In information theory and statistics, negentropy is used as a measure of distance to normality. It is also known as negative entropy or syntropy.

The concept and phrase "negative entropy" was introduced by Erwin Schrödinger in his 1944 book What is Life?. Later, French physicist Léon Brillouin shortened the phrase to néguentropie (transl. 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.^{[citation needed]}

In a note to What is Life?, Schrödinger explained his use of this phrase:

... if I had been catering for them [physicists] alone I should have let the discussion turn on 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.

In information theory and statistics, negentropy is used as a measure of distance to normality. Out of all probability distributions with a given mean and variance, the Gaussian or normal distribution is the one with the highest entropy.^{[clarification needed][citation needed]} 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.^{[citation needed]}

Negentropy is defined as

where ${\displaystyle h(Y_{G})={\tfrac {1}{2}}\log \left(2\pi \mathrm {e} \cdot \sigma ^{2}\right)}$ is the differential entropy of a normal distribution ${\displaystyle Y_{G}\sim N(\mu ,\sigma ^{2})}$ with the same mean ${\displaystyle \mu }$ and variance ${\displaystyle \sigma ^{2}}$ as ${\displaystyle Y}$, and ${\displaystyle h(Y)}$ is the differential entropy of ${\displaystyle Y}$, with ${\displaystyle p_{Y}}$ as its probability density function:

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