Negentropy

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?

[1] Later, French physicist Léon Brillouin shortened the phrase to néguentropie (negentropy).

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.

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.

Thus, negentropy is always nonnegative, is invariant by any linear invertible change of coordinates, and vanishes if and only if the signal is Gaussian.

It corresponds exactly to the definition of negentropy adopted in statistics and information theory.

[13] 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,[14] applied among the others in molecular biology[15] and thermodynamic non-equilibrium processes.

[16] In particular, mathematically the negentropy (the negative entropy function, in physics interpreted as free entropy) is the convex conjugate of LogSumExp (in physics interpreted as the free energy).

In 1953, Léon Brillouin derived a general equation[17] stating that the changing of an information bit value requires at least

This is the same energy as the work Leó Szilárd's engine produces in the idealistic case.

In his book,[18] he further explored this problem concluding that any cause of this bit value change (measurement, decision about a yes/no question, erasure, display, etc.)

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 . Qε and Qη are sections of the planes η = 0 and ε = 0, and therefore parallel to the axes of ε ( internal energy ) and η ( entropy ) respectively. AD and AE are the energy and entropy of the body in its initial state, AB and AC its available energy ( Gibbs 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.