Negative entropy or negentropy or syntropy of a living system is the entropy that it exports to maintain its own entropy low (see entropy and life). The concept and phrase (Negative Entropy) were introduced by Erwin Schrödinger in his 1943 popular-science book What is life?^[1] Later, Léon Brillouin shortened the phrase to negentropy,^[2][3] to express it in a more "positive" way: a living system imports negentropy and stores it.^[4] 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 Fantappič, who tried to construct a unified theory of biology and physics. (This attempt has not gained renown or borne great fruit.) Buckminster Fuller tried to popularize this usage, but negentropy remains common.

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

Information theory

In information theory and statistics, negentropy is used as a measure of distance to normality.^[5][6][7] Consider a signal with a certain distribution. If the signal is Gaussian, the signal is said to have a normal distribution. Negentropy is always nonnegative, is invariant by any linear invertible change of coordinates, and vanishes iff the signal is Gaussian.

Negentropy is defined as

J(p_x) = S(\phi_x) - S(p_x)\,

where S(\phi_x) stands for the differential entropy of the Gaussian density with the same mean and variance as p_x and S(p_x) is the differential entropy of p_x:

S(p_x) = - \int p_x(u) \log p_x(u) du

Negentropy is used in statistics and signal processing. It is related to network entropy, which is used in Independent Component Analysis.^[8][9] Negentropy can be understood intuitively as the information that can be saved when representing p_x in an efficient way; if p_x were 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 p_x 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.

Correlation between statistical negentropy and Gibbs' free energy

Willard Gibbs? 1873 available energy (free energy) graph, which shows a plane perpendicular to the axis of v (volume) and passing through point A, which represents the initial state of the body. MN is the section of the surface of dissipated energy. Q? and Q? are sections of the planes ? = 0 and ? = 0, and therefore parallel to the axes of ? (internal energy) and ? (entropy) respectively. AD and AE are the energy and entropy of the body in its initial state, AB and AC its available energy (Gibbs free energy) and its capacity for entropy (the amount by which the entropy of the body can be increased without changing the energy of the body or increasing its volume) respectively.

J = S_\max - S = -\Phi = -k \ln Z\,

where:

J - negentropy (Gibbs "capacity for entropy")

\Phi ? Massieu potential

Z - partition function

k - Boltzmann constant

Organization theory

In 1988, on the basis of Shannon's definition of statistical entropy, Mario Ludovico^[18] gave a formal definition of syntropy, as a measurement of the degree of organization internal to any system formed by interacting components. According to that definition, syntropy is a quantity complementary to entropy. The sum of the two quantities defines a constant value, specific of the system of which that constant value identifies the transformation potential. By use of such definitions, the theory develops equations apt to describe/simulate any possible evolution of the system, either toward higher/lower levels of "internal organization" (i.e., syntropy) or toward the system's collapse.^[19]

In risk management, negentropy is the force that seeks to achieve effective organizational behavior and lead to a steady predictable state.^[20]

Notes

See also

• Ectropy
• Exformation
• Extropy
• Free entropy
• Entropy in thermodynamics and information theory
• Entropy and life

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