Negative Entropy

Information about Negative Entropy

In 1943 Erwin Schrödinger used the concept of “negative entropy” in his popular-science book What is life?. Later, Léon Brillouin shortened the expression to a single word, negentropy. Schrödinger introduced the concept when explaining that a living system exports entropy in order to maintain its own entropy at a low level (see entropy and life). By using the term negentropy, he could express this fact in a more "positive" way: a living system imports negentropy and stores it.

In a note to What is Life? Schrödinger explains his usage of this term.

Let me say first, that 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 1974, Albert Szent-Györgyi proposed replacing the term negentropy with syntropy, a term which may have originated in the 1940s with the Italian mathematician Luigi Fantappiè, who attempted to construct a unified theory of the biological and physical worlds. (This attempt has not gained renown or borne great fruit.) Buckminster Fuller attempted to popularize this usage, though negentropy still remains common.

Information theory

In information theory, "negentropy" is used as a measure of distance to normality. Consider a signal with a certain distribution. If the signal is Gaussian, the signal is said to have a normal distribution. Negentropy is always positive, is invariant by any linear invertible change of coordinates, and vanishes iff the signal is Gaussian.

Negentropy is defined as

$\text{[math]}$

where $\text{[math]}$ stands for the Gaussian density with the same mean and variance as $\text{[math]}$ and $\text{[math]}$ is the differential entropy:

$\text{[math]}$

Negentropy is used in statistics and signal processing. It is related to network entropy, which is used in Independent Component Analysis.^[1]. Negentropy can be understood intuitively as the information that can be saved when representing $\text{[math]}$ in an efficient way; if $\text{[math]}$ where a random variable (with Gaussian distribution) with the same mean and variance, would need the maximum length of data to be represented, even in the most efficient way. Since $\text{[math]}$ is less random, then something about it is known beforehand, it contains less unknown information, and needs less length of data to be represented in an efficient way.

Organization theory

In risk management, negentropy is the force that seeks to achieve effective organizational behavior and lead to a steady predictable state.^[2]

Notes

1. ^ P. Comon, Independent Component Analysis - a new concept?, Signal Processing, 36:287-314, 1994.
2. ^ Pedagogical Risk and Governmentality: Shantytowns in Argentina in the 21st Century (see p. 4).

Much writing and research has been devoted to the relationship between the thermodynamic quantity entropy and the evolution of life. In 1910, American historian Henry Adams printed and distributed to university libraries and history professors the small volume
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In thermodynamics, the term thermodynamic free energy is a measure of the amount of mechanical (or other) work that can be extracted from a system, and is helpful in engineering applications.
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energy (from the Greek ενεργός, energos, "active, working")^[1] is a scalar physical quantity that is a property of objects and systems of objects which is conserved by nature.
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Albert Szent-Györgyi de Nagyrápolt (September 16, 1893 – October 22, 1986) was a Hungarian physiologist who won the Nobel Prize in Physiology or Medicine in 1937. He was also active in the Hungarian Resistance during World War II and entered Hungarian politics after the war.
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Luigi Fantappiè (15 September1901-28 July1956) was an Italian mathematician, known for work in mathematical analysis, where he was a student and follower of Vito Volterra. Later in life he proposed scientific theories of sweeping scope.
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Richard Buckminster “Bucky” Fuller (July 12, 1895 – July 1, 1983)^[1] was an American visionary, designer, architect, poet, author, and inventor.
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Information theory is a branch of applied mathematics and engineering involving the quantification of information to find fundamental limits on compressing and reliably communicating data.
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distributions (also known as generalized functions) are objects which generalize functions and probability distributions. They extend the concept of derivative to all integrable functions and beyond, and are used to formulate generalized solutions of partial differential
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GAUSSIAN is a computational chemistry software program, first written by John Pople.^[1] The name originates from Pople's use of Gaussian orbitals to speed up calculations compared to those using Slater-type orbitals.
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normal distribution, also called the Gaussian distribution, is an important family of continuous probability distributions, applicable in many fields. Each member of the family may be defined by two parameters, location and scale: the mean ("average",
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IFF, Iff or iff can stand for:

if and only if, a mathematical and logical connector indicating that either both statements are true or both are false
Identification friend or foe, an electronic radio based identification system utilizing transponders

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In statistics, mean has two related meanings:

the arithmetic mean (and is distinguished from the geometric mean or harmonic mean).
the expected value of a random variable, which is also called the population mean.

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variance of a random variable (or somewhat more precisely, of a probability distribution) is one measure of statistical dispersion, averaging the squared distance of its possible values from the expected value.
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Differential entropy (also referred to as continuous entropy) is a concept in information theory which tries to extend the idea of (Shannon) entropy, a measure of average surprisal of a random variable, to continuous probability distributions.
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Statistics is a mathematical science pertaining to the collection, analysis, interpretation or explanation, and presentation of data. It is applicable to a wide variety of academic disciplines, from the physical and social sciences to the humanities.
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Signal processing is the analysis, interpretation and manipulation of signals. Signals of interest include sound, images, biological signals such as ECG, radar signals, and many others.
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Shannon entropy or information entropy is a measure of the uncertainty associated with a random variable.

Shannon entropy quantifies the information contained in a piece of data: it is the minimum average message length, in bits (if using base-2 logarithms), that must
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Independent component analysis (ICA) is a computational method for separating a multivariate signal into additive subcomponents supposing the mutual statistical independence of the non-Gaussian source signals. It is a special case of blind source separation.
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Risk management is the human activity which integrates recognition of risk, risk assessment, developing strategies to manage it, and mitigation of risk using managerial resources.
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Exformation is a term meaning explicitly discarded information. It was coined by Danish physicist Tor Nørretranders in his book The User Illusion published in English 1998.
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