家，我应该让讨论转向<font color="#ff8000">“[[热力学自由能|自由能 free energy]]”</font>。在这个语境中，自由能是更熟悉的概念。但是，这个高度专业的术语在语言学上似乎太接近于<font color="#ff8000">能量 energy</font>，无法让普通读者生动地看到两者之间的区别。

In 2009, Mahulikar & Herwig redefined negentropy of a dynamically ordered sub-system as the specific entropy deficit of the ordered sub-system relative to its surrounding chaos.<ref>Mahulikar, S.P. & Herwig, H.: (2009) "Exact thermodynamic principles for dynamic order existence and evolution in chaos", ''Chaos, Solitons & Fractals'', v. '''41(4)''', pp. 1939–1948</ref> Thus, negentropy has SI units of (J kg⁻¹ K⁻¹) when defined based on specific entropy per unit mass, and (K⁻¹) when defined based on specific entropy per unit energy. This definition enabled: ''i'') scale-invariant thermodynamic representation of dynamic order existence, ''ii'') formulation of physical principles exclusively for dynamic order existence and evolution, and ''iii'') mathematical interpretation of Schrödinger's negentropy debt.

In 2009, Mahulikar & Herwig redefined negentropy of a dynamically ordered sub-system as the specific entropy deficit of the ordered sub-system relative to its surrounding chaos.<ref>Mahulikar, S.P. & Herwig, H.: (2009) "Exact thermodynamic principles for dynamic order existence and evolution in chaos", ''Chaos, Solitons & Fractals'', v. '''41(4)''', pp. 1939–1948</ref> Thus, negentropy has SI units of (J kg⁻¹ K⁻¹) when defined based on specific entropy per unit mass, and (K⁻¹) when defined based on specific entropy per unit energy. This definition enabled: ''i'') scale-invariant thermodynamic representation of dynamic order existence, ''ii'') formulation of physical principles exclusively for dynamic order existence and evolution, and ''iii'') mathematical interpretation of Schrödinger's negentropy debt.

In information theory and statistics, negentropy is used as a measure of distance to normality. Out of all distributions with a given mean and variance, the normal or Gaussian distribution is the one with the highest entropy. Negentropy measures the difference in entropy between a given distribution and the Gaussian distribution with the same mean and variance. Thus, negentropy is always nonnegative, is invariant by any linear invertible change of coordinates, and vanishes if and only if the signal is Gaussian.

In information theory and statistics, negentropy is used as a measure of distance to normality. Out of all distributions with a given mean and variance, the normal or Gaussian distribution is the one with the highest entropy. Negentropy measures the difference in entropy between a given distribution and the Gaussian distribution with the same mean and variance. Thus, negentropy is always nonnegative, is invariant by any linear invertible change of coordinates, and vanishes if and only if the signal is Gaussian.

Negentropy is used in statistics and signal processing. It is related to network entropy, which is used in independent component analysis.

Negentropy is used in statistics and signal processing. It is related to network entropy, which is used in independent component analysis.

The negentropy of a distribution is equal to the Kullback–Leibler divergence between <math>p_x</math> and a Gaussian distribution with the same mean and variance as <math>p_x</math> (see  Differential entropy#Maximization in the normal distribution for a proof). In particular, it is always nonnegative.

The negentropy of a distribution is equal to the Kullback–Leibler divergence between <math>p_x</math> and a Gaussian distribution with the same mean and variance as <math>p_x</math> (see  Differential entropy#Maximization in the normal distribution for a proof). In particular, it is always nonnegative.

一个分布的负熵等于 <math>p_x</math> 和与 <math>p_x</math> 具有相同均值和方差的正态分布的 Kullback-Leibler 散度(参见正态分布的微分熵和最大化)。特别是，它总是非负的。

一个分布的负熵等于 <math>p_x</math> 和与 <math>p_x</math> 具有相同均值和方差的正态分布的 Kullback-Leibler 散度(参见正态分布的<font color="#ff8000">微分熵 Differential entropy</font>和最大化)。特别是，它总是非负的。

There is a physical quantity closely linked to free energy (free enthalpy), with a unit of entropy and isomorphic to negentropy known in statistics and information theory. In 1873, Willard Gibbs created a diagram illustrating the concept of free energy corresponding to free enthalpy. On the diagram one can see the quantity called capacity for entropy. This quantity is the amount of entropy that may be increased without changing an internal energy or increasing its volume. In other words, it is a difference between maximum possible, under assumed conditions, entropy and its actual entropy. It corresponds exactly to the definition of negentropy adopted in statistics and information theory. A similar physical quantity was introduced in 1869 by Massieu for the isothermal process (both quantities differs just with a figure sign) and then Planck for the isothermal-isobaric process. More recently, the Massieu–Planck thermodynamic potential, known also as free entropy, has been shown to play a great role in the so-called entropic formulation of statistical mechanics, applied among the others in molecular biology and thermodynamic non-equilibrium processes.

There is a physical quantity closely linked to free energy (free enthalpy), with a unit of entropy and isomorphic to negentropy known in statistics and information theory. In 1873, Willard Gibbs created a diagram illustrating the concept of free energy corresponding to free enthalpy. On the diagram one can see the quantity called capacity for entropy. This quantity is the amount of entropy that may be increased without changing an internal energy or increasing its volume. In other words, it is a difference between maximum possible, under assumed conditions, entropy and its actual entropy. It corresponds exactly to the definition of negentropy adopted in statistics and information theory. A similar physical quantity was introduced in 1869 by Massieu for the isothermal process (both quantities differs just with a figure sign) and then Planck for the isothermal-isobaric process. More recently, the Massieu–Planck thermodynamic potential, known also as free entropy, has been shown to play a great role in the so-called entropic formulation of statistical mechanics, applied among the others in molecular biology and thermodynamic non-equilibrium processes.

存在一个与自由能(自由焓)密切相关的物理量，它具有熵的单位并且与统计学和信息论中我们所知的负熵同构。1873年，威拉德·吉布斯创建了一个图表，说明了自由能对应于自由焓的概念。在图表上，我们可以看到称为熵的容量的物理量。这个量表示在不改变内能或增加体积的情况下，可以增加的熵值。换句话说，它是在假定条件下可能的最大熵值与实际熵之间的差异。它正好符合统计学和信息论中负熵的定义。1869年，Massieu 在等温过程(两个量只有一个图形符号不同)中引入了一个类似的物理量，然后 Planck 引入到等温-等压过程中。最近，Massieu–Planck 热力学势，也被称为自由熵，已被证明在所谓的统计力学熵表述中发挥了重要作用，应用于分子生物学和热力学非平衡过程。

存在一个与自由能(<font color="#ff8000">自由焓 free enthalpy</font>)密切相关的物理量，它具有熵的单位并且与统计学和信息论中我们所知的负熵同构。1873年，威拉德·吉布斯创建了一个图表，说明了自由能对应于自由焓的概念。在图表上，我们可以看到称为<font color="#ff8000">熵的容量 capacity for entropy</font>的物理量。这个量表示在不改变<font color="#ff8000">内能 internal energy</font>或增加体积的情况下，可以增加的熵值。换句话说，它是在假定条件下可能的最大熵值与实际熵之间的差异。它正好符合统计学和信息论中负熵的定义。1869年，Massieu 在<font color="#ff8000">等温过程 isothermal process</font>(两个量只有一个图形符号不同)中引入了一个类似的物理量，然后 Planck 引入到<font color="#ff8000">等温-等压 isothermal-isobaric process</font>过程中。最近，Massieu–Planck 热力学势，也被称为自由熵，已被证明在所谓的统计力学熵表述中发挥了重要作用，应用于分子生物学和热力学非平衡过程。